1. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 1 Chapter 11 Testing for Differences Differences betweens groups or categories of the independent variable Statistical tests of difference reveal whether the differences observed are greater than differences that might occur by chance –Chi-square –t-test –ANOVA

2. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 2 Inferential Statistics Statistical test used to evaluate hypotheses and research questions Results of the sample assumed to hold true for the population if participants are –Normally distributed on the dependent variable –Randomly assigned to categories of the IV Caveats of application

3. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 3 Alternative and Null Hypotheses Inferential statistics test the likelihood that the alternative hypothesis is true and the null hypothesis is not Significance level of.05 is generally the criterion for this decision –If p .05, then alternative hypothesis accepted –If p >.05, then null hypothesis is retained

4. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 4 Degrees of Freedom Represented by df Specifies how many values vary within a statistical test Collecting data always carries error df help account for this error Rules for calculating df for each statistical test

5. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 5 Four Analytical Steps 1. Statistical test determines if a difference exists 2. Examine results to determine if the difference found is the one predicted 3. Is the difference significant? 4. Evaluate the process and procedures of collecting data

6. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 6 Chi-Square Represented as χ 2 Determines if differences among categories are statistically significant –Compares the observed frequency with the expected frequency –The greater the difference between observed and expected, the larger the χ 2 Data must be nominal or categorical

7. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 7 One-Dimensional Chi-Square Determines if differences in how cases are distributed across categories of one nominal variable are significant Significant χ 2 indicates that variation of frequency across categories did not occur by chance Does not indicate where the significant variation occurs – only that one exists

8. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 8 Example of One-Dimensional Chi-Square

9. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 9 Contingency Analysis Also known as two-way chi-square or two- dimensional chi-square Examines association between two nominal variables in relationship to one another –Columns represent frequencies of 1 st variable –Rows represent frequencies of 2 nd variable –Frequency of cases that satisfy conditions of both variables inserted into each cell

10. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 10 Example of Contingency Analysis

11. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 11 Limitations of Chi-Square Can only use nominal data variables Test may not be accurate –If observed frequency is zero in any cell, –If expected frequency is < 5 in any cell Cannot directly determine causal relationships

12. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 12 t-Test Represented by t Determines if differences between two groups of the independent variable on the dependent variable are significant –IV must be nominal data of two categories –DV must be continuous level data at interval or ratio level

13. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 13 Commons Forms of t-Test Independent sample t-test –Compares mean scores of IV for two different groups of people Paired comparison t-test –Compares mean scores of paired or matched IV scores from same participants

14. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 14 Types of t-Tests Two-tailed or nondirectional t-test –Hypothesis or research question indicates that a difference in either direction is acceptable One-tailed or directional t-test –Hypothesis or research question specifies the difference to be found

15. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 15 Limitations of t-Test Limited to differences of two groupings of one independent variable on one dependent variable Cannot examine complex communication phenomena

16. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 16 Analysis of Variance Referred to with acronym ANOVA Represented by F Compares the influence of two or more groups of IV on the DV One or more IVs can be tested –must be nominal –can be two or more categories DV must be continuous level data

17. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 17 ANOVA Basics Planned comparisons –Comparisons among groups indicated in the hypothesis Unplanned comparisons, or post hoc comparisons –Not predicted by hypothesis -- conducted after test reveals a significant ANOVA

18. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 18 ANOVA Basics Between-groups variance – differences between groupings of IV are large enough to distinguish themselves from one another Within-groups variance – variation among individuals within any category or grouping For significant ANOVA, between-groups variance is greater than within-groups variance

19. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 19 ANOVA Basics F is calculated to determine if differences between groups exist and if the differences are large enough to be significantly different A measure of how well the categories of the IV explain the variance in scores of the DV –The better the categories of the IV explain variation in the DV, the larger the F

20. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 20 ANOVA Design Features Between-subjects design –Each participant measured at only one level of only one condition Within-subject design –Each participant measured more than once, usually on different conditions –Also called repeated measures

21. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 21 One-Way ANOVA Tests for significant differences in DV based on categorical differences of one IV –One IV with at least two nominal categories –One continuous level DV Significant F –Difference between groups is larger than difference within groups

22. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 22 Two-Way ANOVA Determines relative contributions of each IV to the distribution of the DV –Two nominal IVs –One continuous level DV Can determine main effect of each IV Can determine interaction effect -- if there is a simultaneous influence of both IVs

23. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 23 Example of Two-Way ANOVA

24. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 24 Main and Interaction Effects Main Effect Unique contribution of each IV One IV influences scores on the DV and this effect is not influenced by other IV Interaction Effect One IV cannot be interpreted without acknowledging other IV If interaction effect exists, main effects are ignored

25. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 25 Factorial ANOVA Accommodates 3 or 4 IVs –Still determines main effects of each IV –Determines all possible interaction effects 3 x 2 x 2 ANOVA –First IV has 3 categories –Second IV has 2 categories –Third IV has 2 categories –1 DV

26. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 26 Limitations of ANOVA Restricted to testing IV of nominal or categorical data When 3 or more IVs used, can be difficult and confusing to interpret

27. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 27 Tests of Differences