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# Computer PSY364

Drexel

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This 20 page Class Notes was uploaded by Yessenia Walsh on Wednesday September 23, 2015. The Class Notes belongs to PSY364 at Drexel University taught by ChristopherRamey in Fall. Since its upload, it has received 15 views. For similar materials see /class/212498/psy364-drexel-university in Psychlogy at Drexel University.

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Date Created: 09/23/15

Crash course in PSY 364 682011 85400 PM Statistics o Descriptive Statistics 0 Describe information distribution observations 0 Summarizing groups like a mean or other measures of central tendency like mode median range Mode observation that occurs most frequently Median is the middle 50 Mean is the most useful and fundamentally all of our significance testing is about looking at the means Range is pretty useless Variance Standard Deviation o Inferential Statistics 0 No longer describing actual collective data 0 Going beyond what you have actually recorded to come to some kind of conclusion you are not telling it as it is but the conclusion is based off of certain predictions that you are making 0 Probabilistic anytime you make a claim you say at the same time that that might actually not be the case 0 Nothing is certain o Measurement 0 If the measuring devices are not precise the numbers themselves do not really make sense Then it is junk GIVE A CLEAR CUT EXAMPLE OF NOMINAL ORDINAL AND INTERVAL RATIO DATA Nominal Data Classification into mutually exclusive categories Numbers do not matter It is the amount of something in a category that matters The only thing you can do with nominal data is to count No logical order is needed only that the categories differ Numbers may be used but only to identify categories Census Examples 0 Gender male female 0 Religion Baptist Catholic Jewish Muslim Ordinal Data o Classification using numbers though not always where the numbers 0 Represent mutually exclusive quantities Have ordering based on the relationships of gtandlt Now things can be put into order that actually makes sense A ranking The interval between ranks does not need to be equal o Examples Grades A B C D F So what happens when a student gets an A and then a B You cant know that the interval between A and B is the same 0 Olympic medals O O O O O O O O Interval data Ratio o Numbers represent mutually exclusive quantities that have an ordering and have equal steps along the measured variable o In other words a 1point difference in any location along the measured variable is the same as a 1point difference at any other location 0 So like a thermometer The intervals are the same 0 And also like the historical time measured in BCE o So what does zero mean 0 Nothing zero means something o Numbers represent mutually exclusive quantities that have an ordering with equal intervals along the measured variable and have the property that a true zero point exits o The zero point indicates the total absence of the measured attribute Amount of something that we are measuring Negative numbers do not exist You cannot have a negative amount of something Examples 0 Temperature in Kelvin Drug dosage Time elapsed 0 Because there is a zero point you an make ratio statements The Random Sample The distinguished Chimpanzee and Chuck Norris o The random sample is of particular interest to us 0 A random sample has the following characterizes 0 Every observation in the population has an equal chance of being inclu e o The choice of any one observation does not change the likelihood of the choice by any other observation Population Group on interest Sample Subset of a population Calculating the mean WW sample of scores X 0 Symbol used for the mean X barquot 7 2X 2X 0 Formula for the mean of a sample X T p i o For a population of scores X ol used for the mean is the U mu 0 Formula for the mean of a population Are you dealing with a sample or a population Properties of the mean 0 The sum of the deviations around the mean equals zero 0 The sum of the deviations from the mean is smaller than the deviations from any other po39 t 39 with n on the top and i1 on the bottom xi xbar 0 Measures of Central Tendency in symmetrical and asymmetrical distributions 0 In negatively skewed distributions the mode has the highest value followed by the median and finally the mean which is the lowest value In a positively skewed distributions the mean has the highest value followed by the median and then finally the mode which has the lowest value Why central tendency is not enough istribution could be short and fat the other tall and skinny and they could both have the same mean Sometimes vou can nave tne sarne variabiiitv but tne rneans are ditterent vvnv wouid anvone use the S2UBE instead of the o2 our sarnbie is svsternaticaiiv biased in favor of picking certain scores as opposed to otners A sarnbie as a subset ot tne bobuiation nas tne brobabiiitv otrnissing tne outiiers The s2ube is tne unbiased estirnate otvour sarnbie variance ne o2 tning is tne bobuiation variance What is tne differenceicaicuiationrwiseibetweeh a true sarnbie variance and a sarnbie UBE variance h versus hrl Sampies are excuses to taik about our bobuiation The UBE is more in ated so we can generaiize it rnore to tne bobuiation In ated caicuiation so tnat it iooks rnore iike tne popuiatiohi Ssquared is true sarnbie varianc gtltbar i5 5 tvpicai x z pobuiation variance 2 M Sum otSquares and the variance N he surn ot tne squares or surn ot tne squared deviations trorn tne rnean is known as 88x 88x Sigrnaxaxbar2 88x So tne formuias tor tne variance becorne o pobuiation orxsquared Sigmagtltrux2 divided bv N aiso SSXN o Sampie Svsquaered sigrna xaxbarp divided bv n aiso 88X h 80 anv answer vou get is tne answer squared deviation score point ot controversv o In t e brevious evarnbie for caicuiation tne variance we dtoi the 82 10 5 and then the SZUBE14i o It we are interested in generaiizing tne tindings trorn tne sarnbie to tne bobuiation tne s2 UBE is tne torrnuia tnat snouid be used tor caicuiation tne sarnbie variance What is tne Z Score ConceptuaiiW And in a distribution wnat us anotner narne for z or o The number of SD s a score is away from the mean 0 Z XXbar divided by S o Z X ux divided by ox o Z 0 means that the score is equal to the mean It corresponds to the mean o The mean is a summary term for an entire distribution If a score is u o 20 what percentage of scores are at or above it o Within the parentheses population mean the standard deviation of the population 2 times the standard deviation of the population o So you move 1 SD to the left and then you move two SD s to the right So you end up at 1 SD away from the mean c 23 or 68 is between 1SD and 1SD o The more the X differs from the mean relative to the typical difference the more deviant the score is The numerator will be bigger than the denominator Tyoe I error o Probability of rejecting the null when there are really no differences between the groups 0 Equal to your p value c Courtroom Finding someone guilty of a crime they didn t commit o Reject the null hypothesis and support the scientific hypothesis o Not reject the null hypothesis refute the scientific hypothesis Type II error o Probability of failing to reject the null hypothesis when it is actually false 0 Missing an effect that exists o Courtroom Not finding someone guilty when they actually committed the crime o Being to conservative with our alpha level Type IIIlogical kind of error TTests 682011 85400 PM Hypothesis Tests with Mean of Samples the Distribution of Means o Distribution of individual scores 0 Curve Measures of central tendency eg mean o Distribution of means 0 Curve sample of size n drawn randomly form the same population 0 So like a mean for each class room and then you would take the means of the classrooms and that would be your population mean o Hypothesis Tests 0 Comparison distribution is distribution of means 0 A sample mean gets compared to a distribution of means of samples instead of a population mean of individuals 0 If you had a claim that us as a class are deviatly older than the class next to us we would have to show that our mean is much greater than the typical mean So the difference between the class rooms divided by the typical difference 0 Relating variables to other variables Xbar s to Xbar s Different kinds of distribution o Distribution of a population of individuals perfect bell curve o A specifically shaped distribution of a given sample a blocky distribution o Distribution of means tall and skinny smooth distribution 0 Shape is approximately normal if Each sample includes gtor equal to30 or more individuals or The distribution of the population of individual scores is normal How our Xbar compares to other Xbar s The distribution of Means o The distribution of means the distribution of sample means See notes 1 o The mean is the population mean 0 The variance is the variance of the population divided by the number of individuals in the samples 0 The standard deviation see notes 2 Of a distribution of means the distribution of sample means a AKA standard error of the mean SEM o You are looking at a distribution of Xbar39s and you are looking to make claim to a population mean o You are not sure really if any given xbar is the best estimate for the population mean u AKA standard error o Want the standard error to be small Want low variability between the Xbar39s n quotIt has this name because it tells you how muchthe means of samples are typically in error as estimates of the mean of the population of individuals 0 A population mean is the mean of means It is the mean of all the x s but remember we are no longer going to be looking at individual x s we are interested in groups and how they differ form other groups in terms of distribution Averages of the averages is also the population mean 0 How much do sample means differe from the means of their means TTest for a Single Sample o Comparing a single sample to a population o Estimating population variance from sample 0 Biased and unbiased estimates Notes 3 o T tells us how much does our sample deviate from the typical sample and what the difference is is it any different from the normal deviance o The larger the T the bigger the difference between the numerator and denominator So the denominator is the standard way that groups differ and the bigger the numerator the greater it is past 1 you want a T greater than 1 o The t distribution varies in shape 0 According to the degrees of freedom 0 Notes 4 O o SPSS O O O O O O O The larger the T the more your sample is especially different from what is typically the case The smaller the standard error is the more the Xbar39s are closer to each other and the better it is confidence in HW sample analyzeecompare meansetake variable and move it into test variable test value is for the population mean We made it 5 Descriptive 2 decimal places P value 3 decimals no zero in front t16 195 p 069 think of the t as a ratio So lets think oft as 2 So we can think of it as 2 over 1 and that is a ratio saying that the numerator is twice the denomentator So the numerator is about twice the size as the denominator So if we look at xbar Greek letter m even though it does not look like much a difference what matters ist the ratio of our sample and how groups are typically confident What we show is how our group is twice what is happening in the denominator Twice what is normal Numerator for the scientific and denominator for null hypothesis Signal to noise ratio Ttest for dependent means paired sample ttest o Unknown population mean population variance o Paired scores for each person bivariate O 0 Repeated measures design pre an posttests Difference scores Subtract one score form other Hypothesis test with difference scores Population of difference scores with a mean of 0 o Notes 5 O This refers to the average difference between two dependent groups equivalent to the difference between the averages How much do groups typically differ from themselves Independent Samples ttest foundation for anova o Comparing two samples 0 Experimental group control group 0 Scores of two groups ie observation are independent of each other 0 ONE INDEPENDENT VARIABLE AND ONE DEPENDENT VARABLE The independent variable can have 2 levels drug versus no drug 0 Two independent samples do they belong to the same population The population is the target distribution of interest 0 What level of the independent variable are you receiving and what is the dependent variable o Example 0 Medicationreceive one or two levels of the independent variable So drug versus no drug Distance self from the word group use the word o The distribution differences between means 0 If null hypothesis were true The two populations have equal means The two distributions of means have equal means The mean of the distribution of differences equals 0 See notes 11 The more the means differ from each other the less likely the null hypothesis is true Analysis of Variance ANOVA 682011 85400 PM Part 1 One way ANOVA What is a test of significance Ttest ztest Ftest Significance test size of effect x size of study 0 You can have a big effect or a big study T statistic is signed or or has direction 0 One mean versus another mean 0 12 F o t square root ofF A one way anova you can have two or more levels for an independent variable 0 No drug 1 pill 2 pill etc 0 An extension of a independent samples ttest We can now have more than two levels We want to know group differences 0 Mean of group 1 vs 0 Mean of group 2 o Standardize that difference 0 Notes 12 What is variability SPSS Sum of squares 0 Property of the mean Ftable o F is a ratio Put 2 t and f next to each other and see how they are alike The bigger the numerator versus the nominator the bigger the z the more likely it is that you can support your scientific hypothesis The bigger the t the more extreme the differences between the groups The bigger the fthe greater variability you find between the groups Experiment three conditions There will be an example in the 365 folder o Are there differences between groups overall o Another kind of variabilirty the standard deviation The bigger the SD the more the data is spread out around the mean but it is still 68eh o Notes 13 for a f could you actually tell the curves apart o F is the difference between the groups compared to within groups sufficiently large ANOVA table is SPSS o Sum of squares measure of variability One step away from variance The numbers don t really mean much o Mean The Fratio O O O O O O 0 Between groups differences between among our levels Are the humps different from the other humps Within groups how spread out the distributions are within themselves So how spread out is the hump The less variability within each group the more the scores tend to hover around the xbar The more variability there is within a distribution the less xbar summarizes the data accurately between groups so however many levels you have minus 1 within groups three group samples 1 subtracted from each so in this case our total n was 30 with 3 levels so our df is 27 Square short for variance The sum of squares divided by the degrees or freedom mean squares Between groups the average squared deviation score The variance between the groups Within groups the variance within the groups The ration of mean squares So the between groups mean of square divided by the within groups mean of square Telling you how many times the numerator is larger that the denominator Each sample are all estimating the same population variance Different populations The null hypothesis cannot be true o The variance between groups divided by the variance that exists with groups chance factors o MS is mean squares NOTES 14 FOR EQUATION o Estimates of population variance The t and the F o No drug vs one pill 18 238p 029 o You will not be able to predict a sign in the ANOVA o Oneway ANOVA two groups F118 566 p 029 o The 1 is the between groups and the 18 is the within groups df o Directionality General Procedure F WILL ALWAYS BE A POSITIVE NUMBER o Notes 14 o SO lets say you want your sum of squares to be explained by squared deviation scores use the transform and o Variance is sum of squares divided by n1 Distribution of differences between means o Independent samples ttest 2 groupsnotes 15 o Oneway ANOVA F more than 2 groups 14 The F distribution o Inferential statistics 0 How we relate the differences to something else XX 1 o See notes 16 o The greater the F is the less and less likely it is to occur if the null hypothesis is true 0 Population mean u of Xbar39s o The larger the F the more likely it is the case that the scientific hypothesis can be supported and the null hypothesis can be rejected o The mean square between divided by the mean square within o A ratio 0 Top partnumerator the extent to which the levels of the independent variable differ form one another The more the dependent variable mean is higher the larger the differences are Mean square between 0 Bottomnumerator mean square within Sum of squares a measure of variability higher numbers are more variable Sum of squares SS divided by df S2UBE The support for the scientific hypothesis All things being equal a higherfwill give you a low p value SPSS HW 2 Review Set up like a Ttest with two columns Experimental design Say the hypothesis bit and then put down the technical information of F in APA format acceptably low risk of committing a type I error Adding a 2 pill group indicates that you believe that having a higher drug level relates to mood You need a good conceptual reason to have this many levels Omnibus Test A test that has degrees of freedom specifically between groups df greater than 1 If you did have 1 that indicates that you only have 1 level but if you have greater than 1 then it means that you have more than 1 level Limit the extent to which we can make a specific conclusion Prevent us form making specific recommendation 0 How much of a drug to take need to follow them up Investigate a post hoc test 0 Series of tests that happen after the Omnibus One Way ANOVA Only if it is statistically significant n Which entitles us to keep looking a If it was not statistically significant you are not entitled to follow up Gate keeper to prevent you from fishing for test results that benefit what ever you believe Overall relation POST HOC TEST One to one comparisons Performing multiple ttests sort of 1 One way anova 2 Post hoc 3 Tukey HSD 4 Tukey Post Hoc Tests reveal that there is a significant difference between no pills and two pills harder to get statistically significant data conservative Note the more test you do the more p you have the probability of committing a type I error increases PART II Reported measures Factorial ANOVA and Mixed Repeated measures 682011 85400 PM What are Factorial ANOVAs o What are oneway ANOVAs o How one IV effects a DV but potentially how it relates to another IV And how they might come together in an interaction o Interaction 0 So like if the pills only work for a male and not a female 0 A level of a drug affects you r health as long as we take into account what sex you are What can you learn from factorial ANOVAs o No drug one pill two pills 0 Effect on dependent variable o Factorial ANOVA s 0 Main effect How an independent variable and an DV are related to one another your drug amount if related to your mood 0 Main effect We have two because we now have two independent variables your drug amount effect one differently depending on sex 0 Interaction effect How many pills you take is related to your health irrespective to your sex Knowing whether or not you are male or female I can predict your mood irrespective of the amount of pills you take I cannto consider how sex or how drugs affect your mood independently of one another a ExYes sex affects your mood but only if you are taking one pill Or if you are female Maybe it is the case that drugs matter but only if you are male Example 12 x 2 factorial ANOVA design Need to understand what the twos are we are creating a kind of grid 0 4 groups of people 2 IV so each 2 is an IV and it means that they each have two levels paying attention in class 0 paying attention or not and this is related to the grade in course 0 group 1 people who pay attention 0 group 2 people who do not pay attention will to live 0 those who want to live 0 those who want to not live grade in course note if you only were looking at attention and live you would want to use a t instead of a t an fwill always be positive and at can be positive of negative And you can actually have directional positions So like for weight loss this would be good the important stuff is attention live attention and live and error paying attention is related to the grade and is irrespective of willingness to live your willingness to live irrespective of whether you are paying attention omnibus test you have a vary vague uneasy kind of conclusion which is one variable is realted to another if you want specifics you need a tuky post hoc tests Though conservative they allow you to actually compare on level to another level Omnibus tests are tests when you have df greater than 1 do a tuky post hoc test if you get statistical significance for an omnibus ANOVA test Mid Term Review 682011 85400 PM p 01 would not tell you about statistical significance alone it would tell you that you have a 1 chance of making a type I error the error has to do with the decisions regarding the hypothesis if you do the following support the scientific hypothesis and reject the null and it is this decision that could be a mistake your p value is less than your alpha level was so p lt alpha is statistical significance A scientific hypothesis a relation between the variables you are studying o if there is a relation and you have an experimental design then there are differences between the two groups however if it is not experimental I do not think you can actually have a null hypothesis no relation Descriptive statistics describes data summarizing data like a mean median and mode condense data do not give you a detailed description Inferential statistics hypothesis testing like ttests and anova s and such Sample subset of your population Population ultimate group of interest Sample UBE versus Population variance o use if you were measuring a population c or use if you are measuring a sample 0 where you are trying to estimate the population Alpha Level o threshold that you are comfortable with of making a type I error p value c tells you the probability of making a type I error ANOVA Factorial 682011 85400 PM 2 X 2 ANOVA Arrest Record have you been arrested or not Desire to kill GPA Hypothesis 0 Arrest Record related to GPA o Desire to kill and your GPA 0 Interaction between desire to kill and arrest How your arrest record related to gpa independent or irrespective to your desire to kill it turns out that this effect is not statistically significant How your desire to kill related to gpa independent of arrest record it turns out that this effect is not statistically significant Interaction Main Effect two relations between our IV to our DV irrespective of the other IV Directions for SPSS univariate Repeated Measures ANOVA 682011 85400 PM must update spss to do analysis you must go to general linear model and pick repeated measures anova select the 4 kills and make it the within subjects factor within subjects factor of time use greenhouse geisser o APA Format 0 F18136163343 plt001 Linear contrast statistically significant people in there desire to kill goes down over time in a linear way which is to suggest that it looks like a line Quadratic a squared variable a bend statistical significant more or less our data has a bend to it a quadratic trend cubic function not statistical it looks like a wavy line so like Av don t use language of change difference or over time Contrasts will get you all your levels of factors of times that you want o Simple o Different o Repeated Mixed repeated measures ANOVA so just like above but add an interaction variable like sex how do males ad females differ from each other over time sex matters with respect for a particular time point like a factorial design but one of the variables now is a within subjects factor repeated measures must download the thing Factorial HW review 682011 85400 PM This is for the HW on factorial ANOVA s o in order to have a variable you need to have something that is varying so you need to have more than one level Statistical significance is a type of relation between variables The line called medication For the medication main effect is seemingly related to gpa irrespective of how depressed you are c The main effect of medication How to phrase an interaction c we would have a 41 percent chance of making a type I error if we claimed there was a statistical significance of a relation between medication and gpa with respect to levels of depression o differences in GPA39s in medicated and non medicated people When doing multiple ttests you must create a new alpha level of that 05 divided by the number of tests you do Statistically significant relation between medication and gpa for those people who are severely depressed

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