Single Factor, Within-Subjects Analysis of Variance

1
Single Factor, Within-Subjects Analysis of
Variance
2
Repeated Measures

• 6.1 A researcher wishes to test the rate at
  which students learn a video game (Blasting
  Asteroids). Four students play three trials of
  the game of 2 min each. Number of asteroids
  destroyed is the dependent variable.

(a) Does the evidence indicate that performance
differs according to trial? (? .05) (b) If so,
which pair(s) of population means differ? (?
.05)
3
Interpretive Problem Encountered in a
Within-Subjects Design
Sources of variation in within subjects designs
Between groups variation reflects treatment
sampling error. Within groups variation reflects
blocks sampling error. The ratio of the two
values is ambiguous Solution remove variation
due to blocks from the denominator. Hence The
within-subjects ANOVA accomplishes this task.
Easily interpreted
4
Preliminary Calculations
5
Summary Table and Hypothesis Test
6
SPSS Information
7
Post hoc and a priori comparison strategies

• post hoc comparisons
• use Tukeys HSD
• same as in the single factor, between subjects
  case
• example in a moment
• planned comparisons
• use the a priori t-test strategy
• same as in the single factor, between subjects
  case

8
Tukeys Test on the Asteroid Data
Reject H0.