Keywords: repeated measures, three-way analysis of variance, non-parametric regression
"Discovery Day" is a day set aside by the United States Naval Postgraduate School in Monterey, California, to invite the general public into its laboratories. On Discovery Day, 21 October 1995, data on reaction time and hand-eye coordination were collected on 118 members of the public who visited the Human Systems Integration Laboratory. The age and sex of each subject were also recorded. Visitors were mostly in family groups.
One experiment which demonstrates motor learning and hand-eye coordination, is rotary pursuit tracking. The equipment used has a rotating disk with a 3/4" target spot. The subjects task is to maintain contact with the target spot with a metal wand. Trials were conducted for 15 seconds at a time, and the total contact time during the 15 seconds was recorded. Four trials were recorded for each of 108 subjects.
The target spot on the Circle tracker keeps constant speed in a circular path. The target spot on the Box tracker has varying speeds as it traverses the box, making the task potentially more difficult.
|Sex||Male (M) or female (F)|
|Age||Age of subject in years|
|Shape||Box or Circle|
|Trial1||Contact time for 1st trial|
|Trial2||Contact time for 2nd trial|
|Trial3||Contact time for 3rd trial|
|Trial4||Contact time for 4th trial|
Data File (tab-delimited text)
Data courtesy of Captain Frank Petho, Department of Operations Research, Naval Postgraduate School.
There was a marked learning pattern across the four trials. In general, the older the subject the better they did, but the oldest subjects had difficulty with the box tracker.
One can use this as an example of two-way or three-way analysis of variance and interaction by grouping age into categories and predicting the mean time for the four trials.
> A <- factor(cut(Age,breaks=c(0,7,11,20,30,40,60))) > m <- tapply(sqrt(Tracking),list(A,Shape),mean) > round(m,2) Box Circle 0+ thru 7 0.83 0.88 7+ thru 11 1.53 1.60 11+ thru 20 1.73 2.12 20+ thru 30 2.51 2.58 30+ thru 40 2.12 2.71 40+ thru 60 1.60 2.77 > lm.int <- lm(sqrt(Tracking)~A*Shape) > anova(lm.int) Analysis of Variance Table Response: sqrt(Tracking) Terms added sequentially (first to last) Df Sum of Sq Mean Sq F Value Pr(F) A 5 29.16828 5.833656 42.80114 0.000000000 Shape 1 2.47569 2.475694 18.16400 0.000047372 A:Shape 5 2.87454 0.574909 4.21807 0.001649232 Residuals 96 13.08449 0.136297