PSYCH 210 1st EditionFinal Exam Study Guide Lectures: 18 - 26Chapter 12 (Introduction to ANOVA; Between-subjects ANOVA)- What primary advantage do ANOVAs have over t-tests, in terms of flexibility of experimental design?-ANOVA allows for any number of experimental groups; specifically, it allows for 2 or more (whereas previously we only had the capability for a maximum of 2 Treatment (Tx) groups using Independent-sample t or Related-samples t) - What types of research designs are tested with between-subjects (i.e., single-factor, independent-measures) ANOVAs?-More than 2 Tx groups-Different Participants in each group- Understand how to set up hypotheses for a between-subjects ANOVA; why is the H1 stated as “not H0”?-H0: μ1=μ2=μ3=μetc- H1: Not H0-It is too complicated to explain H1 in statistical notation because there are many possible ways (and patterns) with which H0 can be untrue- Why does ANOVA use variances, instead of differences between means, to determine significant effects?-For ANOVA, we want to compare two or more sample means. With more than two samples, the concept of “difference between sample means” becomes difficult to measure.- Suppose you want to look at the effect of an independent variable that has five conditions. Why should you use ANOVA to analyze the data (that is, why should you not simply run lots of individual t-tests to compare the conditions)?- If you ran many individual t-tests, the experimentwise alpha would be far too large (violating rules of statistics) because the Testwise alpha is additive- What is the difference between ‘between-group’ variance and ‘within-group’ variance?- Between: Intergroup Variability; why do participants in one group get different scores than in another group?- Within: Intragroup variability; why do participants in the same group get different scores?- What are the components of ‘between-group’ variance?- Treatment Effect- Individual Differences- Chance (Error)- What are the components of ‘within-group’ variance?-Individual Differences-Chance (Error)- How does the F-ratio compare the different types of variance mentioned above? Understand how variance is ‘partitioned’ into different pieces by the ANOVA analysis.-F = MS Between/MS Within = Between-groups variance/Within-groups variance-F = [Tx+Indv Diff+Error]/[Indv Diff+Error]- Understand how to use the notation and formulas for ANOVA calculations (e.g., T, k, G, etc.)-T = Column total (Σx for each individual condition/group)-k = number of treatments/conditions-G = Grand sum of x (or sum of all the T values)- N = total number of participants (or observations, in within-subjects)- n = number of individuals in individual groups- Be able to calculate a between-subjects ANOVA, including the usual hypothesis testing steps. This includes: How to calculate sums of squares (SS) for each type of varianceo See formula sheet How to find degrees of freedom (df) for each type of varianceo Formula sheet How to find mean squares values used in the final F-ratioo MS=SS/dfo F= MSbtwn/MSwithin How to use the F-table to determine critical values of Fo df numerator = dfbtwno df denominator = dfwithin (or error, for within-subjects)- Be able to summarize the results of an ANOVA in words- State result of overall ANOVA, including F-statement- Template: Say that there were significant differences in the DV according to levels of the IV- State result of Tukey test, including means for all conditions, and the ‘significance status’for all pairwise comparisons- Describe pattern of Means- How do you summarize ANOVA results in a source table?-Fill in Values for SS, df, MS, Fobs and Fcrit for Between, Within- What are post-hoc tests, and when are they needed?-Compares all possible pairs of means to determine whether each pair is significantly different-Used when the F is significant -Determine specifically what pattern is occurring- Understand how to calculate a Tukey test, and how to translate the results of a Tukey relative to a hypothesis.-Tukey crit = qt√MSerror/n-For qt use table-Tukey crit value = minimum difference between means that must be met, or exceeded, in order for a particular mean difference to reach significance- What is the relationship between ANOVA and t-tests? How is the t-ratio related to the F-ratio?-t = [Actual difference btwn Ms]/[Differences expected by chance]-F = [Variability across groups]/[Variability within groups]- What are the assumptions for a between-subjects ANOVA?-Homogeneity of Variance-Normal Distribution-Interval or ratio data-Independent ObservationsChapter 13 (Within-subjects ANOVA or Repeated-measures ANOVA)- How does a within-subjects ANOVA differ from a between-subjects ANOVA?-Participants are the same in each condition (whereas in Between-subjects, different individuals were used for each group- How does the F-ratio for a within-subjects ANOVA change, relative to a between-subjects ANOVA?-Denominator changes from MSwithin to MSerror because MSindividual differences is removed, since the same people are used-Individual differences within groups still exist, but can be measured and mathematically removed- How is the concept of individual differences important to understanding how within-subjects ANOVA works?- Individual differences refer to participant characteristics such as age, personality, and gender that vary from one person to another and may influence the measurements that you obtain for each person- What are the components of between-groups variance for a within-subjects ANOVA?-Tx effect and Error- What are the components of within-groups variance?-Error and Individual Differences-Individual Differences removed mathematically for Within-Subjects Design- Why do you have to compute five sources of variance for within-subjects ANOVA (vs. three sources for between-subjects)? What do the two new sources add to your analysis?-Calculating error and Individual differences allows us to mathematically remove Individual differences so that the denominator of F-ratio is smaller (only MSerror)- Understand the notation and formulas for a within-subjects ANOVA-N= total number of observations (not participants)- Understand how to calculate a within-subjects ANOVA, including the usual hypothesis testing steps- Understand how to calculate a Tukey post-hoc test for a