Analysis of Variance with Repeated Measures

Repeated Measurements: Within Subjects Factors Repeated measurements on a subject are called within subjects factors. Example: Strength was measured pre, 8 weeks, 16 weeks and 24 weeks. Strength is a within subjects factor with 4 levels (pre, 8, 16, 24). Subjects rode for 15 minutes, divided into five 3-minute periods for the purpose of collecting data. Data were collected on the number of balance errors during the last minute of each 3- minute period, and resistance was increased at the end of each 3-minute period. In this design, the dependent variable is balance errors and the independent variable is increase in resistance (fatigue).

Advantages of Repeated Measures over Independent Groups ANOVA In repeated measures subjects serve as their own controls. Differences in means must be due to: the treatment the treatment variations within subjects variations within subjects error (unexplained variation) error (unexplained variation) Repeated measures designs are more powerful than independent groups designs.

Roller Ergometer Data. Within Subjects Factor with 5 levels (3, 6, 9, 12, 15 min)

Repeated Measures ANOVA Summary Table How is the F ratio of computed? How are the Mean Squares computed? Does fatigue effect balance? If so, which means are different?

Post hoc comparisons

Repeated Measures ANOVA: Data Entry Each level of a within subjects factor is entered as a separate variable. Fatigue (3, 6, 9, 12, 15 min)

Repeated Measures ANOVA

Name and Define the Within Subjects Factors Click Add to enter each within subjects factor.

Click Define to define both Within and Between Subjects Factors.

Defining Within & Between Subjects Factors Within Subjects Factors Between Subjects Factors (Gender)

Repeated Measures Options

SPSS Output General Linear Model

Repeated Measure ANOVA Assumptions: Sphericity? Mauchly’s Test of Sphericity indicated that sphericity was violated [ W(9) =27.59, p =.001 You don’t want this to be significant. Since Sphericity is violated, we must use either the G-G or H-F adjusted ANOVAs

SPSS Output: Within Subjects Factors If Sphericity was okay then the statistics would be F(4,36) = 18.36, p =.000, power = But since Sphericity was violated we use the adjusted values: F(1.485,13.367) = 18.36, p =.000, power =.995, effect size or partial η2 =.67 Which means are significantly different? What is the difference between this power (post hoc) and an a priori power analysis?

SPSS Output: Between Subjects Effects If we had a between subjects factor like Gender, the ANOVA results would be printed here.

SPSS Output: Effect Size & Confidence Intervals

Post hoc Tests for Main Effects (Treatment means) 4 (12 min) is diff from: 1,2,3 (3,6,9 min) 5 (15 min) is diff from: 1,2,3 (3,6,9 min)

Excel Spreadsheet of Means & sds Minutes of Exercise Balance Errorssd Post hoc: 3, 6 & 9 minutes are significantly different from 12 minutes; 3, 6 & 9 minutes are significantly different from 15 minutes.