Class 23: Thursday, Dec. 2nd. Today: One-way analysis of variance, multiple comparisons. Next week: Two-way analysis of variance. I will e-mail the final homework, Homework 9, to you this weekend.
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(1) Proximity vs. Remote; (2) Proximity vs. Touch-Proximity; (3) Proximity vs. Voice-Feedback; (4) Remote vs. Touch-Proximity; (5) Remote vs. Voice-Feedback; (6) Touch-Proximity vs. Voice-Feedback
that the group means are the same is rejected using the Tukey HSD procedure, which
controls the familywise Type I error rate at 0.05. A confidence interval for the difference
in group means that adjusts for multiple comparisons is shown in the third and fourth
Strong evidence that the group mean voltage squared levels are not all the same.
Strong evidence that remote has higher mean voltage squared level than proximity
and touch-proximity and that voice-feedback has higher mean voltage squared level
than touch-proximity, taking into account the multiple comparisons.
Constant variance is reasonable – (Largest standard deviation/smallest standard
deviation)^2=(1.79/1.48)^2=1.46. There are less than 30 observations per group
so we need to check normality but a check of the normal quantile plot for each
group indicates that normality is OK.
Test of H_0: Mean of all five videotapes is the same vs. H_A: At least two of the
videotapes have different means has p-value 0.0301. Evidence that there is some
difference in the means of the videotapes.
The only conclusion we can make about how the videotapes compare, taking
account of the fact that we are making multiple comparisons, is that
Crutches has a higher mean than Hearing.