1 Chi-square & T-test Comm Fall 2007 Nan Yu

2 Warming up Please download practice 1, practice 1 answer, ChisquareData, Ttestdata Use ChisquareData to complete the questions of practice 1.

3 Effect Sizes  Statistical Significance vs. Strength of Effect Strength of Effect: 0 to 1 0 = Least Effect 1 = Maximum Effect

4 Strength of Association for Chi-Squares: Cramér’s V

5 Effect size for Chi-square

6 Influence of Sample Size on Statistical Significance (p-value) versus Strength of Association (Cramer ’ s V)  Sample size will not affect the strength of association, only significance level.

7 Vote Yes No Yes No Organizations Chi-Square Value = 1.72 Degrees of Freedom = 1 Significant? No, p =.19 Cramér’s V =.17 Chi-Square Value = Degrees of Freedom = 1 Significant? Yes, p <.001 Cramér’s V =.17 Yes No Organizations Vote YesNo Note: The number in each cell is mean.

8 Run Chi-square to test the following question People from different race will have a different opinion on the selection of countries that represent a great danger to the U.S.. (race, q36). Chi-Square:_17.46_ DF _5_ p _<.01_ Cramer’s V: _.44_

9 The Chi-square test showed that people from different race have a different opinion on the selection of countries that represent a great danger to the U.S.,  2 (6, N=45) = 17.46, p<.01, Cramer’s V=.44.

10 T-test: Testing Differences in Means

11 I. The Issue of Variability withinbetween Variability within Groups Variability between Groups mean 1 mean 2

12 Different Groups:  Large Between-Group Variability  Small Within-Group Variability Similar Groups:  Small Between-Group Variability  Large Within-Group Variability

13 Which one represents similar groups?

14 Independent Sample t-test Independent Sample t-test is used to test differences between only 2 groups. Ex. Female test scores will differ from male test scores.

15 T-test assumptions IV is nominal and has two categories DV is interval/ratio DV is normally distributed. T-test will robust with larger samples Cases represent a random sample (representative). Cases are independent of one another.

16 Example: Males likes TV sports more than females Put the interval or ratio-level variable here. (DV) Put the variable representing the groups here. (IV) Click “Define Groups" IV? DV?

17 Define your groups by the values. In this case, it is “0” for males and “1” for females.

18 Compare the means. T-test statistic Degrees of freedomp-value

19 T-test statistic Degrees of freedom p-value Are these two groups similar or different (within-group) ? If p >.05, means they are similar, use the top row If p<.05, means they are different, use the bottom row.

20 Report: Males (M=3.04, SD=1.89) do like TV sports more than females (M=1.97, SD=.88), t(34)=2.66, p<.05. T-test statistic Degrees of freedomp-value

21 - Paired Sample t-test is used to test differences between 2 scores. - Variables must be interval or ratio-level and measured on the same metric. Ex. Aggression scores will be higher after viewing a violent film than before viewing a violent film. Variables: Before Film Stimulus After - Here, IV has only one level, but there are two DVs: before aggression, after aggression Paired Sample t-test

22 Paired Sample t-test Place your “before” and “after” variables here.

23 T-test statistic Degree of freedomP-value Report: Aggression scores after viewing the film (M=3.95, SD=.96) were significantly higher than were scores prior to viewing the film (M=2.55, SD=1.11), t(57)=6.89, p<.001.

24 Directional and non-directional hypotheses Females and males have different levels of liking toward dramas. Females likes to watch dramas more males. Liking toward dramas will be different as a result of gender. Which one is a directional hypothesis?

25 One-tailed or two-tailed test Non-directional hypothesis: one-tailed test Directional hypothesis: two-tailed test

26 Probability Distribution 95% of chances that we found the two means are different. 5% of chances that didn’t found the difference. Females and males have different levels of liking toward sitcom. Mean of females is not equal to mean of males

27 Two-tailed tests—split the alpha Females likes to watch sitcom more males. Mean of females > Mean of males 2.5% of chances that didn’t found means of females is higher than that of males. 2.5% of chances that didn’t found means of females is lower than that of males.

28 In-class practice 1 (Ttestdata.sav) H1: Males likes to watch TV reality crime more than females. (gender, tvrcrime) Please use t-test to test the H1 and answer the following questions: Males: Mean _____ SD _____ Females: Mean______ SD ______ t(__)=____, p______ Can we reject the null here?

29 Answers to practice 1 Males: Mean _2.58_ SD _1.17_ Females: Mean _3.32_ SD _1.49_ t(_55_)=_2.11_, p_<.05_ Can we reject the null here? No. We proposed males > females, but we found males < females

30 In-class practice 2 H2: Happiness scores will be higher after viewing a sad film than before viewing a sad film. Please use t-test to test the H2 and answer the following questions: Before: Mean _____ SD _____ After: Mean______ SD ______ t(__)=____, p______ Can we reject the null here?

31 Answers to practice 2 Before: Mean _2.53_ SD _1.13_ After: Mean _4.02_ SD _.83_ t(_57_)=_-7.70_, p_<.001_ Can we reject the null here? Yes