PSYCH 311 1nd Edition Exam 4 Study Guide Lectures 19 24 Lecture 19 November 12 What is the difference between a test and a design A design is when you have two or more variables that exist naturally and are measured and recorded for each individual A design is created with the intent of determining if there is a relationship between the variables but does not determine cause and effect A test on the other hand is a hypothesis test that yields a Pearson Correlation Coefficient r It is a numerical value that describes the relationship between the variables by providing the direction of the relationship how the variables are related positive correlation means variables change in same direction negative means variables change in opposite directions and the strength of the relationship how closely related the variables are closer the value to 1 00 the stronger the relationship What is the Pearson Correlation Coefficient r The Pearson Correlation Coefficient is a statistical method used to measure and describe the relationship between the two variables The variables will covary or vary together when the variables consistently change together in strength and direction Formulas Sum of Products of Deviations SP SP X Mx Y My measures covariability Sum of the Squared Deviations SS SS x M 2 measures variability for single variable Pearsons Correlation Coefficient r r x Mx y My SSx SSy or r SP SSx SSy numerator the extent to which the variables covary carries sign denominator the extent to which the variables vary independently Lecture 20 November 14 Mapping onto Generic Test Stat Formula A test is the observed or obtained difference due to the IV difference due to SE The r test and test have same logic but with different wording An r test is an observed or obtained relationship naturally occurring variability in each variable When r 0 then x and y are not related the closer r is to 0 the more likely we are to FTR our Ho If every change is x is accompanied by a consistent change in y then the variability in x is completely shared with y therefore the numerator and denominator measure the same thing What is the Coefficient of Determination r 2 The Coefficient of Determination r 2 is the effect size measure for r It specifies the degree of overlap between the two variables Effect size Small 0 01 r 2 0 09 Medium 0 09 r 2 0 25 Large r 2 0 25 Steps for doing a Hypothesis Test using r Step 1 State hypothesis and set Step 2 Set critical level reference comparison distribution Distribution of Covariance Step 3 Collect data and compute r Step 4 Make decision Step 5 Compute effect size Lecture 21 November 19 What is ANOVA ANOVA is Analysis of Variance Its purpose is to detect systematic variance numerator and disregard unsystematic variance denominator ANOVA is comparing the variability between groups systematic against the variability within groups average of unsystematic The difference between groups gives insight to whether our IV had an effect while the spread of scores determines if there are differences within groups The most important thing is to detect between group variance and to minimize within group variance minimize SE What are the different types of ANOVA A One Way ANOVA is used for an independent sample design design with separate samples You use this when you have one independent variable with two or more levels separate groups or conditions A Repeated Measures ANOVA is used when you have one IV with two or more levels measure sample two or more times A Two Way Factorial ANOVA is when you re evaluating two IV s each with two or more levels What is F and how do you interpret it F is test used when measuring ANOVA s You can differentiate a F test from a t test because Ftests have two or more levels The value you get for F is interpreted the same way no matter ANOVA test is being used F between group variance within group variance OR F systematic variance unsystematic variance Type I Error Rate Type II Error Rate 1 1 c c of comparisons The larger c is the more inflation there is in our Type I Error Rate ANOVA allows you to make the comparisons while keeping Type I Error Rate at What is the reference distribution for ANOVA The reference distribution for ANOVA or F distribution is a positively skewed distribution that extends from 0 00 to with the highest point at 1 00 It is impossible to have a negative f value since you square the values and therefore can never have a negative variance If F 1 00 then between group variance and within group variance measures the same thing then there is no systematic variance IV didn t have an affect In order to reject Ho you need F 1 00 The larger the test statistic the more likely you are to reject your Ho Lecture 22 November 21 Steps for computing a One Way ANOVA Step 1 State hypothesis and set Step 2 Find our critical region Step 3 Collect data and compute F test statistic Step 4 Make a decision Step 5 Calculate effect size Step 6 Post hoc test Lecture 23 December 3 What happens if you change the values for M2 or SS in a One Way ANOVA Remember F between group variance within group variance F MSbt MSwi wi average of the 2 variances bt difference between means If you increase the value for M2 then the between group variance numerator will increase therefore causing the SSbt and F value to increase as well If you decrease the SS value then SSwi denominator will decrease as well causing the F value to increase Repeated Measures ANOVA vs One Way ANOVA and Parsings You use a Repeated Measures ANOVA when you measure the same group two or more times The basic logic behind a Repeated Measures ANOVA is the same as the logic behind a One Way ANOVA although it differs in that there is a second parsing of variance in a Repeated Measures ANOVA First Parsing occurs in both One Way and Repeated Measures ANOVA s The total variance is split into the BTG between groups variance IV without ID s and WIG within groups variance the SE Second Parsing occurs only within Repeated Measures ANOVA s The WIG is then split into the BTS between subjects variance with ID s is removed using the test and Error Variance remaining SE becomes denominator after we remove BTS What are the ID s in a Repeated Measures ANOVA and how do we fix them The ID s individual differences are the characteristics the individuals bring to the group Although by using the same group multiple times the design ultimately eliminates the individual differences from the between group variances while the test