Chapter 8 and Chapter 13

1. Chapter 8 and Chapter 13 T-test and Chi-Square

2. Research Paper • Double space ENTIRE paper • Number EVERY page in upper right • Cover page with title and your name • One page introduction to your topic • Lit review of at least 10 journal articles • At least 10 pages of lit review text • Describe each study and statistics briefly • One page summary of your topic • References on separate page, numbered and alphabetized by author’s last name • Refer to each article in the paper by number ONLY

3. Comparing Means (2 types) • Compare means of two samples (are the mean scores different) • Test for equal variances (Levene’s test) • Compare two differentgroups on the same test • Compare samegroup on same test performed twice

4. t-test • PURPOSE: Difference between means • Independent samples t-test • Dependent samples t-test (paired samples t-test) • Independent t-test when group 1 are different people than group 2 • Dependent t-test when same group is measured twice

5. t-test cont… • Independent is a between subjects test • Dependent is a within subjects test • Only two groups can be measured • Are the mean scores different? • Compares actual mean difference with expected mean difference • Expected mean difference = SEMdiff

6. T Test • Used to determine if 2 mean values are significantly different. • General formula:

7. t-tests cont… • t-statistic compared to critical values (pg 263) • Degrees of freedom-values free to change (n-1) • P-value & alpha determine significance • Significant: it did not happen by chance (rare)

8. Conclusion Statement • t-test conclusion statements • Use variable names • Past tense • Significant • p-value or Alpha • Direction • Males were significantly (p<0.05) taller than females. • Height between groups was not different.

9. Degrees of Freedom • Determines the critical value of a test statistic. If calculated value > critical value then reject HO. • “the number of observations less the number of restrictions placed on them”. • If sum = 150, and there are 10 scores that make up the sum, and 9 of those scores = 125, what is the 10th number? How do you know this?

10. Hypothesis Testing • General • Assess the probability that a sample mean differs from another sample mean due to chance alone (sampling error or SEM). • Test null hypothesis that mean1 = mean2. Even if HO is true, there should be some differences between mean1 and mean2 just due to chance (sampling error or SEM). If differences are too large to be due to chance alone then reject HO and accept HA.

11. Hypothesis Testing • Alpha () – level of probability needed to reject HO; usually set at .05. • p value – from computer; the probability that you could have gotten the data that you have if HO is true. • If p < , then reject HO.

12. Hypothesis Testing Truth Table for Null Hypothesis:

13. Hypothesis Testing • Tails – where to put the region of rejection? • Two-tailed test: hypothesis is non-directional, i.e., we make no claim that one condition is better then another, only that they are different; 50% of  goes in each tail. • One-tailed test: hypothesis is directional, i.e., we test that one condition is better then the other; all of goes in one end of the distribution.

15. If HO is false, then the population distributions for PT and PA students on IQ might look like this, i.e., PT and PA students do not come from the same population in terms of IQ.

16. Hypothesis Testing •  = probability of making a Type I error (if HO is true). • If HO is true, just due to chance, we could get values that fall in the region of rejection. • The probability of this happening (if HO is true) = . • Type I error – incorrectly rejecting HO, when HO is true. • Type II error – incorrectly accepting HO when HO is false. •  = probability of making a Type II error when HO is false. • Power = probability of rejecting HO when HO is false.

19. T Test • Misc T test information • Sample size  n then  denominator of t therefore  power • Effect size  mean difference then  t • Variance  group variance then  t which  power • Within - dependent t is more powerful due to less variance • t = true variance/error variance • If HO is true, t = 1. • If calculated t > critical t then reject HO • If p <  then reject HO.

20. Nonparametric Statistics • Tend to be less powerful than parametric statistics. • Common Tests: • Chi-Square • Mann-Whitney U Test • Kolmorgorov-Smirnov Test • Spearman’s Rho (correlation) • McNemar Change Test • Sign Test • Binomial Test

21. Nonparametric Statistics • Chi-Square (2)Test • PURPOSE: Used to analyze data in situations where one wishes to test whether the observed number of responses in a category differs from the expected number that fall in that category. • Dependent Variable is nominal. • It is a bean count of the number of values in different categories. • H0 expects them to be equal

22. Where k = # of categories, Oi = observed number of cases in each category, Ei = expected number of cases in each category. • When Ho is true, Oi  Ei and 2 will be small. If Ho is false, then Oi  Ei and 2 will be large. • Simple and complex – one variable or multiple variables

23. Next Class • SPSS practice • No class next week due to Holiday • Test 2

24. Homework • Paired samples on remaining selected variables w/conclusion statement • Independent test on all variables by nominal variable w/conclusion statements for each • Simple chi-square on group w/conclusion statement • Complex chi-square on sex by group