Statistics for Education Research Lecture 8 Tests on Three or More Means with Repeated Measures: One-Way ANOVA with Repeated Measures Instructor: Dr. Tung-hsien He

General Linear Models (GLM) with Repeated Measures General Linear Models (GLM) with Repeated Measures 1. GLM with Repeated Measures are used to test 3 or more related means on a single dependent variable when a measure is used repeatedly or considered to be used repeatedly (i.e., when a measure tests 3 or more levels of a single dependent variable).

2. Two Conditions for Repeated Measures: a. The same measure is applied to the same sample for 3 or more than 3 times to measure a single dependent variable. Note: If the same measure is repeated for only two times, then paired-sample t tests will be used to test these paired means (e.g., pretest vs. posttest).

b. A measure is applied to a sample for only one time, but the measure tests 3 or more levels of a dependent variable (e.g., achievement goals can be classified into three types of goals: mastery goals, performance goals, and avoidance goals). Note: (1) If the measure tests 2 levels of a single dependent variable, then paired-sample t tests will be used to test the paired means (e.g., a foreign language learning anxiety scale tests communication anxiety and test anxiety).

(2) The maximum scores for all of these different levels (either 2 levels or more than 2 levels) must be close enough to each other or one another; otherwise, the variance-covariance will NOT be equal, and Ho will be rejected easily.

(3) The assumption of the equality of variance- covariance (or termed as Sphericity) is important for Condition 2. E.g., provided a scale measures 3 levels, the maximum score for Level 1 is 100, for Level 2 is 10,000, and for Level 3 is ,000. In this situation, the three related means do not need to be tested because they will be significantly different. But, these significant differences come from the inherited huge differences in the scale, not really from within-subject or between-subject differences.

(4) To test whether Sphericity is confirmed or not, Mauchly’s test is used. A significant Mauchly’s W means the violation of Sphericity. Thus, a nonsignificant Mauchly’s W is favored since it confirms the assumption of Sphericity. 5. What happens when Sphericity is violated? Reporting the following two tests (SPSS reports both tests in the output): a. Using Geisser-Greenhouse Test Values b. Using Huyn-Feldt Test Values

3. Types: a. GLM with repeated measures are conceptualized as “ANOVA” since 3 or more means are tested, although these means are related means. b. Use Conditions for One-Way ANOVA with Repeated Measures: (1) One Sample (2) One dependent variable that has at least 3 levels or (3) One dependent variable is tested for at least 3 times.

(c) One-Way Mixed ANOVA with Repeated Measures: Two groups, females vs. males, are tested by a reading comprehension test for three times. (d) Two-Way Mixed ANOVA with Repeated Measures: Two groups, females vs. males, are tested by an anxiety scale that has 3 levels for two times. (two independent variables will be: gender & points in time for testing)

4. Example: (1) Scenario: In a study that focuses on the effects of Phonics instruction on reading comprehension, the researcher randomly select 35 subjects from the population as a sample. Then phonics instruction is given to these subjects. After 4 weeks, the researcher tests this sample’s three levels of reading comprehension: (a) word recognition, (b) phrase comprehension, and (c) sentence comprehension. (1) Scenario: In a study that focuses on the effects of Phonics instruction on reading comprehension, the researcher randomly select 35 subjects from the population as a sample. Then phonics instruction is given to these subjects. After 4 weeks, the researcher tests this sample’s three levels of reading comprehension: (a) word recognition, (b) phrase comprehension, and (c) sentence comprehension.

The test has 6 items and each item occupies 5 points (maximum score is 30). Item1 and item2 are used to test word recognition, whereas item3 and item4 are to test phrase comprehension. Item5 and item6 test sentence comprehension. The researcher wants to know: (a) whether the instruction will make significant effects on the three levels of the sample, and (2) on which levels does the sample perform better?

(2) Conditions: a. One sample b. One dependent variable has three levels.

(3) Hypothesis: H o : X level1 = X level2 = X level3 H a : X level1 ≠ X level2 ≠ X level3 (4) Technique: One-Way ANOVA with Repeated Measures. (5) SPSS Procedures: (6) Caution: Must check the assumption of Sphericity by using Mauchly’s test.