MEASUREMENT AND EVALUATION IN KINESIOLOGY AND RECREATION
MEASUREMENT AND EVALUATION IN KINESIOLOGY AND RECREATION KIN 411
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This 164 page Class Notes was uploaded by Kayla Balistreri on Saturday September 26, 2015. The Class Notes belongs to KIN 411 at James Madison University taught by Michael Goldberger in Fall. Since its upload, it has received 23 views. For similar materials see /class/214020/kin-411-james-madison-university in Kinesiology at James Madison University.
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Date Created: 09/26/15
Unit 1 Part 1 Research Designs Approaches to problem solving and decisionmaking Unscientific approaches Intuition uneducated hunch guessing Irrational offthetop thinking Personal preference Observation Case study Authority Scienti c approach logical rational empirical Defining and delimiting the problem Formulating the hypothesis Gathering objective data Analyzing data Interpreting results Draw conclusions What is research Research defined Be may defined as structured problemsolving It is a process that follows the scientific method Statement of the problem research question stated in the interrogative Review related literature Hypothesis and null hypothesis Empirical data collection and summarize results Hypothesis testing and conclusions What is research Some of the characteristics are Systematic Follows a set of predetermined steps from question to results L0gical Steps make sense Empirical Results are observable Replicable The stepsprocess can be repeated Reductive The results attempt to explain a complex effect through a simple cause Kinds of research Basic research is carried out for the sake of increasing knowledge Scientists trying to answer fundamental questions in science Often takes place in pristine research labs with lots of equipment Very expensive Applied research is carried out to solve practical problems Daytoday answers to local problems or questions Marketing a product is a form of applied research ModelsTypesApproaches Methods of Research An Overview 1 Descriptive Familv 2 HistoricalQualitative Familv SUFVeY Historical Questionnaire Qualitative Interview Group comparison DEVelopmental 3 Experimental Familv LongitUdinal Quasiexperimenta1 Case study True experimental Observational Correlational Descriptive Research A Definition The main goal of Descriptive Research is to describe statistically the characteristics of what is going on at a particular point in time Although this research is highly accurate it does not determine the causes behind a situation It does not attempt to determine cause and effect It does tell you accurately what is happening at a particular point in time and is used when one wants an objective perspective about what is going on Descriptive research Survey Research Written Questionnaire most popular format of survey research What is the opinion ofJMU students and alumni about JMU oncampus housing What physical activities do parents participate in and value What do clients enjoy during a typical visit to the ball park Descriptive research Types of written Survey items Multiple choice single entry or multiple entry Provides respondent with choices Single entry one choice multiple entry more than one choice Likert scale Rating scale between often between extremes of strongly agree and strongly disagree Not providing a neutral option forces the respondent to take sides Text entry Allows respondent to enter own word or words limited Bipolarsemantic differential Provides for rating between two bipolar extreme Side by side comparison Allows the participant to make sideby side comparison in making choices Qualtrics httpimuquatricscomSESDSV 9RAquw03Fvnw5C Descriptive research Survey Research Interview format Person to person Phone Internet Other More effective than the questionnaire because of two way communication However an interview is a lot more time consuming and expensive Descriptive research Other research formats Group comparison research Are Republicans wealthier than Democratics Are women more exible than men Do athletes have better reaction time than non athletes LongitudinalDevelopmental research Do the attitudes of J MU KIN graduates change over the rst ten years after graduation about the Internship or Student Teaching experience Could do it using a crosssectional format Descriptive research Other formats Case study What is the rate of non JMU visitors to a typical dorm per week and who visits beside parents of dorm students Observational How do fourth grade children spend their time during health education class Correlational What are the relationships among vertical jump agility speed and strength Modelsfl39ypesApproaches Methods of Research 1 Descriptive Family Survey Group comparison Longitudinaldevelopmental Case study Observational Correlational Assignment 1 is due Sept 15 Go to Blackboard Assignment 1 and follow this link httpimuquatricscomSESDSV 9RAquw03Fvnw5C 2 Historicalg Qualitative F amily Historical Qualitative Historical Research the systematic examination of change in human affairs Primary and secondary sources of historical evudence Secondary sources 0 SW ence Books articiesand other media egfiirnwritten by historians based ontne recoiiections ofand materiais from others Primary sources of SW ence Firsthand evidence Direct participation or observation Court records Originai documents Archeoiogicai dig Wim ls regarded ssthe inunderoithe modem Olympics a Avery Biunda e 2 Juan Antonin Samaranch ILPierre e Cuuhanin Ii Demeirius Vlkelas Qualitative research also referred to as interpretive or ethnographic research Qualitative research seeks to answer 39anthropoiogicai questions concerning he ys of life of living human beings Ethnographic questions generally n the link between culture and behavior andor how i i processes develop overtime The data bas f thnographies is usually exte sive description ofthe details of social life or cultural phenomena in a small number of cases Margaret Mead 190176 Cultural anthropologist from the United States She Wanted to do a comparative study of life of adolescents in the US and Samoa Going Native becoming paIt of the social milieu Comparing Quantitative and Qualitative Research Quantitative Laboratory Measuring instruments Large and random Value free Cause and effect Statistics Qualitative Natural world quotnativequot Researcher as an instrument Small and purposive Value bound Continual shaping Interpretive Experimental Research 39 r tns mutefor laboratory Aqimal Research quotVISID OH EAHTH amp LIFE STUDIES Trying to establish a Cause and Effect relationship between a Treatment or Intervention and a Result Experimental designs Trying to establish Cause and Effect T treatment or intervention the independent variable CAUSE O observation or test the dependent variable EFFECT or RESULT group mean or average Collecting the data on one group One shot preexperimental T 0 One group pretestposttest quasi O T 0 Two group comparison quasi T 01 02 Two group prepost comparison quasi 01 T 02 In these four designs you can only apply the results to the group you studied the subjects involved in the study The next two designs involve rst randomly selecting subjects from a population a larger group This subset of the population is called a sample and the sample is assigned to groups before starting the experiment R randomized groups You have a random sample Randomized groups true R T 01 R 02 Pretestposttest randomized groups true R 01 T 02 In these true experimental designs you can compare these posttests statistically and then infer or generalize the results to the population Unit 1 Part 2 Populations and Samples Population and Sample Many research studies experiments surveys etc don t use everyone in the study The researchers select and use part of the entire group a subset called a sam le Before discussing a sample let s first define the concept of population The population is defined by the researcher Any specifically defined group of things or persons may be considered a population When it comes time to do a study researchers sometimes don t use the entire population It is often too expensive and time consuming to test everyone So they select a sample to study The idea is if the sample is carefully selected the sample s characteristics likely will closely resemble the characteristics of the population Therefore results from the sample can be inferred to the population from which is was drawn By using a sample the researcher can devote more time and care to data collection to help ensure valid data are collected There are a variety of ways of selecting the sample It has been found that the best way of selecting a representative sample is through random selection In random selection each member of the population has an equal chance of being selected for the sample Random selection does not eliminate the chance of obtaining an error sample It does not guarantee the sample is a true sample Random selection m however provide the best chance for a true sample and it w inform the researcher of the risk the chance of having an error sample Population and Sample Forillustration take a lake that is Population and Sample tested regularly for several chemical agents Let s say the worker takes a sample from along the shore and finds relatively high amounts of certain undesirable chemicals Perhaps it is a spillage point near a farm Does this sample represent the lake s chemicals The worker takes samples from different locations around the lake and finds them all to be fine It is possible to draw a sample that does not represent the population the entire lake Yes but we can estimate the risk that the sample drawn is an error sample Population and Sample So researchers are willing to accept a certain amount of risk that their results and conclusions might be incorrect Using statistical inference which is based on the laws of probability researchers can estimate the chance that their sample is an error sample In our professions the typically agreed on standard is a 5 percent risk that our results are error results In other words if we were to collect another 99 random samples total of 100 95 of them would produce similar results Chances are that in five samples the results would not be similar If we determine that the risk that our sample is an error sample is less than 5 plt05 we can generalize our sample findings to the population These are referred to a significant results or findings On the other hand if we determine the risk that our sample is an error sample is greater than 5I then we cannot generalize our findings and they are consider statisticallv nonsignificant Example of Assignment 2 Prospectus Due Oct 6 upload to Assignment2 in Blackboard Statement of the Problem Do women and men differ in terms of their flexibility Hypothesis Women are significantly more flexible than men Rationale Women are shorter shorter levers thinner less bulk and care more about flexibility and work harder at maintaining it than men Assignment 4 Review of Related Literature Due Oct 27 upload to Assignment 4 in Blackboard Start with Procedures for your assigned test found on Blackboard under Course Documents Review textbook material on reserve in ECL Start using databases to search for related literature Sport Discus is recommended Review literature and note relevant information Prepare a synthesisintegrationsummary of the relevant information not an annotated bibliography Include references Use APA style and write in the third person Dynamic balance develops differently in males and females athletes and non athletes and varies by age In the research done for background information it has focused on the dynamic balance difference in males and females The idea behind the research was the women have a lower center of gravity therefore having better dynamic balance The background information focused primarily in different age groups but showed varying results depicting which gender has a more developed dynamic balance The research done had varied information and studies that indirectly addressed the topic Although the limited information about dynamic balance and gender is not vast the background information gathered can help develop an understanding about the development in each gender In a study that focused on postural control but dynamic balance was a criteria to test the difference between genders found that women were able to recruit more muscles to maintain their balance during a Star Excursion Balance Test SEBT Gribble 2009 In the study it was hypothesized that women performed better because of the lower center of gravity Gribble 2009 In another study done by Holviala showed the effects ofmuscle training on balance and other capabilities in women the end result showed that it benefited women in various aspects The study focused how strength training influence muscle strength characteristics functional capabilities and balance the study pretest the subjects and tested periodically during a 21 week time span Holviala 2006 The study showed improvement from the pretest to the post test after muscle strength training in dynamic showed that the muscle recruitment improved over the given time Holviala 2006 The two studies show that women with training can recruit more muscles for balance compared to men In a study that focused on men compared non athletes and athletes within balance and how prior sport performance affected dynamic balance of each subject Raty 2002 In the study it was founded that subjects that was not an elite athlete was impaired in dynamic balance as they age Raty 2002 The subjects that were elite athletes completed the test in a faster time compared to the control subjects Raty 2002 In another study that compared the scores of pre and post test scores about dynamic balance through programmed or random conditioning Bloomfield 2007 The scores showed that the type of conditioning was not significant to performance in either gender Bloomfield 2007 The type of conditioningthat a subject has prior to testing or during the study may not greatly affect the result A study that focused primarily on tennis players but compared them by gender showed that dynamic balance was a factor on how well they performed competitively Filipcic 2010 In the study it showed that dynamic balance enable fem ales to perform at a more competitive level as it did not greatly affect the males Filipcic 2010 In a different study that focused on an older population that dynamic balance did not greatly differ in men or women Islam 2004 In the same study it showed that dynamic balance was not correlated with any physical activity Islam 2004 References Gribble PA Robinson RH Hertel J amp Denegar CR 2009 The Effects of Gender and Fatigue on Dynamic Postural Control Journal of Sport Rehabilitation 18 SportDiscus Filipcic A Filipcic T amp Pisk L 2010 Relationship between the Results of Elected Motor Tests and Competitive Successfulness in Tennis for Different Age Categories Retrieved from SportDiscus Islam MM Takeshima N Rogers ME 2004 Relationship between Balance Functional Fitness and Daily Physical Activity in Older Adults AJESS Retrieved from SportDiscus Holviala J Sallinen J 2006 Effects of Strength Training On Muscle Strength Characteristics Functional Capabilities and Balance In Middle aged and Older Women Journal of Strength and Conditioning Research Retrieved from SportDiscus Raty HP Impivaara O amp Karppi SL 2002 Dynamic Balance in Former Elite Male Athletes and in Community Control Subjects Scandinavian Journal of Medicine amp Science in Sports Retrieved from SportDiscus Bloomfield J Polman R 2007 Effective Speed and Agility Conditioning Methodology for Random Intermittent Dynamic Type Sports Journal of Strength and Conditioning Research Subject Number Avg Score 1815 655 55 45 1015 1 Dynamic Balance Test Balance Beam 2 Patrick Pelletier Yvonne Parker Nikki Peros 3 Column A Subject Number Column B Average distance in inches Population and Sample Illustration Let39s say we were interested in comparing JMU women and men in terms of low back flexibility We have approximately 16000 undergraduates atJMU We go to the University Registrar and request a random sample of 60 students It turns out that in our sample we have 33 women and 27 men We test these 60 students on the sit and reach a test of low back flexibility We find the average score for the women was 1546 and for the men 1395 So the women were 15 inches better than the men in this sam le of 60 randoml selected individuals What about the population of 16000 students Population and Sample Using inference based on the laws of probability we can generalize the results from our randomly selected sample back to the population from which the sample was drawn with a given degree of confidence that our sample was not an error sample In this case the difference between the means of the women and men 15 inches was large enough for us to be able to conclude that the difference was statistically significant Hypothesis Testing Statement of the problem Do college women at JMU have better low back flexibility than their male counterparts Hypothesis The mean flexibility score for a group of JMU women 71 will be better than for a group of JM U men X 2 Research hypothesis u 1 gt u 2 Null hypothesis p 1lt1 2 Randomly select 60 students from JMU undergraduate majors n16000 Test them on Sit and Reach Get results Mean N Std Deviation male 1395 27 144 female 1546 33 193 Total 1471 40 187 On average females outperformed males by 15 inches We do a statistical test ttest and find out that we can reiect the null hypothesis plt05 We can conclude that JMU women have better low back flexibility than JMU men Hypothesis Testing 6 The writeup might be something like this As can be seen in the data table females performed significantly better than their male counterparts on the flexibility test plt05 The hypothesis is supported 7 Let s look at the frequency polygons for males and females Aggggaaagggagaiaeg 13 A randomly selected group of volunteer women enrolled in a large health Club agree to participate in a study on gaining strength This group is randomly assigned into two subgroups Subgroup 1 gets a strength program three days a week and subgroup 2 does not They are tested after three months of the program Research hypothesis X1 X2 Null hypothesis X1lt72 The results indicate no differences between the groups so you accept your null hypothesis The program was ineffective Let s say the strength program really doesn t work it is truly ineffective So your null hypothesis is really true and you ve accepted it You ve made the correct decision However let s say instead that your results indicate a positive difference so you reject your null hypothesis and accept the hypothesis that the program works But the null hypothesis is really true So you ve made an error You ve rejected a true null hypothesis This is called having a false positive or a Type I error Accept Reject Truth Table Null H Correct False Positive True Decision Type I error Null H False Negative Correct False Type II error Decision Let s say instead that the program really is effective It truly works the null hypothesis is false and should be rejected Your results indicate signi cant differences between the groups so you reject the null hypotheses and accept your hypothesis You ve made the correct decision But let s say your study indicated that the program didn t work although it really does So your null hypothesis is really false and you ve accepted it You made an error You accepted a null hypothesis that should have been rejected This is called a false negative or a Type 11 error You ve said something is ineffective when it really is Accept Reject Truth Table Null H Correct False Positive True Decision Type I error Null H False Negative Correct False Type II error Decision Hypothesis Testing Statement of the problem Do college women at JMU have better low back exibility than their male counterparts Hypothesis The mean flexibility score for JMU women will be better than for JIVI U men Research hypothesis ul gtu 2 Null hypothesis H 1ltu 2 Randomly select 60 students from JMU undergraduate majors n16000 Test them on Sit and Reach Get results Mean N Std Deviation male 1395 27 144 female 1546 33 193 Total 1471 40 187 On average females outperformed males by 15 inches We do a statistical test ttest and find out that we can reiect the null hypothesis plt05 We can conclude that JMU women have better low back flexibility than JMU men Hypothesis Testing 6 The writeup might be something like this As can be seen in the data table females performed significantly better than their male counterparts on the flexibility test plt05 The hypothesis is supported 7 Let s look at the frequency polygons for males and females Aggggaaagggagaiaeg 13 Unit 1 Part 3 Concepts of Measurement and Evaluation Concepts of Measurement amp Evaluation An Overview Define Tests measurements and evaluation Scores and their meaning Test selection Why test purposes Who to measure What to measure What are the qualities of a good test How to select an appropriate test Distinguish between types of evaluation Criterionreferenced Normreferenced Definitions Measurement and Evaluation Testing or measuring The process of collecting quantitative numeric information Test A measurement instrument to collect quantitative information Score or measurement The numeric result of testing A quantitative representation of an individual s or group s performance The data yield or dependent variable Evaluation Determining the worth of data The process of using measurements for decisionmaking Involves Taking a measurement Getting a criterion Comparing measurement against criterion Drawing conclusion Purposes of measurement and evaluation Placement Diagnosis Prediction Motivation Achievement Measurement Ol39 score Measurement two meanings It is a eld of study and it is a score A score represents the performance of an individual or group expressed by a number or symbol Level of a score or measurement Nominal scores Names Ordinalscores Rank order Interval scores Equal interval without absolute zero Ratio scores Equal interval with absolute zero Graduating Class 2002 Smith High School Student Q Gender Class Rank G Susan 11 1 1 400 Frank 03 2 2 329 Sam 10 2 3 328 Arthur 04 2 4 318 Rosie 08 1 5 317 Sally 09 1 6 281 Kurt 06 2 7 279 Amanda 01 1 8 250 Fred 04 2 9 203 Lillian 07 1 10 202 Warren 02 2 10 202 Test Theory Sources of error Errors in the instrument validity andor reliability Errors in the person doing the testing objectivity Errors associated with the test taker Goal is to maximize true score and minimize error score Four qualities of a test Validity Does a test measure what it purports to measure Reliability Consistency Will the test provide the same scores consistently Obiectivity Will different testers get the same results Feasibility Given reality time access to subjects funding etc is this test practical or feasible to do Dependent and Independent Variables for Term Project Research question about 1 Group comparison 2 Relationships Dependent Variables psychomotor attributes Muscular strength Muscular endurance Cardiovascular endurance Balance Flexibility Agility Speed Power Others Groups independent variables Gender Athletenonathlete Body sizecomposition Others Height Weight Handedness BMI Etc New Slide Validity A test measures what is purports to measure Validity is specific to an attribute or behavior Cognitive domain Knowledge Memoryrecall most school tests are knowledge Comprehension Understanding Give an example Application Applies knowledge Analysis Breaking it down into component parts Synthesis Putting parts together to form a whole Creativity Going beyond the box Motor domain Reflexive Sub cortical Universal forms of movement Endemic to human function Specialized form of movement Work and play forms sport Creative Going beyond the box New Slide Validity A test measures what is purports to measure Affective domain Attitudes and values Feelings httpwwwanesicomfscalehtm httpwwwyoutubecomwatcllva3TKK1ltS g18 Validity Degree to which a test measures what it purports to measure We validate scores not tests If a set of scores lacks validity it is functionally worthless Validity methods Logical or face Determined by panel ofjudges Criterion Relationship to already validates test Rehab y Calculating reliability coeffient r Stability multiple trials Usually a day or more apart Tuneconsun ng nternaconthency Using multiple trials for example skin folds Acceptable r not lt7 usually between 8 and 9 Factors affecting reliability of scores Subjects number size of group Test difficulty Etc Increasing the reliability of a set of scores Validity is assumed Trials n5 If a set of scores is not valid its 2 reliability is irrelevant 8 Increase the number of test trials to improve 8 reliability 6 In summarizing a set of Q trials use the median not Mean 68 the mean as the score Median 80 Objectivity Objective When tWO or more testers score the same test and assign the same score Improving Objectivity Have stroneg defined scoring system and are administered by trained testers Subjective Lacks a standardized scoring system which introduces a source of scoring error Feasibility Test must be Appropriate for subjects age gender etc Time and cost effective Safe protection of human subjects Evaluation Evaluation implies a value It is a statement of quality goodness merit value or worth Evaluation implies decision making Timing of evaluation Formative Evaluation along the way at formative stages of a process Are you ontarget or do adjustments need to be made Summative Afinal evaluation No going back Formative Summative Purpose Feedback to tester and Certification or grading person being tested Time During the process At the end of process Emphasis in Explicitly defined Broader categories of Evaluation behaviors behaviors or combinations of several specific behaviors Standard Criterionreferenced Usually normreferenced but can be criterion referenced Evaluation Norm and Criterion referenced Criterionreferenced Used to find if someone has attained a certain level of competence Positives Negatives Normreferenced Used to judge an individual s performance in relation to the performance of other members of a well defined group Positives Negatives Issues with Norm referenced standards Developed by using a large of people of a defined group Standards developed by performing descriptive statistics ie percentile ranks A major concern of using normreferenced standards is the characteristics of the group on which the standards were developed Be sure to consider the the appropriateness of the groups to which you are comparing the individual Relationship of Measurement and Evaluation Review for Exam 1 Research and the Scientific Method defined Structured problemsolving Stating or defining the problem Formulating the hypothesis and null Review related literature Data collection Analyzing data and interpreting results Conclusions Research is systematic logical empirical reductive and replicable Basic and applied Families of research designs Descriptive Survey Developmental longitudinalcrosssectional Correlational Case Study and Observational Analytical Historical Qualitative Experimental Inferential research P0pulati0ns and samples sampling techniques Internal and external validity Setting an alpha level signi cance and reducing chances of getting a false positive or false negative Measurement and Evaluation Definitions Test Measurement Evaluation Purposes of measurement Selection Placement Diagnosis Achievement Prediction Motivation Levels of measurement What to measure Domains of human attributes Motor domain Cognitive domain Affective domain Qualities of a test Validity Reliability Objectivity Feasibility True and error measurement Sources of error True vs error measurement Evaluation Formative and summative Norm and criterion referenced standards Unit 2 Basics of Statistical Analysis Overview of unit Defining statistics Organizing quantitative data Using statistics to analyze data Major issues addressed by statistics Descriptives Group comparisons Relationships Branches of statistics Use of SPSS Unit 2 Part 1 Defining Statistics Statistics defined The science that deals with the collection analysis and interpretation of quantitativenumerical information we call data Statistics provide an objective means for organizing and interpreting measurements gleaned from tests or observations Some stat symbols X a score n number of scores in a distribution 2X sum of scores 7 ZXn mean 5 standard deviation A difference lt less than gt greater than at not equal S equal or less than 2 equal or greater than Ability to use specific statistical techniques depends on the nature of the data you have Levels of measurement Nominal Scores assigned to label levels within a category Ordinal Scores that can be ordered but that do not have a standard or common interval Percentile ranks are ordinal data Also limited in terms of what you can do mathematically Interval Scores that have a common unit of measure between them Most variables produce interval data Ratio Same as interval but with a true zero point Another way of describing the nature of measurements Discrete variables There are m gradations between integers Home runs Course grades Continuous variables There are infinite gradations between integers Longjump in inches Time in days hours minutes seconds miniseconds etc Maj or issues addressed by statistics 1 Quantitative descriptions of groups Describe quantitatively how scores in a distribution are 51m1lar Describe quantitatively how scores in a distribution are different 2 Inferring from a sample to a population 3 Group comparisons 4 Relationships betweenamong variables Unit 2 Part 2 Organizing Quantitative Data Using statistics to describe a distribution of scores Example n 50 7I4I3I6I5I8I5I7I9I7I3I 7 I8I2I10 7I4I2I5I3I6I4I5I3I4I5I5I5I1I6I3I5I4I5I8I2I6I 5I7I4I 7I3I6I 6I3I4I4I I 9 2 8 You have a distribution of scores When you look at these unorganized scores it is difficult to describe them Find highest and lowest scores Low score 1 High score 10 Range 9 Make a list of potential scores from low to high If more than 10 categories combine two or three scores together Score i A GO i KNUJbUIChNOO Organizing scores into a Frequency Distribution 7436585797328210742536453455516354582 65747366344789 Low score 1 High score 10 Make a tally mark for each score Frequency Distribution Score Tallies Frequency 10 1 9 2 8 4 7 7 6 6 5 10 4 8 3 7 2 4 1 l n 50 Frequency Polygon Distribution of n 50 scores Score F 10 1 9 2 8 4 7 7 6 6 5 10 4 8 3 7 2 4 1 1 n 50 By smoothing the frequency polygon we create a curve that by its shape tells us the nature of the distribution Different way of representing same data set From the Frequency Distribution transfer data into a Frequency Polygon H AauanbaJJ onwhmmuoomo 012345678910 SCOFE Frequency Polygon Distribution of n 50 scores A distribution that is shaped like the curve to the right is known as a normal or bell shapedquot curve more on this later ONwDWOSNMKDO 012345678910 score Frequency 12 10 8 Using statistics to be a set of scores Frequency Histogram Distribution of n 50 scores VAR00001 100 200 300 400 500 600 700 800 900 1000 VAR00001 Create Frequency Histogram The Y axis is Frequency The X axis is Score The numbers run from low to high and from left to right Note the shape of this histogram A different dataset n15 15 scores n 15 817886749767829 Frequency Polygon High Score9 and Low Score 1 0 Frequency Distribution X f cf Hwauimxiocw i i Oi o4gt4gt s vARoooo1 How would you describe this frequency polygon Negative skew Most did well f How would you describe this frequency polygon Positive skew Most did poorly f m How would you describe this frequency polygon Leptokurtic Most did similar How would you describe this frequency polygon Platykurtic Most did different A Graphing of Scores frequency polygons Few People receiVed low scores Few people received high scores 39 Negatively Skewed Curve Positively Skewed Curve Very homogeneous groups Very heterogeneous groups Leptokurtic Curve Platykurtic Curve Unit 2 Part 3 The Normal Curve Laws of probability For many bifurcated variables two choices eg gender coin f flips 5050 chance heads tails For many distributed variables many options the normal curve Laws of probability effect of large numbers For many bifurcated f variables two choices eg gender coin ips 5050 heads tails chance For many distributed variables many options the normal curve The Normal Curve 477 A 47790 ean I edian andMode 341 341 n a 3 2 4 2 3 a 39 39 39 quot quot the Laws of Probability with the following characteristics Symmetrical Center point is mean median and mode Mean of zero and a standard deviation of 1 682 of the cases fall between one standard deviation on either side of the mean 954 of the cases fall between two sds of the mean 999 of the cases fall between three sds of the mean Curve does not meet the base line Bob Beamon 1968 Mexico City Olympic Games The Normal Curve 2 13 34 34 13 quotn 73 72 4 n 1 2 3 11 14 17 20 23 26 29 Let us label the baseline 2 with 0 being the mean standard deviations above and below the mean labeled accordingly Let s take an example We have a group of vertical jump scores of high school students n50 with a mean of 20 and a standard deviation of 3 We know vertical jump scores are normally distributed Central Tendency Measures of Central Tendency Indicate where scores tend to be concentrated 10 Mode 9 8 Median 7 6 Mean 5 4 3 2 0 012345678910 score Unit 2 Part 4 Using Statistics to Analyze Data Central Tendency 0 Mode The score most frequently received It is used with nominal data Can be more than one bimodal trimodal etc What is the mode of the scores below 10 9 8 8 7 7 6 6 6 6 644 2 1 Central Tendency Median The quotmiddle score 12 the scores are above amp 12 below or it is the score where 50 of the distribution is above and 50 is below Cannot be calculated unless the scores are listed in order from best to worst Calculating approximate median Set of ve scores 34 n 1 32 Medlanapprox 2 19 15 The median is the score above which and below which half 50 of the distribution falls What is the median for What is the median for this this distribution of scores distribution of scores 10 10 NU IOWLD NNUUU39II Central Tendency Mean arithmetic average The sum of the scores divided by the number of scores ie the average score X Zsumof 5 2X 20 X 4 n XorYscore gz zzl 1 5 X mean Note scores do not rst need to be 11 of scores ordered Often the most appropriate measure of central tendency with Interval or Ratio data Central Tendency When to use mode median mean Mean is most commonly used and likely the best measure of central tendency If scores are very skewed or you are using ordinal scores the Median is the best measure Mode usually only used when mean amp median cannot be calculated Le nominal scores or when the only information wanted is most frequent score Le most common uniform size which question on a test was missed by the most students When the frequency polygon of a set of scores resembles the normal curve the mode median amp mean are at the same place Score LC o I NUUDU39IOWNOO How scores in a distribution are similar Using the original set of 50 scores cf 50 49 47 43 36 3O 20 12 5 1 fX 10 18 32 49 36 50 32 21 16 1 ZX 257 Mean arithmetic average ZXnMean Mean 25750 514 Median 50thile The score above w ich and elow which half the distribution falls Go up cf column to 25th score Median 55 Mode most popular score Look in the f column Mode 5 Measures of Variability Variability deals with how scores are different Measures of quotspreadquot or quotheterogeneityquot of scores Group 1 Group 2 9 6 5 5 1 4 Mean amp Median for both groups is 5 Does this mean the two groups are similar In terms of Centrality they are But they are different when we compare variability Measures of Variability We are going to look at three measures of Variability Range Easiest measure of variability to determine Calculated as the difference between highest amp lowest scores Used when measure of central tendency is mode or median I Range Xmighest XOOWCSD Group 1 Group 2 9 6 5 5 1 4 Range of these two groups Range 8 Range 2 Not a very stable or precise measure of variability It depends on only 2 scores and is affected by a change in either score How are scores Within a distribution different Interquartile deviation Range between 25th ile and 75th ie Given this distribution of eight scores 9 8 7 7 6 6 5 2 75th iIe 75 50th ile median 65 25th iIe 55 Interquartile deviation 20 Measures of Variability Standard Deviation s The appropriate measure of variability when mean is used Indicates amount that all scores differ or deviate from the mean I I S The more scores deviate from the mean the higher the Formula for standard deviation 2X2 EX2 n 2X2 sum of squared scores n 2X sum of scores n of scores S Calculating Standard Deviation 2X2 EXPm 1 1 Scores 7276562 X2 203 SSE7 49 l 7 4 L 7 7 4 49 l 203 12257 203 175 82 36 25 36 4 2X 35 2X2 203 S S S S S Graphing of Scores frequency polygons Few People receiVed low scores Few people received high scores 39 Negatively Skewed Curve Positively Skewed Curve Very homogeneous groups Very heterogeneous groups Leptokurtic Curve Platykurtic Curve Calculating Standard Deviation The average sum of squares variance Scores 7276562 variance or s2 ZXX2 scores deviations deviations squared X X 7 X 702 n 7 7 5 2 4 7 7 5 2 4 6 6 5 1 1 s zgxxy g 6 6 5 1 1 5 5 5 0 0 n 7 2 2 5 3 9 39 2 2 5 3 9 xx 35 206 0 209302 28 4 Z 2 sum of squares X 5 Two samples Effects of mean and standard deviation Sa mpIe l Sample 2 10 10 9 9 9 9 8 3 2 2 Mode 9 Mode 9 Median 9 Median 9 Mean 76 Mean 66 Range 8 Range 8 SD 287 SD 33938 varZ var1 f score score 3 11881769646666666541 01234567890 12345678911111111112 E 1223547BEMM6432422111 m 012345678900 12345678911111111112T 115 Tbtal Descriptive Statistics N Min Max Range Med M s var1 115 1 20 19 101 977 357 var2 115 1 20 19 92 967 546 mm mm mu WED m xsuu 39Nnn mun mu Hun ma w m m 1am m w 1131 m i t i mm mm 19m mu mu mu mu mu nu ma an t u mnn gt m an m m m m w 1am W van Major issues addressed by statistics 1 Quantitative descriptions of groups Describe quantitatively how scores in a distribution are similar Describe quantitatively how scores in a distribution are different 2 Inferring from a sample to a population 3Gr0up comparisons 4 Relationships betweenamong variables Between Group and Within Group Variability Illustration 1 Illustration 2 Experimental Group Experimental Group Pre 101 Post 102 Pre 101 Post 102 50 6O 50 50 50 6O 50 50 50 6O 50 50 50 6O 50 50 E Q E m 250 300 250 300 h450 h460 h450 h460 Control Group Control Group Pre 103 Post 104 Pre 103 Post 104 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 E E E E 250 250 250 250 h450 h450 h450 h450 In comparing means between two groups you create a Ratio with the between group variability in the numerator called true difference and the average within group variability in the denominator called the error difference Illustration 1 Mpre 50 sIDre 1 leost s 1 post Ml M2 Between group TRUE SISZ Within group ERROR ratio 1001 100 Illustration 2 MIDre 50 sIDre 1 Mpost 60 s 20 post ratio 1021 048 So the error variability in the second group 20 is greater than in the first group 1 thus making the second Ratio smaller Two sets of scores with the same means but with different standard deviations ILLUSTRATION 1 standard deviations small ILLUSTRATION 2 standard deviations gtltL 165 175 Variability analysis Between group variability is considered true we know what caused the variability t resulted from a Cause and the change is the Effect Within group variability is considered error because it is uncontrolled Because the treatment was the same for all you would expect all scores to be the same The within group variability is a reflection of dissimilarity of individuals within the group Group comparisons Are the means of two or more groups Sig ni cantly different Group comparisons Comparing the means of two groups The ttest is a ratio comparing the actual difference in the means of two groups numerator and the sum of the variability within both groups denominator If the ratio is large more between group variability than within group variability the groups will be judged to be significantly different If the ratio is small more within group variability than between group variability the groups will be judged to be significantly equal To answer the question Are the means of two independent groups significantly different t test formula To determine if the means of two independent groups are different use an independent t test If the groups are related use a correlated or dependent t test t test formula for independent samples m the difference between the two means true variability t 71 X2 Denominator the average variability within each group error variability slzn1 szzn2 Group differences Are the means of two or more group different students n100 is 150 pounds using one rep max ORM There are a total of The averafe strength for a randomly selected group of middle school PE 1200 stu ents in the school You randoml divide the group in half 50 in one grou and 50 in the other The average YORM score for each group is 150 poun 5 You randomly assign one grou to an extra stren th development program two days a week this is in ad ition to their regu ar PE classes You continue their workouts After several months you test them again The experimental group improved to an average of 175 ounds and the contro goroup improved to an average of 165 poun s o ot groups improve But the question is Are these two groups 39signi cantly different Group differences Are the means of two or more group different Experimental group mean 175 Control group mean 165 There is a difference of 10 pounds Are the means different enough so we can conclude that the difference wasn t just due to chance The stat test we use to compare two means to determine if they are significantly different is called the ttest To answer the question Are the means of two independent groups significantly different Results Group Mean N Std Deviation Experimental 175 50 332 Control 165 50 640 Total 170 100 711 ttest formula for independent samples t X1 12 Wnz Let 5 look at how th1s 1s done 1n SPSS t 175165 Q 97 1041 103 A second version of the ttest ttest for dependent samples Five men who went through a weight loss program Did they lose a signi cant amount of weight Dependent Variable body weight in pounds Before 200 200 210 225 195 After 190 195 205 215 190 Comparing the means of two dependent groups using a ttest 39 Question Did these subjects improve significantly dependent or correlated sample n t a n ED2 ZD2n1 Subiect Pre Post D D2 1 200 190 10 100 2 200 195 5 25 3 210 205 5 25 4 225 215 10 100 5 195 190 5 25 1030 995 35 275 t 35 i 571 52753524 6124 Look up critical value of t computed value 571 With df4 Letas see in SPSS Group comparisons ANOVA To determine if the means of more than two groups are statistically different use an Analysis of Variance ANOVA Oneway Analysis of Variance Used with two or more groups to test the hypothesis that the means of the groups are significantly different For example Here are 15 scores on an exam to test knowledge Group 1 read a book and had a discussion group Group 2 only read the book Group 3 just took the test X1 12 10 11 7 10 X2 LOOWNLO 4 X3 Are these means significantly different 6 7 2 3 2 Means group 1 10 n5 group 2 7 n5 group 3 4 n5 Oneway Analysis of Variance Groupl Grou92 Grou93 X1 X12 X2 X22 X3 X32 12 144 9 81 6 36 10 100 7 49 7 49 11 121 6 36 2 4 7 49 9 81 3 9 E 1 E 2 1 Z 50 514 35 263 20 102 M 10 7 4 A 2 2x2 x22 x22 x32 514 263 102 879 B zx2n 5o3520215 735 C 2 X12n1 2 X22n2 2 X32n3 25005 12255 4005 825 Oneway Analysis of Variance page 2 A 2 2x2 x12 x22 x32 514263102879 B ZX2n 503520215 735 C 2 X12n1 Z X22n2 Z X32n3 25005 12255 4005 825 ANOVA Summary Table Source of Variation Sum of Sguares DF Mean Sguare F Between true C B 90 K12 450 100 Within lerror A C 54 nK12 45 Total A B 144 n114 p 402 with 2 and 12 clf plt05 Computed value of F 10 Critical value of F 388 Reject null Results Means are significantly different plt05 Mean group 1 10 Mean group 2 7 Mean group 3 4 Post hoc analysis to find out where significant differences are located Using SPSS ANOVA to determine if means are significantly different What is the relationship between vertical jump and gender s there a relationship between athletes maintaining endurance for a longer period of time than nonathletes s there a relationship between gender and speed Are younger individuals more flexible than older individuals Does body mass index have an effect on speed as measured by the 40 yard dash Do shorter students perform betterdo more curl ups than taller students Does weight affect the distance covered on the balance beam ANOVA Summary Table Source of Variance Sum of Sguares MS FLtio Between True k1 Within Error nk Total n1 ANOVA Summary Table Source of Variation Sum of Squares DF Mean Square F Between true 90 2 450 100 Within error 54 12 45 Total 144 14 p 402 with 2 and 12 clf plt05 Computed value of F 10 Critical value of F 388 Reject null Example 1 means Example 2 means XHI C Xpre Elm M F M TRT 10 10 TRT 10 10 12 8 CNT 10 10 CNT 10 10 10 10 Two factors Treatment and Gender Two levels of each factor Treatment yes and no Gender female and male There is a treatment by gender interaction Two way ANOVA There are two independent variables A and B Summary Table Twoway ANOVA Source of Variation Sum of Squares DF Mean Sguare F Between true A Treatment B Gender C A x B interaction First look here Within error for signi cant F Total Other ANOVA models Oneway ANOVA Used when you have one independent variable Twoway ANOVA Used when you have two independent variables Factorial ANOVA Use when you have more than two independent variables eg gender ethnicity and year in school would be a 2X4X5 Factorial design Repeated measures ANOVA Used when each person is measured on two or more occasions repeated measures ANCOVA Analysis of Covariance Used when you want to control for an extraneous variable MANOVA Multiple analysis of variance Used when you have more than one dependent variable Major issues addressed by statistics 1 Quantitative descriptions of groups Describe quantitatively how scores in a distribution are similar Describe quantitatively how scores in a distribution are different 2 Group comparisons 3 Relationships betweenamong variables Correlation Looks at how two or more variables relate to one another A bivariate correlation computes the relationship between two variables Tells you what variable Y does as variable X changes For example What are the relationships between height X and weight Y and between IQ score X and grades in school Y In both these cases the relationship tends to be positive As X increases Y increases However remember not CAUSE and EFFECT Correlation The correlation statistic ranges from a 10 perfect positive correlation to a 10 perfect negative correlation Negative does not mean bad In a positive correlation as X increases Y increases In a negative correlation as X increases Y decreases In a zero order correlation there is no relationship as X increases or decreases Correlation Name Height Weight A bivariate correlation Pearson 01 84 300 r estimates the degree of 02 78 25 relationship between two sets 03 72 200 of scores 04 66 150 05 60 100 r ranges from 10 to 10 The and tell you whether the two variables varyin the same 84 X direction as one goes up the other goes up or in the 78 opposite direction as one goes Y 72 up the other goes down H 66 r gt08 high lt03 low 60 r 01 or less zeroorder or no correlation 100 150 200 250 300 x height Bivariate Correlation eg heightweight weight 100 200 300 n Observed D Linear 0 Height Y Weight X 60 100 66 150 72 200 78 250 84 300 My 72 MX 200 S 85 S 707 The straight line drawn through the plot points is called the Regression Line or the Line of Best Fit VAROOOO I Perfect positive and perfect negative correlations 3 VAR00002 VAR00001 1 3 2390 3390 40 VAR00002 If the Regression Line hit each plot point that yields a perfect correlation r 10 VAR00001 Curvilinear and Zeroorder correlations VAR00001 4 VAR00002 2390 3390 40 13 2390 3390 40 VAR00002 As plot points fall away from the Regression Line this decreases the correlation Calculating the Pearson r bivariate X X2 Y Y2 XY 60 3600 100 10000 6000 66 4356 150 22500 9900 72 5184 200 40000 14400 78 6084 250 62500 19500 84 7056 300 90000 25200 360 26280 1000 225000 75000 72 200 85 70 7 r2 Coef cient of Determination r nzxv ZXZY n Sf n r 575000 3601000 l 5262803602 sr 522500010002 I r 15000 424233555 15000 10 14234 To determine the alpha level p use nZ degrees of freedom and enter table 100 Types of correlations overview Bivariate correlation Pearson r Partial correlation r123 Spearman s Rho ordinal data Multiple correlation R A multivariate correlation involves the relationships among more than two variables Example of Correlation Matrix from SPSS Correlations VAR00001 VAR00002 VAR00003 VAR00004 VAR00005 VAR00001 Pearson Correlation 1 400 294 010 320 Sig 2tailed 252 410 977 367 N 10 10 10 10 10 VAR00002 Pearson Correlation 400 1 845 756 870 Sig 2tailed 252 002 011 001 N 10 10 10 10 10 VAR00003 Pearson Correlation 294 845 1 745 759 Sig 2tailed 410 002 013 011 N 10 10 10 10 10 VAR00004 Pearson Correlation 010 756 745 1 575 Sig 2tailed 977 011 013 082 N 10 10 10 10 10 VAR00005 Pearson Correlation 320 870 759 575 1 Sig 2tailed 367 001 011 082 N 10 10 10 10 10 Correlation is signi cant at the 001 level 2tailed Correlation is signi cant at the 005 level 2tailed Partial correlation Allows you to tease out a spurious variables to better see the true relationship between two variables Statistic r113 Which looks at the relationship between variables 1 and 2 with variable 3 partialed out Sgearman s Rho Used if you have ranked or ordinal data This is a nonparametric technique doesn t need to meet assumptions to use parametric statistics Rank information from Observer 1 and Observer 2 on the same subjects Question Are these scores correlated rs 1 6ZDZnn2 1 D difference between 1 and 2 Multiple correlation R Correlates the relationship of one variable X also called the criterion variable and a combination of two or more other variables Y1 Y2 Y3 etc called the predictor variables X Y1Y2Y3 For example Y1sit amp reach Y2vertical jump Y3leg 1 rep max Xlong jump Model Summary Adjusted Std Error of Model R R Square R Square the Estimate 1 6308 397 085 7119864 a Predictors Constant VAROOOO5 VAROOOO4 VAROOOO3 VAR00002 Correlation and regression A bivariate correlation Pearson r estimates the degree of relationship between two sets of scores r ranges from 10 to 10 The and tell you whether the two variables vary in the same direction as one goes up the other goes up or in the opposite direction as one goes up the other goes down H r gtO8 high lt03 low R 01 or less zeroorder or no correlation Regression or prediction is a statistical technique that uses the correlation between two variables to predict one score criterion from another score predictor if the correlation is known Prediction or regression Regression or Prediction Estimating one measurement based on the value of one or more other measurements One measurement Simple Regression More than one measurement Multiple Regression Regression Line is Y a bX Where The predicted score is Y The slope ofthe regression line is b b rsy sX The intercept is a a My b Mx And X is the predictor the known Prediction or Simple Regression Regression Line is Y a bX Also called the quotLine of Best Fit Int rcepta Where The predicted score is Y The slope of the regression line is b b rsy sX The intercept is a a My b Mx And X is the predictor the known Regression or Prediction Simple Regression Y a bX Multiple Regression Y a b1X1 bZX2 biXi Multiple Regression Multiple Regression Using several predictor variables to predict a criterion score Y a b1X1 b2X2 biXi Where Y is the Criterion variable a is the constant bl is the coefficient for the first predictor variable bZ is the coefficient for the second predictor variable And so on For example what would be the predicted first year GPA for a high school senior with an SAT score of 1000 an average of 84 and a rank of 35 out of 64 Unit 2 Part 5 Branches of Statistics Statistics two branches types or categories Parametrics are preferred because they are more Powerful But parametrics have certain assumptions that must be met Your datavariable must be normally distributed The variances from samples must be equal homogeneity of va ancel Independence of measurement Nonparametrics do not require these assumptions be met and can be used with frequency nominal and ranked data Downside non parametics are less powerful Categories of Statistics There are two types or categories of statistics parametrics and nonparametrics Parametrics are preferred because they are more Powerful But parametrics have certain assumptions that must be met Sometimes you cannot meet these assumptions and then nonparametrics come in handy To use parametrics assumptions that must be met Your datavariable must be normally distributed The variances from samples must be equal homogeneity of variance Independence of measurement Nonparametrics do not require these assumptions be met and can be used with frequency nominal and ranked data Parametrics has certain assumptions to use Variables are normally distributed Variances of X samples of the variable are equal Homogeneity of variance Observations are independent At least at the interval level of measurement Nonparametrics no assumptions but less powerful Nonparametric Tests sampling Chi Sguare Can be used with frequency data from nominal variables MannWhitney U Test Nonparametric equivalent to the independent t test Wilcoxon MatchedPairs SignedRank Test Nonparametric equivalent to the dependent ttest KruskalWallis ANOVA by Ranks Comparable to a oneway ANOVA Friedman TwoWay ANOVA by Ranks Comparable to a repeated measures ANOVA Spearman RankDifference Correlation Comparable to a Pearson r Chi Square Compares observed versus expected frequencies For example a tennis coach notices that his team loses on Court 4 more than the other three courts he uses s thisjust chance or is Court 4 really bad for his team Loses M 1 2 3 4 total ObservedActual 26 31 20 43 120 Expected 30 30 30 30 120 Question Are the 40 losses on Court 4 significantly more than losses on the other courts Court number 1 2 3 4 tota Actual Losses 0 26 31 20 43 120 Expected Losses E 30 30 30 30 120 OE 4 1 1o 13 OE2 16 1 100 169 OE2E 053 03 333 563 Chi square ZOE2E Chi square 5303333563 952 df c1r1 3 Looking in Table A8 the critical value of Chi Square for 3 degrees of freedom is 782 So the computed Chi Square 952 is more than the critical value and so statistically there is a significant difference Unit 2 Part 6 Using SPSS Descriptives Frequencies Provides a frequency distribution Descriptives Cross tabs Provides frequency distributions for more than one variable at the same time Provides mean and standard deviation Descriptives Descriptives Provides means and standard deviations broken down by an independent variable Compare Means Means Compare Means Compares means of two Independent samples ttest groups Analyze Descriptives select Frequencies Analyze Descriptives select Cross Tabs Analyze Descriptives select Descriptives Analyze Compare means Means variable broken down by group Analyze Compare Means select Independent Samples t test Compare Means ANOVA Compares means of more Analyze Compare Means than two groups select ANOVA Correlations Provides bivariate Correlate select Bivariate correlation matrix Separate out a sub group for Identifies selected sub Data Select Cases groups within dataset Identify the group you want analysis eg Gender 2 Create two or more groups Creates groups out of set of Transform Recode into for group comparison interval scores Different variables analysis Create a new variable Transform Compute Variable Graphics Histogram Show frequency polygon in shape of histogram Graphics Scattergram Relationship shows scatter plot of two variables Preparation for Test 2 Basic Statistics Levels of measurement Normal curve Characteristics Zscores Measures of central tendency and dispersion Group comparisons True and error variance t test ANOVA Correlation and regression Correlation coefficients Partial correlation Multiple correlation Regression Nonparametrics Less powerful but do not require meeting assumptions Chi square
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