COM304 Lecture Notes and Study Guides
COM304 Lecture Notes and Study Guides COM304
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COM304 Quantitative Methods for Research Lecture Notes For Midterm Exam GoalsQualities of Social Science Focuses on EMPIRICAL QUESTIONS Seeks GENERAL EXPLANATIONS Focuses on FALSIFIABLE PREDICTIONS Empirical Questions 0 Questions that can be judged in large part based on observations and measurements of social world 0 Questions that have a descriptive orientation not an explicitly evaluative orientation 0 Line here is blurry Procedures that can be REPLICATED General Explanations Explain 0 To relate particular events to a ore general principle that helps us understand why those events occurred Causeeffect General 0 Explanations that focus on what s COMMON about people events or actions Rather than what makes a particular personevent unique Emphasis on NOMOTHETIC general case more than the ideographic speci c case Falsi able Predictions Predictions 0 Statement about what behaviors or events are likely to occur under speci c conditions in the future Falsi ability o Empirically testable could possibly be refuted It may not be but could be 0 Predictions must be clear and speci c in order to be falsi able Otherwise there is always wiggle roomquot in interpreting ndings after the fact Final Thoughts 0 Social science is de ned based on its goals rather than reliance on any single rigid scienti c methodquot 0 This is true of natural and social sciences Missed Material from Class Cancellation Research isn t speci c enough to say I want to study lovequot 0 Must de ne it o What is observable Example how to measure if someone is nervous before giving a speech 0 How easy is the operational de nitionmeasurement for you to actually put in place Directional hypothesis 0 Directional tell you what they expect the difference to be 0 Nondirectional does not tell you what they expect the difference to be 0 Variables 0 Independent variable the variable that CAUSES the dependent variable 0 Dependent variable DEPENDENT on the independent variable Video games cause violent behaviorquot a Video games independent variable a Violent behavior dependent variable Variables and Levels of Measurement 0 What are Variables 0 Any entity that can take on a variety of different values 0 EMPIRICAL indicators of constructs Mutually exclusive a Each unitobservation falls into only ONE category Exhaustive a Every unitobservation falls into ONE of the categories Operationalizing Variables Levels of Measurement 0 Two types of variables 0 Four levels of measurement Categorical n Nominal Quantitative n Ordinal n Interval n Ratio Nominal Scale Categorical variable 0 Numerical ranking is arbitrary means absolutely NOTHING 0 Can do less with this variable than all other variables Ordinal Scale 0 Quantitative variable 0 Numbers indicate order of categories Numbers do not indicate HOW MUCH higherlower one category is in relation to another category o ordinal rankquot Interval Scales Quantitative variable 0 Numbers indicate order of categories 0 Assume categories are the SAME DISTANCE APART Likert Scales n Strongly agree strongly disagree Semantic differential I Has two anchors that you have to decide which you are closer to o If it s quotmore thanquot or quotless thanquot it is NOT interval it is ordinal Ratio Scale 0 Quantitative variable 0 Has absolute zero point 0 Very top of the scale How many brothers do you havequot 0 l absolute zero point 0 can do the most with this level of data income exam scores speed counts etc Interval and Ratio Scales Quantitative variables 0 FOR BOTH Assume equal distance apart Numbers indicate order of categories 0 FOR RATIO ONLY Has an absolute zero Can form meaningful fractions Levels of Measurement 0 Lowest Highest 0 Nominal l ordinal l interval l ratio There are two types of statistics 0 Statistics 0 Set of procedures used to organize data make inferences from data 0 Descriptive 0 Used to summarize responses from a sample characterize the sample 1St half of semester mean median mode range IRQ SD zscores Cohen s d correlation r o lnferential 0 used to estimate population parameters test hypotheses about what s likely in the population 2nOI half of semester con dence intervals etc Frequency distributions show the frequency of occurrence at each categorylevel of a variable 0n the nal project we have to report all descriptive data and people always put the mean instead of the mode or the median USE THE CORRECT MEASUREMENT 0N FINAL PROECT Measures of DispersionNariability What is Dispersion Measures of Dispersion 0 Range 0 Interquartile Range IQR and Boxplots 0 Standard Deviation S o Homework Assignment due Wednesday 212 What is Dispersion The degree to which scores in a distribution vary 0 The way scores are spread out 0 Does it go from 0 to 1000 0 to 100 0 to 4 0 Example Public Com Anxiety Scores 0 Measured with 7 items each item on a 4 point scale 0 Possible scores 728 0 Scores for two groups of students n 4 per group 0 Group 1 16171819M175 0 Group 2 7 13 22 28 M175 Do the two groups differ in terms of central tendency Even so would you teach them the same way Measures of Dispersion Range 0 The difference between the highest and lowest score in the distribution 0 Range highest score lowest score 0 Limits of Range 0 Because it depends ONLY on two most extreme scores Range stretched out by outliers extreme scores Inappropriate for describing a distribution with outliers Range is unstable Measures of Dispersion IQR The range of the middle 50 of the distribution 0 IQR 75th percentile score 25th percentile score 0 Percentile of participants at or below a point in a distribution 0 Step 1 0 Order your data scores MUST be in order 0 Step 2 0 Find the median of the lower 50 and upper 50 o 710121315181828 Step 3 0 75th percentile 18 0 25th percentile 11 o IQR 1811 7 points 0 NOT based on just two most extreme scores 0 More stable than the range IQR is tied to the median o if scores on variable are highly skewed use median not mean for central tendency use IQR for dispersion Exercise What is the Median and IQR 3 4 4 4 7 10 11 12 14 16 16 18 0 Median 105 0 25th percentile 4 0 75th percentile 15 IQR 154 11 Visual Displays of IQR Boxplots Bold line median 50th percentile m 25th to 75th percentile IQR Whiskers extend out to largest and smallest cases that are NOT outliers Measures of Dispersion Standard Deviation S or SD 0 A measure of how much ALL scores tend to vary from the sample mean 0 The square root of the average squared deviation from the mean The average squared difference from the mean 0 Low SD not a lot of variability Standard Deviation Formula MUST KNOW FOR MIDTERM 6 Steps in Computing SD 0 Step 1 0 Calculate sample mean M 0 Step 2 0 Subtract mean from each raw score deviation x XM Step 3 0 Square each deviation score X Z 0 Step 4 0 Sum up the squared deviation scores E 0 Step 5 0 Divide by total number in sample N 0 Step 6 0 Take the square root Desirable Qualities of S 0 Stable 0 Based on ALL scores not affected strongly by one extreme score Interpretable 0 Related to normal distribution Approximate 23 rule 15 a When scores are normally distributed 68 of cases fall within 1 S of the mean Approximate 95 rule ZS a When scores are normally distributed 95 of all cases fall within 25 of mean 0 Looks like a normal curve bell shaped Review Standard Normal Distribution 0 Normal distribution 0 Symmetrical bellshaped curve 0 Most cases in middle 0 Tails approach but never touch xaxis Standard Normal Distribution a normal distribution that is marked off in standard deviation SD units curve where M 0 SD 1 0 SD square root of average squared deviation from mean 0 Last time said in most cases use SD to describe dispersion 0 True in part bc of relationship bt SD and normal curve Key Points About SND Can specify of people units falling between each SD area under curve 0 of people between Mand 1SD is identical 3413 symmetrical of people between Mand 150 is not same as between 150 and 250 1359 0 Very few units fall beyond 3SD 997 of scores in distribution within 3SD Simple Rules About SND 23 Rule 0 about 23 68 of scores in a SND fall between 15D of the mean 0 middle 23 of the distribution 0 95 rule 0 about 95 of scores in a SND fall between ZSD of the mean 0 99 rule 0 about 99 of scores in a SND fall between 3SD of the mean Standard Scores 0 Standard 2 scores 0 Speci es how far a speci c unit person is above or below the sample mean in SD units Numerator one person s deviation score x Denominator S or SD for sample a Z XMS XS Properties of zscores When converting an entire distribution of raw scores to zscores o M 0 SD 1 0 True for ANY set of raw scores 0 Example 2 3 4 4 6 o M 38 S 133 Ezquot2 N o Zscores 135 O60 015 015 165 MOS10Ezquot25 How can we use zscores zscores can be used to 0 Determine the percentile for any z score of scores in SNC below that z score 0 Determine the of cases falling in between any two z scores any two places in SNC 0 Combine raw scores from two measures with different possible ranges Determining the percentile corresponding to any score Percentile of scores at or below a given score given place in SNC Text Table 18 p 351 o Hint If you have confusion draw out the normal curve plot your zscore and ask if your answer makes sense 0 Examples of nding percentiles o If your z score on public com anxiety 0 then what is your percentile What does this tell us 0 If your Zscore 110 then what is your percentile What of students are less nervous than you about public speaking What are more nervous than you 0 If your z score O6O then what is your percentile What of students are less nervous than you about public speaking What are more nervous Hint draw the normal curve answer these questions visually Determining the of scores people between any two zscores 0 Procedure 0 Determine of scores bt each zscore and M using text table 18 p 351 If zscores are OPPOSITE in sign ADD THEM If zscores are SAME in sign SUBTRACT smaller from larger Correlation What are correlations Interpreting Scatterplots Four types of relationships Interpreting Pearson correlations o Direction of effect 0 Effect size for relationships hypothesis Coef cient of Determination What is a Correlation Degree to which a group s scores on two variables X and Y are associated 0 Does knowing your score on X tell us anything about what your score is likely to be on Y or vice versa 0 Both variables X and Y must be QUANTITATIVE 0 Usually interval or ratio level of measurement 0 Use correlation to assess Relationship Hypothesis Interpreting Scatterplots Graph representing the relationship between TWO variables X and Y 0 Vertical Y axis DV 0 Horizontal X axis IV 0 Each olot 1 unit person 0 Place where person s scores on two axis intersect Fit line line drawn so as to minimize the squared deviations of dots from the line roughly the line that on average is closer to all dots than any other line 4 Types of Relationships 0 No Relationship Unrelated 0 Scores on variables X and Y share no systematic relationship no shared variance 0 Knowing people s level of variable X tells us nothing about their level of variable Y 0 Positive Direct Linear Relationship 0 POSITIVE DIRECT As people s scores on X increase their scores on Y also increase 0 LINEAR the relationship between X and Y can be represented by a straight line 0 Negative inverse Relationship 0 As scores on X increase scores on Y decrease 0 Still a linear relationship 0 Still able to predict from X to Y and vice versa 0 Curvilinear Nonlinear 0 Relationship between X and Y is curved departs substantially from a straight line 0 Direction of Relationship between X and Y changes over range of X DV GPA IV Amount worry about grades N 7 students Interpreting Pearson Correlations r 0 Pearson Correlation r 0 Provides a numerical estimate of direction and strength of the linear relationship between two variables X and Y o Presumes relationship between X and Y is LINEAR check scatterplot 0 Possible range of r100 to 100 Pearson r is calculated using standard 2 scores for X and Y Zoxxzy n 1 Sign of Correlation positive or negative 0 DIRECTION of relationship between X and Y Size of Correlation absolute value 0 Strength of relationship between X and Y EFFECT SIZE How accurately can predict a person s score on Y if know their score on X and vice versa r 0 NO RELATIONSHIP r 1 or 1 l PERFECT LINEAR RELATIONSHIP Effect Size r 10 is a SMALL relationship r 24 is a MEDIUM relationship r 37 is a LARGE relationship 30 Correlations com anxiety com anxiety group public speaking Sisters com anxiety group Pearson Correlation 1 660 000 Sig 2 tailed 000 998 N 1540 1540 1465 com anxiety public Pearson Correlation 660 1 003 speaking Sig 2tailed 000 910 N 1540 1541 1466 Sisters Pearson Correlation 000 003 1 Sig 2 tailed 998 910 N 1465 1466 1473 Correlation is significant at the 001 level 2 tailed Coef cient of Determination rquot2 the of variance in Variable X that is shared with variance in Variable Y vice versa 0 The of all variation in X that is explained by Y or vice versa Measurement Reliability 0 What is measurement What is scaling Measurement reliability and error Two types of measurement reliability 0 Temporal stability 0 Internal consistency 3 indices What is Measurement 0 the assignment of objects to numbers according to a rulequot 0 general issues in scaling Quantitative Measurement Example 0 Construct Belief in Supernatural Conceptual De nition belief in phenomena that defy scienti c explanation such as UFOs space aliens ESP palm reading and ghosts Operational De nition Paranormal Belief Scale Questionnaire 9 o What type of scale is PBS Quantitative Measurement Scoring Rules Operational De nition 0 Reverse score participants responses to all of the quotoddquot numbered items sb1r sb3rsb19r 15 24 33 42 51 0 Sum participants responses to the 20 items sb1sb2sb3 sb20 make sure to use the reversed items 0 Divide sum by 20 of items to put scores back on original 15 scale 0 Measure used to determine the level of a person s belief in the supernatural by assigning a score according to rules Key Issues in Measurement 0 Is it a good measure Two key issues 0 Is it RELIABLE o Is it VALID Measurement ReliabilityError Measurement Reliability are scores stable under conditions where similar scores should be obtained 0 Measurement Error random uctuations in scores due to factors that are temporary and shifting All measurements contain some degree of error 0 What factors could lead to random errors in your responses to the Paranormal Belief Scale 0 Observed Score True Score Error T Measurement Error l Reliability 0 Problem with Measurement Error reduces chance of detecting systematic relationships between that measure and measures of other variables Temporal Stability is a Type of Reliability TEMPORAL STABILITY o the degree to which people s scores on measure are stable over time 0 example administer the Paranormal Belief Scale in Jan 2013 again in Feb 2013 0 question what is the quotrightquot length of time between measurements 0 tImE1 me 2 TestRetest r is a speci c measure of Temporal Stability Testretest correlation assesses strength of relationship between the same group s scores on the same measure at two or more points in time 0 Example N 5 students take Paranormal Belief Scale twice six weeks apart TestRetest Reliability 0 Testretest r 90 Desirable eve at least r 70 depends on length of time between 2 measurements Linear 1312 EEtime 3D SEtimE1 0 There are 3 indices of internal consistency Average interitem correlation Splithalf Cronbach s alpha Average Interitem correlations an index of internal consistency Average Interitem Correlation the mean correlation between all pairs of items making up a measure 0 to what extent do people s responses to individual items making up the measure go together o If all the items measure a single underlying concept then 0 Internal Consistency Histograms for SAS items 8 and 14 0 Item 2 quotSome people are able to levitate or lift objects just by thinkingquot 0 Item 18 quotSome people have a special gift that enables them to see things in the future that have not yet happened 0 1 Strong disagree 5 Strongly agree 0 Item 2 quotSome people are able to levitate or lift objects just by thinkingquot 0 Item 18 quotSome people have a special gift that enables them to see things in the future that have not yet happened 0 1 Strong disagree 5 Strongly agree 0 N 1607 COM 304 students 0 key question are people s scores on different items correlated o r 37 0 Why aren t these items correlated even more highly Internal Consistency Average Interitem Correlations For 20item Supernatural Belief Measure 0 180 different interitem correlations sb1 with sb2 sb1 with sb3sb19 with sb20 0 Average interitem correlation across 180 pairs r 31 o T average interitem correlation T internal consistency of measurement Split Half Correlation Splithalf Correlation correlate participants responses to 12 of items eg all odd items with their responses to the other 12 items eg all even items 0 Supernatural Belief Scale 20 items Even Items sb2sb4sb6sb201O Odd Items sb1sb3sb5sb1910 0 Correlation between 2 halves r 76 r2 58 Cronbach s Alpha 0 The MOST COMMON index of internal consistency Cronbach s alpha or the average of all possible splithalf correlations oddeven items 1St half2nOI half of items Halialailityr Etatiatica Eranbath39a Alpha aaatl an Granulath39a Standardize Alpha llama N afllama El 9 E 0 Measures for Internal Consistency Standards forJudging Alpha 0 Alpha gt 80 good 0 Alpha 708O adequate 0 Alpha 6570 minimally acceptable 0 Alpha lt 65 undesirable For SB Scale 0 Alpha 90 Implication SB scale seems to be measuring ONE concept Why do we need 20 items InterRater Reliability is a Type of Reliability 0 Percentage agreement 0 Correlation between two coders 0 Continuous variable Reliability vs Validity What is validity 0 Content 0 Criterionpredictive 0 Construct What is Measurement Validity 0 Measurement Validity o the degree to which a scale measures the construct it is supposed to measure 0 What is the SB scale designed to do Is knowing that the SB scale is reliable enough itself to show that it is a valid measure of belief in phenomena that defy scienti c explanation eg as opposed to just having a cynical personality Measurement Validity There are multiple ways we might assess measurement validity online reading 6 types of measurement validity 0 I ll talk about three Content Validity CriterionPredictive Validity Construct Validity Measurement Validity Content 0 Content Validity does the measure sample relevant content adequately and appropriately Are the items on the measure reasonably representative of the all possible items that could be included 0 How can we judge whether the COM 304 midterm exam has strong content validity Who could we ask A professor someone who does researchis an expert in that particular eld 0 How can we judge whether the SB has strong content validity Who could we ask A psychic someone who does research in that area 0 Criteria forJudging Content Validity eg experts o ls a broad range of content sampled o ls important content emphasized o Are items written at an appropriate level Whoever you intend to use this for can they understand it o Are items written in an appropriate format Measurement Validity CriterionPredictive Predictive Validity does a measure predict what it should predict Does it predict relevant future outcomes criterion 0 Example for the Supernatural Belief Scale Administer SB scale to class today Feb 24th Mar 24th administer a measure of TV viewing in last 30 days a Shows with paranormal themes Mentalist Paranormal State a Romantic comedies eg Friends Perfect Couples a Sports eg college football EPL soccer If the Supernatural Belief Scale has predictive validity what should we nd Should the SB scale predict other types of TV viewing as strongly Measurement Validity Construct o TOUGHE5 T TO FNDPROVE Your results will correspond to other methods of measuring the same construct o PRPSA 34 items just measures public speaking anxiety 0 PRSA 24 six items measure PSA Conclusions about Measurement Validity The validity of a measure is established over time series of studies assessing several different senses of validity 0 Cannot create an instrument today and claim that we have validity Measurement validity degree of con dence that a measure taps what it is supposed to tap does what it is supposed to do not yes or no 0 How con dent are we that we are really measuring your attitudes toward the supernatural 0 YOU MUST HAVE RELIABILITY T 0 HAVE VALIDITY o If you have reliability you might not necessarily have validity Bathroom scaledoctor scale example Sampling 0 Key Terms 0 Population 0 Sample 0 Parameter 0 Sampling error 0 Methods of Sampling 0 Probability unbiased nonprobability biased Population 0 Population an entire group of people events or texts that share one or more characteristic that researchers are interested in 0 Example Population of Purdue studentsquot Sample all students at all Purdue campuses 74341 full and parttime undergraduate graduate and professional students WL NC Calumet Purdue parts of IUPUI and IPFW all Purdue students at WL campus 38788 all Purdue undergraduate students at WL campus 29788 all Purdue undergrads from WL who graduated with a BABS degree in 20122013 6829 all Purdue undergrad Liberal Arts majors at WL campus 3243 all Purdue undergrad COM majors at WL campus 776 including 405 who are precom 0 Purdue Data Digest 20132014 school year Population group to which intend to generalize research ndings Sample a smaller of elements from the total making up the population 0 Example 1 RQ1 What percentage of Purdue undergraduate students from WL campus who graduated with a BABS degree in 20112012 had accepted fulltime paid employment by the time they graduated Survey N 300 students sample want to generalize results to all Purdue undergrads who graduated with a BABS degree in 20102011 6831 0 National stats 2007 51 2008 26 2009 20 2010 24 2011 24 2012 26 Source National Association of Colleges and Employers 0 2012 44 had received at least one job offer 60 of paid interns had an offer Statistic Statistic a numerical characteristicsummary of a sample eg sample M 0 Example 1 28 of N 400 Purdue undergrads who graduated with a BABS in 20102012 had found fulltime paid employment by the time they graduated 0 Example 2 average public speaking anxiety score is M 1583 for 350 students in COM114 classes possible range 728 Parameter Parameter numerical characteristicsummary of the entire population value from a census 0 Example 1 27 of all N 6831 Purdue undergrads from WL campus who graduated in 20102011 had found fulltime paid employment by the time they graduated 0 Example 2 average public speaking anxiety score is M 1722 for all 3388 students in COM 114 possible range 7 28 WE warm m Emiliaam WEE 39L39i39l lu L39l Hick1 1i Ehrlrla with int1g I L i Fiji39quotig ii ai j g5i RH 13 as i 3r 1 J l V gl39ii39ffnxigllram a i lfccl ulil i 39r ESE 5 O fairyisland ma ami Sangria rue31 Sampling Error 0 Sampling Error degree to which a sample statistic deviates from a population parameter 0 Example 1 2827 1 error sample statistic is 1 higher than pop parameter 0 Example 2 15831722 139 point error sample statistic is 139 lower than population parameter Summary of Key Terms f r l 13131 emitter illitqulai 5 ch ll F I l i t t iE using pu Mum statistic L f Charastake using P l39ammel39 use sawmills 1 quotTc drew inference estimates al1 iE mama 22am about population Methods of Sampling Two Broad Groups 0 Probability sampling method that uses some form of random selection different units of the population have an equal chance of being chosen Nonprobability sampling method that does not use random selection leaves us limited ability to estimate how much sampling error may be present Types of Probability Sampling 0 Simple Random Sampling draw sample so that each member of population has an equal chance of being selected in sample 0 Examples Lottery method each member of population given a number numbers placed in bowl and thoroughly mixed blindfolded researcher selects quotnquot numbers members of the population with those numbers are in sample random generator httpstattrekcomTablesRandomaspx 79 students in COM 304 population draw random sample of N 10 0 R01 What percentage of Purdue undergrads from WL campus who graduated with a BABS degree in 20112012 found full time paid employment by the time they graduated how draw random sample of N 300 we cannot give every member of a population an equal chance of being included unless we can identify all members of the population Failure to identify all members of a population is a major source of bias in samplingquot Patten 2007 p 45 o Other Types of probability unbiased sampling 0 strati ed random sampling 0 cluster or multistage sampling 0 both procedures still allow us to specify the probability that an individual from population will end up in our sample NonProbability Sampling NonProbability Sampling draw sample so that 0 elements of population do not have an equal chance of being selected 0 can t determine how likely it was that any speci c element would be selected convenience sample study readily available subset of population snowball sample Nonrandom sampling is not inherently bad Many research studies use nonrandom samples for practical or ethical reasons o a What are clinical trials httpclinicaltrialsgovct2infounderstandClinicalTrials o b Findingrecruiting volunteers for clinical trials httpwwwclinicaltrialsgov 0 Example quotcolon cancer and Indianaquot 0 Point Most of our knowledge about the effects of medical treatments are based on nonprobability samples The samples become increasingly large and diverse over time but they aren t drawn randomly from the target population Conclusions About Sampling 0 DA of nonprobability sampling 0 no basis forjudging the likely amount of sampling error 0 dif cult to judge amount of bias vaery important to estimate the exact values of population parameters precisely and accurately eg political polling it is critical to use random probability sampling fit is enough to know whether groups differ eg in general is a new treatment better than doing nothing or current treatments nonrandom samples often may suf ce Ethics in Research 0 Ethics focus on value judgments concerning degrees of right and wrong goodness and badness in human conduct Johannesen 1995 0 We want to design studies that are Valid research procedures that produce ndings in which we can have con dence eg using measures that are reliable and valid using methods that allow us to assess causeeffect relationships internal validity and generalize ndings to populations of interest external validity Ethical research procedures that treat participants with respect produce bene ts without harming participants Studies Raising Ethical Concerns Tuskegee Syphilis Study 0 Began in 1932 0 Participants 600 African American men patients at Public Health Service in Macon County AL 399 diagnosed with syphilis told being treated for bad bloodquot 201 were not diagnosed with syphilis comparison group 0 goal learn about effects of syphilis over time participants not told this 0 Penicillin shown to be effective treatment by 1940 s 0 Men weren t treated or given such low dose that it wasn t effective followed until 1972 investigative reporter broke study 0 10M in compensation 1997 apology by President Clinton See httpwwwcdcgovFeaturesTuskegee Milgram s Experiments on Obedience to Authority 0 Milgram studies on obedience early 1960 s conducted a series of studies of whether individuals would engage in actions they believed might harm others if told to do so by an authority participants told experiment on the effects of punishment on learning paired with confederate participant teacher confederate learner task word pair memorization task confederate supposedly hooked to electric shock generator experimenter tells participant to administer increasingly severe shocks for wrong answers beyond warning labels after no response often more than 12 of participants obeyed experiment to end participants displayed high levels of stress during study some afterwards participants were thoroughly debriefed at end of study Ethical Principles Key Events 0 1974 Congress passes National Research Act creates National Commission for the Protection of Human Subjects in Biomedical and Behavioral Research 0 1979 Commission issues Belmont Reportquot that outlines three broad ethical principles for research respect for persons bene cence justice 0 1981 Code of Federal Regulations Common Rule adopted by DHHS FDA many other federal agencies based on Belmont Report Ethical Principles 0 Respect for persons 0 individuals are autonomous agents who are capable of making their own decisions about whether to participate o informed consent about purpose procedures risksbene ts alternatives is critical must be comprehensible o participation is voluntary no coercion 0 those lacking autonomy require special consideration eg children prisoners mentally disabled Bene cence protecting participants from harm maximizing bene tsminimizing harm o inhumane treatment of research participants is never warranted 0 all steps taken to reduce serious risk considerations of alternatives 0 riskbene t ratio must be favorable o bene ts may be to participants larger society 0 Justice fairness in distribution of bene tsrisks 0 not offer potential bene ts to only some participants if treatment effectiveness documented offer it to control group too 0 no genderracial bias in inclusionexclusion o vulnerablespecial populations eg prisoners the poor shouldn t be test cases for risky procedures Institutional Review Boards lRBs any agency university hospital wishing to receive federal funding must establish lRB lRB panel of faculty investigators and others who review all research proposals involving human participants biomedical behavioral review proposed procedures before study conducted to assess a voluntary nature of participation b informed consent c risk to participants d bene ts to participantssociety 0 Sample informed consent form Experimental Research 0 Purpose Establishing CauseElEffect Relationship 0 Test whether changes in a dependent variable can be attributed to are caused by an independent variable Sample Experiment Cialdini and Schroeder 1976 0 Purpose investigate effectiveness of a simple technique designed to increase the percentage of people who respond favorably to a charity request 0 Talked to the rst adult who came to the door 0 Flipped a coin to ask for donation in one of two ways Standard standard quoteven a penny will helpquot 0 Effect of Request Type 0 50 of adults donated when they used even a penny will helpquot 0 29 donated with standard question Three Features of a TRUE Experiment Researcher manipulates the independent variable 0 Manipulated the question Researcher randomly assigns participants to conditions 0 Flipped a coin Researcher controls extraneous variables 0 Are there things your experiment isn t taking into account Manipulating the IV Manipulated variable vs attribute variable 0 Condition a level of the independent variable 0 Experimental condition receives some exposure to IV 0 Control condition receives NO exposure to IV 0 In a TRUE experiment researcher ALWAYS manipulates the IV 0 IV manipulated DV measured Random Assignment 0 A procedure for assigning participants to conditions such that every participant has an equal probability of being in each condition 0 R random assignment 0 X treatment 0 O observe 0 Rows group 1 treatment group 2 control Nonrandom assignment is problematic Only reaching a certain population 0 Random assignment helps control for even unanticipated factors bc they are equally likely to end up in each condition 0 Sometimes random assignment isn t feasible or ethical Random Assignment IS NOT EQUAL TO Random Selection 0 Selection how do we select a sample 0 Assignment once sample is selected how do we assign them Experiments Control Extraneous Variables Taking the dog out to collect money is not consistent so it is an extraneous variable Preview 0 Criteria for Establishing Causal Relationships 0 Experiments and Causal Claims Validity of Conclusions from Experiments 0 Lecture HW 11 Criteria for Causal Relationships 0 To evaluate the claim X causes Yquot should consider three criteria Covariation o Are X and Y related Do scores on X and Y covary o If X causes Y X must be associated with Y 0 Time Order 0 Does X precede Y in time o If X causes Y X must occur before Y 0 Alternative Explanations o Is anything besides X causing the observed change in Y 0 Could other things make it look like X is causing Y when in fact X is not a cause Criteria 1 Covariation Could watching a lot of sci TV programs cause stronger belief in the paranormal X gt Y How OR 0 Could believing more strongly in the paranormal cause one to spend more time watching scifi TV programs Y gt X How 0 Correlation is necessary but not suf cient to establish causality Criteria 2 Time Order 0 Issue is X a Y or could Y a X 0 Experiment researcher controls time order 0 Initially Manipulate IV 0 Afterwards Observe DV Ex Does Exposure to EPH X lead to increased likelihood of donation Y lnitially randomly assign participants to EPH treatment or standard request control condition 0 X treatmentIV O Observe DV 0 Two group Posttest Only design Afterwards record whether they donated Know can t be Y a X Criteria 3 Alternative Explanations Internal and External Validity Validity of Experiments Two Types Extraneous Variables those beyond RQ Issues 0 Could an extraneous variable be causing both X and Y spurious 0 Could an extraneous variable be confounded with X and causing Y Spurious Relationship 0 X and Y related only because both are being caused by Z wouldn t be related if took Z into account controlled it Confounding variable 0 a third factor Z also occurs along with the independent variable X and hence one can t tell whether changes in Y are being caused by X or Z Experiments are designed to rule out alternative explanations o Researcher randomly assigns participants to conditions 0 Researcher holds everything else except manipulation of IV constant 0 Researcher may include a control group to isolate the impact of the treatment from other factors INTERNAL VALIDITY degree to which changes in DV can be attributed with con dence to the IV not other factors 0 threat to internal validity anything that reduces our con dence that changes in DV Y are being caused by changes in IV X as opposed to some other variable EXTERNAL VALIDITY degree to which research ndings can be generalized with con dence to the larger population 0 threat to external validity anything that reduces our con dence in the generalizability of a study s ndings Validity of Experiments Key Points 0 Internal and External Validity ask us to evaluate the entire experiment research design not just validity of DV measure construct or measurement validity Experiments are designed to maximize internal validity while providing as much external validity as is possible 0 Internal and external validity are a matter of degree may take multiple studies to make a strong claim for internal validity rule out multiple possible explanations and external validity demonstrate generalizability of causeeffect relationship Preview 0 What are Inferential Statistics 0 Examples of how Inferential Statistics are Used 0 3 Types of Distributions Ways of Describing Sampling Distributions 0 Standard Error of Mean 0 Central Limits Theorem Homework due Wed Lecture HW 12 What are Inferential Statistics Inferential Statistics used to draw conclusions about what s liker true in a larger population based on ndings from a sample 0 Descriptive Statistics characterize sample itself 1St half of class Inferential Statistics make inferences about population from results of sample 2nOI half of class Key Concepts for Understanding Sampling Distributions nature shape today 0 Probability and Normal Curve next couple classes Three Types of Distribution 0 Population 0 Sample 0 Sampling Population Distribution 0 Population Distribution a frequency distribution of individual scores for all members of the population shows the frequency with which individuals in the population as a whole fall into various levels or categories that make up a variable Sample Distribution 0 Sample Distribution a frequency distribution of individual scores for members of a sample shows the frequency with individuals in a sample drawn from the larger population fall into the various levelscategories that make up a variable Sampling Distribution 0 Sampling Distribution frequency distribution of sample statistics eg sample means for multiple samples of a given size which all were drawn randomly from a larger population shows how far samples statistics tend to vary from each other Central Tendency Central Tendency mean of distribution of sample means MM Dispersion The second way to describe the sampling distribution 0 Dispersion SD of distribution of sample means SDM also called Standard Error of Mean SEM formula for estimating SEM from single sample Standard Error 0 Can have a sampling distribution for other statistics besides sample means 0 Standard error of a percentage the degree to which a sampling distribution of percentages from samples of a given size drawn randomly from a population vary around the population percentage eg political polls Shape The third way to describe the shape of the sampling distribution 0 Shape Normal Central Limits Theorem 0 CLT when draw all samples of size N randomly from a larger population the distribution of sample means sampling distribution will be approximately normal EVEN IF the distribution of raw scores population or sample distribution is skewed Quali cation CLT holds except when N is tiny Review Central Limits Theorem 0 Because of CLT we know samples that are greater than 30 o The distribution of the sampling distribution will be normal 0 The mean of the sampling distribution will be equal to that of the population 0 The standard deviation of the sampling distribution will to or approximate the standard error in our sample Standard Error of the Mean 0 A measure of how representative a sample is likely to be of the population 0 Large SE means that there is a lot of variability in the sample means so our sample might not be representative of the population 0 Small standard error indicates that most sample means are similar to the population mean so our sample is probably a fair representative of the population Today s Preview 0 Two Major Functions of lnferential Statistics 0 Estimating Population Parameters Con dence Intervals today 0 Testing Research Hypotheses testing ndings for statistical signi cance next week Estimating Population Parameters Con dence Intervals Con dence Intervals for the Mean a range of values within which there can be some degree of con dence that the true parameter u is likely to fall 95 Con dence interval around mean upper lower mu limit ii Steps in Calculating Con dence Intervals for Means 0 Calculate the sample Mand SD 0 Calculate the SEM from sample SD and N 0 Select level of con dence eg 95 with corresponding 2 score eg 196 why 196 see next slide and see ZTable want intervals that contain 95 of means in sampling distribution sampling distribution of means is normally distributed CLT 95 divided by 2 475 of means bt distribution center and each interval 0 Compute Intervals sample mean is middle of CI go out 196 SEM in either direction 0 95 Con dence Corresponds with z196 2 I 1 I 1 lll 1355 H n lgi39 5 Hf 111113II i f ihl lt cases will he II IEJA39FIE39 than 196 m f l39 ll the mean Either wayquot This is the IIS signi cance Itwe39l in E t il tests Estimating Con dence Intervals Example Belief in existence of God Sample M 586 SD 157 N 1596 SEM 1571596 1573995 039 Level of con dence 95 z 196 Compute 95 Intervals CI95 586 196 0039 586 076 39 CI95 5784 o What does this tell us 0 If we drew 100 random samples of N 1596 Purdue undergrads and calculated CI for each sample 100 CI in total then the population parameter u would fall within the CI from 95 of the 100 samples 0 Can we be CERTAIN that the true population parameter u falls within 57845936 Why or why not see prior slide 0 Can we be CONFIDENT that the parameter falls within these bounds Why or why not 0 O O O 0 Example 2 want to estimate how much TV Purdue undergrads watch per day and want separate estimates for male and female undergrads Report Dailefn minutes He Mean N Male HELDHEI 33 IEETIIIEEE Female 995305 EIIEI 1919132 TD EEII 14IZIIIIEiE 1255 IEDT IHE 0 Exercise Computing Con dence Intervals Steps in Calculating Con dence Intervals for Means do this for females n Calculate the sample Mand SD n Calculate the SEM from sample SD and N a Select level of con dence eg 95 with corresponding zscore eg 196 n Compute Intervals C95 M 0 sample mean is middle of Cl go out 196 SEM in either direction 0 Error Bar Plots display inferential statistics 0 They show us our best estimate of the parameter sample mean 0 They display the range of values in which we can con dently infer that the parameter is likely to lie 0 They are based on a sampling distribution distribution of sample means standard error of the mean 0 Box Plots display descriptive statistics 0 They show us the range of values obtained in our sample IQR median 0 They visually describe our sample but tell us nothing about the larger population parameter 0 They are based on a sample distribution of raw scores they show the spread of individual scores IQR 99 Con dence Level corresponds with z 258 0 Comparing CI95 and Clgg Visually 95 Cl Daily TV in minutes 99 Cl Daily TV in minutes 0000 039 FFFFF Ie Tradeoff 0 Precision and con dence Steps in Hypothesis Testing One Sample ztest Central Limits Theorem CLT o CLT when draw all samples of size N randomly from a larger population the distribution of sample means sampling distribution will be approximately normal EVEN IF the distribution of raw scores population or sample distribution is skewed o Quali cation CLT holds except when N is tiny N lt 30 Implications of CLT bc distribution of sample means is normal 0 can apply knowledge about standard normal curve eg approximate 95 rule to describe sampling distribution 0 can make probability judgments about whether a sample is likely to have come from a larger population with a speci c parameter Two Types of Hypotheses o The Alternative Hypothesis Research Hypothesis 0 The Null Hypothesis Test Hypothesis the hypothesis of no differencerelationship Evaluating Research Hypotheses AlternativeResearch hypothesis a tentative statement about the relationship between two or more variables eg how 2 variable are associated or differences between genderconditions 0 H1 People with college degrees earn higher incomes than people without college degrees 0 H1 M gt J Null Hypothesis Opposite of the alternative hypothesis and usually states that an effect is absent 0 H0 People with college degrees are a representative sample from the general population in terms of salary level Or There is no difference between a sample and population 0 H0 M 1 Evaluating Research Hypotheses AlternativeResearch Hypothesis H1 is tested against Null Hypothesis H0 the hypothesis of no difference 0 H0 implies any observed difference between our sample statistic and the population is just sampling error sampling error hypothesis 0 We will make a decision about the likelihood of H0 if H0 unlikely to be true then conclude data are consistent with H1 0 So if we reject H0 we must accept H1 or our alternative hypothesis Steps in Hypothesis Testing Formulate your Research Hypothesis H1 differencecomparison or relationship Formulate the Null Hypothesis H0 no difference or no association 0 Select a level of Statistical Signi cance probability at which we reject H0 accept H1 usually p lt 05 reject H0 only if results would occur no more than 5 times in 100 by chance if H0 were true 0 Select appropriate inferential statistic to test Ho and compute it examples onesample ztest t test Pearson rc0rreati0n X2 chi square 0 depends on type of research hypothesis 0 Test inferential statistic for signi cance 0 determine the probability that the observed results would have been obtained if Ho were true is p lt 05 When do analyses by hand look up critical value in table compare test statistic to critical value When do analyses in SPSS the program will do this for you and give an exact probability of H0 0 make a decision about Ho and thus H1 Five Steps in Hypothesis Testing Formulate your Research Hypothesis H1 differencecomparison or relationship Formulate the Null Hypothesis H0 no difference or no association Select a level of Statistical Signi cance probability at which we reject H0 accept H1 usually p lt 05 reject H0 only if results would occur no more than 5 times in 100 by chance if H0 were true Select appropriate inferential statistic to test Ho and compute it o examples onesample ztest t test Pearson r correlation X2 chisquare 0 depends on type of research hypothesis Test inferential statistic for signi cance 0 determine the probability that the observed results would have been obtained if Ho were true is p lt 05 When do analyses by hand look up critical value in table compare test statistic to critical value When do analyses in SPSS the program will do this for you and give an exact probability of H0 0 make a decision about Ho and thus H1 ZTest is used to test Hypothesis About The mean of a population based on a single sample we will cover this today The differences in means between two populations based on samples from each population CRITICAL VALUES 0 005 CV 196 0 001 CV 258 Testing Pearson r for Statistical Signi cance Preview Review what is Pearson r 0 1st half of class Describing how a sample s scores on two variables are associated 0 Now Testing hypotheses about a larger population Example of Pearson r Experimental project Testing Pearson rfor statistical signi cance 0 Steps in Hypothesis Testing 0 By hand 0 Interpreting SPSS output 0 Exercise practicing what we ve done 0 Sample Results Section Writeup Review Pearson r 0 Pearson Correlation r provides a numerical estimate of direction and strength of the linear relationship between two variables X and Y 0 Both variables X and Y must be interval or ratio level scale Presumes relationship bt X and Y is linear check scatterplot Possible range of r 100 to 100 0 r 10 and below weak relationship 0 r 24 moderate relationship 0 r 37 strong relationship 0 r O NO relationship Pearson Correlation Old and New 0 Pearson ras a descriptive statistic o What is the direction and strength of association between scores on two quantitative variables in this sample 0 Pearson r as inferential statistic o How likely is it that the correlation found in this sample represents a quotrealquot relationship between the two variables in the larger population as opposed to just sampling error Steps in Hypothesis Testing Formulate research hypothesis 0 State the null hypothesis 0 Select a level of statistical signi cance 0 Pick the appropriate inferential statistic Find the Critical Value CV 0 See page 362 Table B4 0 Must know degrees of freedom df If your test statistic is BIGGER than the critical value then you accept the research hypothesis If your test statistic is SMALLER than the critical value then you accept the null hypothesis Steps in the Results WriteUp Experimental Group Paper Restate the research hypothesis H1 0 State what statistics you used to test the null hypothesis and hence H1 0 Present the ndings test statistic df quotsigquot level 0 Describe effect size how large is the association or difference in the sample 0 Draw conclusions about the research hypothesis are the ndings statistically signi cant What can we conclude about H1 Sample Results WriteUp quotHypothesis 1 predicted that students degree of positive mood would be inversely associated with their level of academic stress A Pearson correlation between levels of positive mood and academic stress was conducted to test this hypothesis The analysis revealed that a statistically signi cant inverse correlation did exist between these two variables r168 22 p 005 Consistent with H1 students degree of positive mood did share a statistically signi cant moderatesized inverse association with their level of academic stressquot Chi Square Preview 0 What is Chi Square 0 Oneway vs Twoway Steps in computing 0 Steps in hypothesis testing 0 Exercise what to conclude about Ho What is Chi Square 0 Chi Square x2 an inferential statistic used to address hypotheses involving only nominallevel categorical variables Oneway Chi Square Frequencies are compared in terms of their distribution across one variable 0 N Nov 1 2012 poll sample of 1200 likely voters n 580 John Gregg n 620 Mike Pence ls Pence leading in pop or is this sampling error Twoway Chi Square Does the distribution of frequencies on one variable differ across levels of a second variable 0 What are the two variables here 0 N Nov 12012 sample of 1200 likely voters 400 Democrats 110 Pence 290 Gregg 400 Independents 210 Pence 190 Gregg 400 Republicans 300 Pence 100 Gregg 1200 total 620 Pence 580 Gregg Twoway Chi Square Twoway chi square does the percentage of people who give to Natalie s differ more than would be expected due to chance depending on whether they received EPH or SR 0 H1 A larger percentage of students will donate to a charity if they receive a request that includes quotEven a Penny will Helpquot EPH in comparison to students who receive only a standard request for a charitable donation Does knowing whether a student was approached with an EPH request or a standard request SR tell us anything about whether or not they donated Steps in Computing Chi Square 0 Step 1 Set up contingency table for observed frequencies f0 actual distribution of people across the two variables 0 The observed data IS THE ACTUAL DATA that we observed No Yes Row 7bta5 Standard Request 76 14 90 Even Penny Help 62 28 90 Column 7bta5 138 42 180 Grand Total 0 Step 2 Calculate expected frequencies fe distribution of people if no relationship between two variables existed if HO true 0 Step 3 Perform calculations 2 x2 z 0 39 E E H 2 the fr qumwi s rm d 2 the frequencies EIpEEtEIzf E E the quotsum 0 You can NEVER have a negative Chi Square value Steps in Hypothesis Testing 0 If no relationship between two variables in sample f0 fe for each and every cell x2 O o In our sample donations occurred more often in the EPH condition as opposed to the standard request condition BUT 0 Question is x2 608 large enough for us to conclude that there is a relationship between request type EPH vs standard request and donation YesNo in the larger population or could this just be sampling error Chi Square Degrees of Freedom df df rows 1 columns 1 0 df 2121 0 df 11 df 1 0 Then look up in the table 0 CV 384 I WANT TO BE HIGHER THAN THE CV SPSS Output Chi Square ChiSquare Tests est mp Sig ExectSi12 ExectSi f1 i feilue clf f2siclecl siclecl siclecl eerson ChiSquare 1232quotquot 1 14 Continuity Correctionb 4 5243 1 1122 Lilcelihoocl Hetio 12132 1 1212 Fisher39s EtectTest I221 I211 Lineer by Lineer 1 Association E39DEE 1 39H N oftielicl I2eses 1312 e I2 cells mayhem etpectecl count less then The minimum etpectecl count is 2122 Chi Square 087 Would occur approximately 1 times in 1 0 by chance Chi Square effect size replication What is x2 1 Chi Square x2 an inferential statistic used to address hypotheses involving only nominallevel variables 2 H1 A larger percentage of students who receive a request for a charitable donation that includes Even a Penny will Helpquot EPH actually will donate to Natalie s compared to students who receive only a standard request for a charitable donation 3 Spring 2014 sample What did we nd this semester Statistical Signi cance vs Effect Size 0 Statistical signi cance Can we be con dent that the difference we observe between the percentage of people who give Yes No in the EPH vs the SR conditions is not just chance sampling error 0 Effect Size How large is the difference between the percentage of people who give Yes No in the EPH vs the SR conditions o Cramer sV Cramer s V Phi 2 Z Nk l X2 value of chi square N total number of cases grand total 0 k of categories of variable with smaller number of categories Calculating Cramer s V Cramer s V ranges from O to 1 o O one variable has no impact on the other 0 1 one variable totally determines the other complete predictability Similar rules as Pearson r o 10 small effect 0 24 moderate effect 0 37 large effect Directions for Writing Research Results Restate the research hypothesis 0 Describe what inferential statistic was used to test the research hypothesis and what variables were involved 0 Report results for the inferential statistic Value of test statistic Degrees of freedom H H o o o p level report the exact sig level 0 o Effect size Cramer s V Descriptive information for groups if relevant Draw an explicit conclusion about the research hypothesis 0 Are results statistically signi cant 0 Do the data support the research hypothesis ttest for Independent Data Today s Preview What is a t test 2 types How to calculate a t test for independent data How to nd the t test critical value Interpreting t test output on SPSS Running the test on SPSS What is a ttest t test an inferential statistic used to determine whether the means for two groups of scores differ statistically ie can differences between two mean scores be generalized to the larger population 0 Use t test when 0 IV categorical variable 0 DV quantitative variable Select Proper Statistics Categorical IV Quantitative IV Categorical DV Comparison Hypothesis NA Chi Square Quantitative DV Comparison Hypothesis Relationship Hypothesis ttest Pearson r 2types of ttest ttest for independent data comparing two mean scores from different unrelated g rou ps 0 R01 Will the average amount of donation differ in the EPH versus the standard request conditions ttest for dependent data comparing two mean scores from the same or related groups 0 H2 COM 304 students will score higher on measures of academic stress when they are surveyed near the end late November as opposed to at the beginning early September of the semester Calculating a ttest m1m2 0 t SDm 0 m1 mean score for group 1 0 m2 mean score for group 2 0 SW standard error of the difference bt means from the sampling distribution 0 Step 1 Calculate SDm Step 2 Calculate t test Steps in Hypothesis Testing 0 Now that we know how to compute a t test talk about how interpret it how tell whether would get the mean difference we did less than 5 times in 100 if null hypothesis were true 0 Same steps as with Pearson r or Chi Square Interpreting the ttest for independent data 0 Step 1 Formulate Research HypothesisQuestion 0 R01 Will uEpH uSRin terms of amount of donation There will be a difference between the twoquot 0 Step 2 Formulate Null Hypothesis 0 IJEPH IJSR Nope there s no difference they re exactly the samequot 0 Step 3 Select proper statistic o t test for independent data 0 DV ratio levelquantitative amount of donation 0 IV nominal levelcategorical request type EPH vs SR different individuals randomly assigned Step 4 select a level of statistical signi cance p lt 05 2tail test 0 WE WILL NEVER USE A ONETAIL TEST IN THIS CLASS call results statistically signi cantquot if and only if wouldn t get a mean difference this large by chance more than 5 times in 100 if the null hypothesis were true Step 5 determine CV o to do this need to nd degrees of freedom look up value in Table 82 page 354 Calculate degrees of freedom of scores free to vary a t test for independent data df N 2 total number of people 2 if dfnot in table then go to the next smallest value Find critical value on Table 82 page 354 Step 6 compute inferential test 0 t 1029 handout Step 7 compare test statistic to CV o 1029 lt 1986 l 0 so probability of H0 is GREATER than 5 p gt 05 we would get a 61 percent mean difference with N 97 more than 5 times in 100 just by chance 0 so fail to reject H0 Conclusion even if we limit the analysis just to people who gave something there is no evidence that the average amount given in response to EPH is signi cantly different than the average amount given for SR Finding the Critical Value Critical Value break point in sampling distribution within with 95 of distribution falls 5 beyond critical value z score nd critical value by locating the appropriate place on the normal curve eg 196 95 of samples in sampling distribution within 196 SD problem when samples are small sampling distribution departs substantially from normality t test based on a FAMILY of sampling distributions one for each sample size When N in nity tdistribution normal curve SPSS Output Independent 3amples Test Lexrene39s Test fcr Equality cf Mtariances ttest fcr Equality cf iu39leans 77777E777 7 7 7 7 77777 Gang l39u39lean F 3iq t df Sid fEta e d i quot quotquot Elif rence mcunt cf Dcnaticn Ijn Equal yariancesquot 77 777777777339 351 1939 95 Jig74393 33134 GENTS assumed rms if 7 7 77797 Equal yariances nct 933 33953 32 33134 assumed Independent 3amples Test ttest fcr Equality cf iu39leans 95 Confidence lntenral cf the Difference 3td EITcr Difference Lctuer Upper I Imcunt cf Elcnaticn in Equal yariances 31335 93392 134939 cents assumed Equal yariances nct 3499 434539 199353 assumed NOTE when interpreting SPSS output you don t have to lo k up critical values in a table you will see an exact p sig value 0 p 306 which is GREATER than 05 so the t test is NOT statistically signi cant this nding would happen more thanQO out of 100 times if HO were true Errors in Hypothesis Testing Today s Preview 0 Errors in Hypothesis Testing 0 Example 0 Two Types of Possible Errors 0 Type Error 0 De nition 0 Factors In uence the rate of Type I error 0 Type II Error 0 De nition and Statistical Power 0 Factors In uencing the rate of Type II error 0 Make sure you have read Chapter 9 166179 HW 18 due Wed Exp Projects Due Wed with group evals De ning Type 1 Error 0 Type I Error Researcher rejects H0 when H0 in reality is true quotfalse positivequot 0 Example EPH exerts no effect on likelihood of donating in larger population but we mistakenly conclude that EPH does increase donations based on our study results which in reality are just sampling error 0 Can ONLY make a Type I error if decide to reject HO 0 When do we reject H0 0 What does it mean to call a research nding statistically signi cant at the p lt 05 level 0 So what determines the likelihood of making a Type I error Ways of Reducing Type 1 Error Adopt a more stringent level of statistical signi cance eg p lt 01 or p lt 001 rather than 0 lt 05 0 Example 2 1 ifplt 05 CV 384 ifplt 01 CV 663 if p lt 001 CV 1083 0 Same for a t test or Pearson r 0 Why not always set our signi cant level really low eg p lt 001 Problem Reducing your signi cance level 0 lt 001 rather than p lt 05 will 1 Type I error but also T Type II error 0 Convention hold Type I error reasonably lowquot 05 take other steps to 1 Type II error Attempt to replicate ndings if several different researchers nd that EPH increases donations over standard requests at p lt 05 level extremely unlikely all of their ndings due to chance since the likelihood of chance each time is low 0 See BB replications of EPH De ning Type 2 Error and Statistical Power Type II Error Researcher fails to reject H0 or you accept it when H0 in reality is FALSE false negativequot 0 EPH really does increase of donations over standard request but we fail to nd a statistically signi cant difference in our study and hence mistakenly conclude the EPH doesn t work Can ONLY make a Type II error if you accept H0 Statistical Power the probability of rejecting H0 when H0 in reality is false 0 Statistical power is like a microscope T power i ability to quotseequot small effects when they are present or it has to do with how well a statistical test can detect and reject a null when it is false Factors that affect statistical power 0 Level of statistical signi cance going from p lt 05 to p lt 10 T power CV 0 Sample Size T N T power CV 0 Effect Size need less power to detect large rather than small differencesassociations Ways of Reducing Type 2 Error increasing statistical power 0 Adopt a more liberal level of statistical signi cance as p value T CV i easier to reject H0 probability of Type II error i 0 Example 121 ifplt 01 CV 663 ifplt 05 CV 384 ifplt 10 CV 271 0 Key Point tradeoff bt Type and Type II error rates 0 Increase Sample size Ill as N T statistical power T probability of Type II error i 0 Example Critical value for Pearson rp lt 05 When N 22 CV 42 When N 222 CV 14 o T N l sampling error brings in tails of sampling distribution but diminishing returns 0 T N T df 1 CV easier to reject H0 0 T N 1 Type II error without T Type I error 0 lt 05 in both cases Need to consider both statistical signi cance and effect size a When N is small even large differencesassociations may not be statistically signi cant bc power is low When N is large even small differencesassociations may be statistically signi cant bc power is high pay attention to ES 0 Design Experiments to Maximize Effect Size 0 Statistical signi cance a function of a sample size b effect size doesn t take such a powerful study to nd big effects 0 Example If rbetween 2 variables in your study is 43 only takes N 22 participants to achieve statistical signi cance If rbetween 2 variables in your study is 13 takes more than N 200 participants to achieve statistical signi cance ConclusionsImplications The best studies are designed so as to hold the rate of Type I error low 0 lt 05 while also maximizing statistical power reducing rate of Type II error as much as possible Con dence in our knowledge about a phenomenon eg the EPH strategy grows as multiple studies are conducted replication Must consider both statistical signi cance AND effect size when interpreting your ndings COM304 Quantitative Methods Professor Melanie Morgan Purdue University Review for Midterm Exam You will need to bring a calculator You can t use a cell phone calculator 1 GoalsQualities of Social Science a What types of questions about communication are socialscience methods best suited to address i Focuses on EMPIRICAL QUESTIONS ii Seeks GENERAL EXPLANATIONS iii Focuses on FALSIFIABLE PREDICTIONS o What are empirical questions i Questions that can be judged in large part based on observations and measurements of social world ii Questions that have a descriptive orientation not an explicitly evaluative orientation 1 Line here is blurry iii Procedures that can be REPLICATED o What are replication anol falsi cation anol why are they important i Falsi ability 1 Empirically testable could possibly be refuted a It may not be but could be 2 Predictions must be clear and speci c in order to be falsi able a Otherwise there is always quotwiggle roomquot in interpreting ndings after the fact 0 Be able to recognize R05 that social scientists would would not like y ask 2 ConstructsDe nitions What are constructs i Construct abstraction generalized from particulars that are constructed from nothing a What are 3 parts of any construct i WILL NOT BE ON EXAM How do we evaluate conceptual de nitions i Tell us the quotessential qualitiesquot of a construct 1 What qualities distinguish examples that fall within the construct from those that don t 2 What do the examples that t have in common a What are operational de nitions i They quottranslate the verbal meaning provided by the conceptual de nition into a prescription for measurementquot Watt et a 1995 p 21 0 Why are they important i quotspecify the procedures for observing and measuring constructsquot Conceptualizing reading p 21 3 Variables o What is a variable i Any entity that can take on a variety of different values ii EMPIRICAL indicators of constructs 1 Mutually exclusive a Each unitobservation falls into only ONE category 2 Exhaustive a Every unitobservation falls into ONE of the categories Categorical vs Quantitative variable i Two types of variables ii Four levels of measurement 1 Categorical a Nominal 2 Quantitative a Ordinal b nterva c Ratio 0 What does it mean to say that le vescategories of a variable are mutual y exclusive Exhaustive 1 Mutually exclusive a Each unitobservation falls into only ONE category 2 Exhaustive a Every unitobservation falls into ONE of the categories a What are the 4 levels of measurement Nominal Ordinal Interval Ratio goom What levels of measurement are associated With categorical and quantitative variables a Nominal categorical b Ordinal Interval Ratio Quantitative Be able to recognize examples of variables measured at each level a Lowest Highest b Nominal l ordinal l interval l ratio 4 What are hypothesis 0 Comparison versus relationship hypothesis a Comparison Hypothesis comparing two groups i quotHypothesis of Differencequot ii quotmales have higher aggression scores than femalesquot b Relationship Hypothesis comparing two variables and how they are moving in relation to one another i quotHypothesis of Relationshipquot ii correlated instead of relationship a Directional versus nondirectional hypothesis i Directional tell you what they expect the difference to be ii Nondirectional does not tell you what they expect the difference to be 0 Independent variable IV vs dependent variable DV i Independent variable the variable that CAUSES the dependent variable ii Dependent variable DEPENDENT on the independent variable 1 quotVideo games cause violent behaviorquot a Video games independent variable b Violent behavior dependent variable a If given a hypothesis be able to recognize examples of all these 5 Intro to Statistics 0 What are statistics i Set of procedures used to organize data make inferences from data 0 Descriptive versus inferential statistics i Descriptive 1 Used to summarize responses from a sample characterize the sample a 1st half of semester b mean median mode range IRQ SD zscores Cohen s d correlation r ii lnferential 1 used to estimate population parameters test hypotheses about what s likely in the population a 2nCI half of semester b con dence intervals etc o What is a frequency distribution i Frequency distributions show the frequency of occurrence at each categorylevel of a variable a What are examples of descriptive statistics a mean median mode range IRQ SD zscores Cohen s d correlation r Describing Distributions What are 3 key questions about any distribution i Shape Normal Skew Kurtosis ii Central Tendency Mean Median Mode iii Dispersion Range IQR SD next class a What are normal positivelyskewed and negativelyskewed distributions be able to recognize each i Normal looks normal even ii Positivelyskewed tail points RIGHT iii Negatively skewed tail points LEFT 0 What does it mean to say that the normal distribution is mesokurtic i It s a normal distribution a What are indicators of central tendency mean median mode be able to calculate them L Mean 1 average ii Median 1 Middle of the set iii Mode 1 Most occurring number 0 When is each most appropriate to report i Important to report mode when 1 Variable is NominalLevel mode doesn t presume scores are ordered 2 Distribution is Bimodal 2 nonadjacent modes ii Important to report median when 1 intervalratio variable AND 2 distribution highly skewed What are three ways we make judgments about a distribution of scores is approximately normal i Mean Median Mode 7 Dispersion What are the range interquartile range and standard deviation be able to calculate them Measures of Dispersion Range i The difference between the highest and lowest score in the distribution 1 Range highest score lowest score ii Limits of Range 1 Because it depends ONLY on two most extreme scores a Range stretched out by outliers extreme scores b Inappropriate for describing a distribution with outliers c Range is unstable Measures of Dispersion IQR iii The range of the middle 50 of the distribution 1 IQR 75th percentile score 25th percentile score iv Percentile of participants at or below a point in a distribution 1 Step 1 a Order your data scores MUST be in order 2 Step 2 a Find the median of the lower 50 and upper 50 b 7 10 12 13 15 18 18 28 3 Step 3 a 75th percentile 18 b 25th percentile 11 c IQR 18 11 7 points Standard Deviation Formula 6 Steps in Computing SD vi Step 1 Calculate sample mean M vii Step 2 Subtract mean from each raw score deviation x XM viii Step 3 Square each deviation score xquot2 ix Step 4 Sum up the squared deviation scores E x Step 5 Divide by total number in sample N xi Step 6 Take the square root Why is the range unstable i It only depends on the two most extreme scores a When would we use the IQR i To nd a percentile Be able to interpret a boXpot 0 Can two groups be similar in terms of central tendency but different in dispersion i YES 1 They can have the same mean but be different in dispersion 2 5 and 7 mean 6 or3 and 3 mean 6 Standard Normal CurveStandard Scores 0 How does the SD related to the normal curve i Symmetrical bellshaped curve ii Most cases in middle iii Tails approach but never touch xaxis When scores are normally distributed what percentage of scores falls approximatey within lS of the mean ZS 3S i 68 ii 95 iii 99 o What are z scores i Standard scores a What do they tell us i Speci es how far a speci c unit person is above or below the sample mean in SD units a If given M and SD be able to compute a z score i Z XMS XS When we convert raw scores to Zscores what are M2 and 52 i When converting an entire distribution of raw scores to z scores 1 M 0 SD 1 o What are percentiles i Percentile of scores at or below a given score given place in SNC If I give you Z Table from your text s appendix be able to determine the percentile for any z score and the percentage of a normal distribution between any 2 z scores 9 Correlation o What is a correlation 0 Degree to which a group s scores on two variables X and Y are associated A scatterpot i Graph representing the relationship between TWO variables X and Y o What are 4 possible types of relationships between 2 variables 0 No Relationship Unrelated Scores on variables X and Y share no systematic relationship no shared variance Knowing people s level of variable X tells us nothing about their level of variable Y 0 Positive Direct Linear Relationship POSITIVE DIRECT As people s scores on X increase their scores on Y also increase LINEAR the relationship between X and Y can be represented by a straight line 0 Negative inverse Relationship As scores on X increase scores on Y decrease Still a linear relationship Still able to predict from X to Y and vice versa 0 Curvilinear Nonlinear Relationship between X and Y is curved departs substantially from a straight line Direction of Relationship between X and Y changes over range of X o What is the possible range of the Pearson r 0 Possible range of r100 to 100 0 What is the difference between the direction versus the strength of association How can we tell each from a scatterpot NOTE If I show you a scatterpot you should be able to recognize the direction of the relationship between scores on two variables as well as have some idea about the strength of the relationship i Sign of Correlation positive or negative 1 DIRECTION of relationship between X and Y ii Size of Correlation absolute value 1 Strength of relationship between X and Y EFFECT SIZE 0 How can you tell direction vs strength from the Pearson r i r 0 l NO RELATIONSHIP ii r 1 or 1 l PERFECT LINEAR RELATIONSHIP What are general rules of thumb for What counts as small moderate and strong relationships i r 10 is a SMALL relationship ii r 24 is a MEDIUM relationship iii r 37 is a LARGE relationship a What is the coef cient of determination how do you calculate it and What does it tell us Would we use Pearson r to assess effect size for a comparison or a relationships hypothesis a Coef cient of Determination rquot2 i the of variance in Variable X that is shared with variance in Variable Y vice versa ii The of all variation in X that is explained by Y or vice versa 10 Measurement Reliability 0 What is measurement a quotthe assignment of objects to numbers according to a rulequot i general issues in scaling Measurement reliability a Measurement Reliability are scores stable under conditions where similar scores should be obtained 0 Measurement error a Measurement Error random uctuations in scores due to factors that are temporary and shifting a How does measurement error in uence measurement reliability a T Measurement Error I Reliability 0 Why is measurement error problematic a Problem with Measurement Error reduces chance of detecting systematic relationships between that measure and measures of other variables a What are temporal stability intercoder reliability and internal consistency a TEMPORAL STABILITY i the degree to which people s scores on measure are stable over time ii example administer the Paranormal Belief Scale in Jan 2013 again in Feb 2013 iii question what is the quotrightquot length of time between measurements b lNTERCODER RELIABILITY i stability across coders ii two people evaluating the speech had to make sure the video is coded the same way by multiple coders iii can do it through percentage agreement or correlation c INTERNAL CONSISTENCY i Items on the measure have to be consistent ii Splithalf or Cronbach 5 Alpha 0 How are each assessed a What are desirable levels for Cronbach s alpha i Alpha gt 80 good 39 Alpha 7080 adequate iii Alpha 6570 minimally acceptable iv Alpha lt 65 undesirable 11 Measurement Validity o What is validity i Content ii Criterionpredictive iii Construct 0 What s the difference between reliability and validity i YOU MUST HAVE RELIABILITY TO HAVE VALIDITY ii If you have reliability you might not necessarily have validity What are content predictive and convergent validity What does each ask 10 i Content Validity does the measure sample relevant content adequately and appropriately Are the items on the measure reasonably representative of the all possible items that could be included ii Predictive Validity does a measure predict what it should predict Does it predict relevant future outcomes criterion iii Construct Validity TOUGHEST TO FINDPROVE Your results will correspond to other methods of measuring the same construct 0 Be able to recognize examples in which each is being assessed 12 Sampling 0 Be able to de ne population sample statistic parameter and sampling error i Population an entire group of people events or texts that share one or more characteristic that researchers are interested in ii Sample a smaller of elements from the total making up the population iii Statistic a numerical characteristicsummary of a sample eg sample M iv Parameter numerical characteristicsummary of the entire population value from a census v Sampling Error degree to which a sample statistic deviates from a population parameter a What is simple random sampling i Simple Random Sampling draw sample so that each member of population has an equal chance of being selected in sample a How does random differ from nonrandom e g convenience sampling i convenience sample study readily available subset of population 0 When is it especially important to use random sampling i vaery important to estimate the exact values of population parameters precisely and accurately eg political polling it is critical to use random probability sampling 13 Survey Development a Survey questions should be driven by What 0 Speci c research questions 0 Hypotheses 11 o What are the primary methods for delivering surveys o Questionnaires Mail Survey Group Administered Questionnaires Online Survey Automated telephone interview 0 Interviews Personal interview Telephone interview a What are advantages of surveys and interviews 0 Questionnaires lnexpengve Standardized Convenient for respondent 0 Interviews Personal Interviews Allows personal contact 0 Can be adapted by using followup questions Easier for the respondent Telephone Interviews 0 Fast 0 Allow for personal contact 0 Allow followup questions a How can you increase response rates 0 Use a clear email subject line 35 characters or less with no Detail who has been invited to participate Explain the survey s purpose and the bene ts Highlight the survey deadline Mention length of survey Explain incentives if any Include personal informationnames when you can Include survey URL and instructions for accessing the survey OOOOOOO What is response fatigue How can it be monitored and reduced 0 Fatigue Participants become tired of the survey task and the quality of the data deteriorate as they move through the survey 0 Monitoring Fatigue Split Randomizing Repeat Questions Reverse Code 12 The Instructional Manipulation Check Data from your survey tool 0 Reducing Fatigue Keep motivation up Make sure sample population has the ability to process the queonns Vary task dif culty 0 Guidelines for writing effective questions 0 Brand the survey 0 Make questions easy to answer 0 Responses must remain visible 14 Memorize formulas for meanmedian 0 Mean Average Add all scores up divide by total number of scores 0 Median 0 Middle Put all scores in order Find the middle 0 Standard Deviation 5 6 Steps in Computing SD 0 Step 1 Calculate sample mean M Step 2 Subtract mean from each raw score deviation x XM Step 3 Square each deviation score xquot2 Step 4 Sum up the squared deviation scores E Step 5 Divide by total number in sample N Step 6 Take the square root OOOOO 39 ZSC or e O Numerator one person s deviation score X 0 Denominator S or SD for sample I Z XMS XS 13 Morgan 2014 COM 304 Final Exam Review Sheet Professor Melanie Morgan Purdue University 1 Experimental Research What is the purpose of conducting experimental studies of communication 0 Establishing a causeljeffect relationship 0 To test whether or not changes in a dependent variable are caused by changes in an independent variable What are three features of a true experiment 0 Researcher manipulates the independent variable 0 Researcher randomly assigns participants to conditions 0 Researcher controls extraneous variables What are experimental treatment and control conditions 0 Experimental condition receives SOME exposure to IV 0 Control condition receives NO exposure to IV What does it mean to manipulate an independent variable vs an attribute variable 0 Manipulating the IV means that the researcher develops different levels of the IV determines which participants are exposed to each level 0 An attribute variable is a preexisting condition of participants can t be manipulated by the researcher sex race age verbal aggressiveness etc What is random assignment and how does it differ from random selection 0 Random assignment participants have an EQUAL probability of being in each condition 0 Random selection NOT EQUAL TO random assignment Why is random assignment important 0 It reaches more than a certain population 0 Helps control for unanticipated factors because subjects are equally likely to end up in each condition What are extraneous variables 0 Variables that are not the same throughout every time the experiment is performed How can they be controlled 0 Assign participants randomly 0 Keep experimental procedures consistent across conditions 0 Add extraneous variable as another IV Be able to distinguish between an experiment vs other types of research eg a survey where no inference can be made about cause and effect Be able to recognize notation eg for a twogroup posttest only experimental design 2 Claims about Causalitv What are 3 criteria for making causal claims 0 Covariation 0 Time order 0 Alternative explanations Morgan 2014 0 Why doesn t correlation causality What is a spurious relationship 0 Spurious relationship an extraneous variable is causing both X and Y 0 Why can we infer time order from an experiment 0 Because a researcher controls time order 0 What does it mean to say that another variable might be confounded with the IV 0 A confounding variable is a third factor Z also occurs along with the independent variable X and hence one can t tell whether changes are being caused by X or by Z 0 How are experiments designed to rule out alternative explanations 0 Researcher randomly assigns participants to conditions 0 Researcher holds everything else except manipulation of IV constant 0 Researcher may include a control group to isolate the impact of the treatment from other factors 0 0 What are internal and external validity 0 Internal Validity degree to which changes in DV can be attributed to IV not other factors 0 External Validity degree to which research findings can be generalized with confidence to the larger population 3 Intro to Inferential Statistics 0 What are inferential statistics 0 Used to draw conclusions about what s likely true in a larger population based on findings from a sample 0 How do they differ from descriptive statistics 0 Makes inferences about population from results of sample 211d half of class not the sample itself 1st half of class 0 What are three types of distributions population sample sampling 0 Population distribution a frequency distribution of individual scores for all members of the population shows the frequency with which individuals in the population as a whole fall into various levels or categories that make up a variable 0 Sample Distribution a frequency distribution of individual scores for members of a sample shows the frequency with individuals in a sample drawn from the larger population fall into the various levelscategories that make up a variable 0 Sampling Distribution frequency distribution of sample statistics eg sample means for multiple samples of a given size which all were drawn randomly from a larger population shows how far samples statistics tend to vary from each other 0 How can we describe the central tendency and dispersion for a sampling distribution of means 0 Central Tendency mean of distribution of sample means mean of all sample means 0 Dispersion SD of distribution of sample means also called Standard Error of the Mean SEm 0 What is the standard error of the mean SEM Be able to calculate it when given the sample SD and N Morgan 2014 0 A measure of how representative a sample is likely to be of the population 0 Why is it called the standard error of the mean What makes it largersmaller 0 Large SE means that there is a lot of variability in the sample means so our sample might not be representative of the population 0 Small standard error indicates that most sample means are similar to the population mean so our sample is probably a fair representative of the population 0 What is the Central Limits Theorem CLT When does it apply 0 CLT when draw all samples of size N randomly from a larger population the distribution of sample means sampling distribution will be approximately normal EVEN IF the distribution of raw scores population or sample distribution is skewed 0 It applies at all times except when N is tiny 4 Confidence intervals GIL 0 What are con dence intervals 0 Gives us a range of scores that we can be confident where the mean of the population lies 0 When given a sample mean M standard deviation SD and sample size N be able to compute 95 and 99 con dence intervals 0 196 95 0 258 99 0 M SEm196 OR 258 0 What do CIs tell us 0 Where the mean of the population lies 0 When estimating parameters in what way is there a tradeoff between precision the size of the CI and con dence eg 95 vs 99 0 The bigger your sample the smaller your error 0 Do you want to be more confident or more precise You ve got to give something up Be able to readinterpret an error bar plot 5 Steps in Hypothesis Testing onesample ztest 0 What is the null hypothesis and how does it differ from the research hypothesis both comparison and relational 0 The hypothesis of no differencerelationship the test hypothesis 0 When we conduct a study which hypothesis do we actually test directly 0 The null hypothesis 0 What does it mean to say that a research nding is statistically signi cant 0 It is unlikely that we would get a difference that large simple by chance sampling error if the sample is really representative of the sample population 0 Statistical significance low probability of getting these findings if we accept the null hypothesis Morgan 2014 F 0 What is a p value and what does it tell us 0 A level of statistical significance 0 Tells us the probability of these ndings if the null hypothesis were true less than 5 times out of 100 times What are the steps in hypothesis testing 0 Formulate research hypothesis Formulate null hypothesis Select a level of statistical significance Select appropriate inferential statistic to test the null hypothesis and compute it Test inferential statistic for significance 0000 What is a critical value 0 005 CV 196 0 001 CV 285 What is a onesample ztest and what type of hypothesis is it used to address 0 Used to test hypothesis about the mean of a population based on a single sample 0 Measure the differences in means between two populations based on samples from each population 0 O 6 Testing Pearson r for Statistical Signi cance What type of hypothesis is this statistic used to test ie when do we use it 0 Interval or ratio scale variables What does the sign of Pearson r tell us The size of Pearson r 0 If your test statistic is BIGGER than the critical value then you accept the research hypothesis If your test statistic is SMALLER than the critical value then you accept the null hypothesis What are rules of thumb for small medium and large effects with Pearson r 0 r 10 and below weak relationship 0 r 24 moderate relationship 0 r 37 strong relationship 0 r 0 NO relationship What are the degrees of freedom for this test 0 df N2 If given a Pearson r and a table of critical values Table be able to tell if a correlation is statistically significant 0 See page 362 Table B4 0 MUST KNOW DEGREES OF FREEDOM 4 Morgan 2014 0 If given SPSS output with a correlation and SIG level be able to tell if the correlation is statistically significant 0 Test statistic bigger than CV I accept research hypothesis 0 Test statistic smaller than CV I accept null hypothesis 0 If given a Pearson correlation be able to calculate and interpret the coefficient of determination and know what constitutes a small moderate and large association 0 r 10 and below weak relationship 0 r 24 moderate relationship 0 r 37 strong relationship 0 r 0 NO relationship 7 ChiSguare 12 0 What type of hypothesis is a chisquare statistic used to test when do we use it 0 an inferential statistic used to address hypotheses involving only nominallevel categorical variables 0 If given a 2 X 2 table of observed frequencies be able to calculate chi square 0 N Nov 1 2012 sample of 1200 likely voters 0 400 Democrats 110 Pence 290 Gregg 0 400 Independents 210 Pence 190 Gregg 0 400 Republicans 300 Pence 100 Gregg 0 1200 total 620 Pence 580 Gregg 0 What are the degrees of freedom for this test 0 df rows 1 columns 1 0 df 2121 0 df 00 0 df 1 0 When given a table of critical values Table be able to tell if a x2 test is statistically significant same for SPSS output 0 WANT TO BE HIGHER THAN THE CV TO BE STATISTICALLY SIGNIFICANT 8 ChiSquare Effect Size 0 What is Cramer s V phi and what does it tell us about the impact of a categorical IV on a categorical DV 0 Cramer s V ranges from 0 to 1 I 0 one variable has no impact on the other I 1 one variable totally determines the other complete predictability 0 Formula for Cramer s V 2 Z Nk 1 Morgan 2014 0 X2 value of chi square 0 N total number of cases grand total 0 k of categories of variable with smaller number of categories 0 What are rules of thumb for small medium and large effects with Cramer s V 0 10 small effect 0 24 moderate effect 0 37 large effect O 9 ttest for independent deg C What type of hypothesis is this statistic used to test when do we use it 0 IV categorical variable 0 DV quantitative variable 0 What is the denominator of this test called 0 Standard error of the difference between means 0 What are the degrees of freedom for this test 0 df N2 0 see table B2 on page 354 for chart 0 When given a table of critical values Table be able to tell if a ttest for independent data is statistically signi cant same for SPSS output 0 We want the p value to be SMALLER than 05 to be statistically significant 0 0 What are rules of thumb for small medium and large differences with Cohen s d 0 d around 20 1539 is a SMALL effect 0 d around 50 4074 is a MEDIUM effect 0 d around 80 75109 is a LARGE effect 10 Errors in Hypothesis Testing 0 What is a Type I error 0 Research rejects the null when in reality the null is true 0 FALSE POSITIVE 0 What single factor determines how likely a researcher is to make a Type I error 0 Significance level 0 What is a Type II error 0 Researcher fails to reject the null or they accept the null when in reality the null is false 0 FALSE NEGATIVE 0 Why do we need to consider both statistical signi cance AND effect size when evaluating research hypotheses Morgan 2014 0 When N is small even large differencesassociations may not be statistically significant because power is low 0 When N is large even small differencesassociations may be statistically significant because power is high Things you need to memorize 1 Formulas for SEM C195 C199 chisquare test X2 and t test NOT formula for SDm Cramers V 2 Degrees of Freedom df for t test for independent data chisquare Pearson r 3 When to use a onesample z test t test for independent data chisquare and Pearson r SELECTING THE PROPER INFERNTIAL STATISTIC and accompanying effect size 1 Does the research hypothesis ask about the association between two nominallevel categorical variables ANSWER Chi Square X2 and Cramer s vphi 2 Does the hypothesis ask about the association between two intervalratiolevel quantitative variables ANSWER Pearson correlation r size of r r2 3 Does the hypothesis compare two groups different unrelated people categorical variable on a quantitative dependent variable ANSWER ttest for independent data Cohen s d 4 Does the research hypothesis predict that results from a sample are not likely to have come from a population with a known parameter ANSWER onesample ztest
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