Keywords: Three-Way Analysis of Variance, Designed Experiment.
The data was collected by Grant Elliott, a statistics student at the Queensland University of Technology in a subject taught by Dr Margaret Mackisack. Here is his description of the data and its collection:
Living at a squash court spurred on the idea of this experiment. Frustrated playing squash one night, I thought that the squash ball I was playing with seemed to bounce and react differently to what I was previously used to. So I conducted this experiment on the squash ball, looking at the type of ball, temperature of the ball and the age of the ball.
Ball type: In this experiment I used a 'yellow dot' squash ball and a 'double x' squash ball. A 'yellow dot' is super slow and a 'double x' is termed extra super slow.
Temperature: When playing with a squash ball it tends to heat up. So I took it to extremes where I had 'room temperature' and 'playing temperature'. To duplicate 'playing temperature' the ball was placed in a cup of boiling water for 45 sec.
Age: I expected age to be my most significant factor. Squash balls, being a sealed ball, shouldn't vary when they get older, so I used a new ball and compared it to an old ball.
Procedure: I first thought of dropping the balls from a set height and seeing how far they bounced against a tape measure. This idea was scrapped as too much error came into it because you couldn't accurately measure when the maximum height of the bounce was. I then thought of a ball machine. I set the ball machine up and measured how far back did the ball come off the front wall when shot out of the ball machine. This eliminated a lot of varying in my figures as the ball machine shoots the balls out at roughly the same speed and trajectory. It doesn't take all the varying out as I wouldn't know whether the ball machine does shoot it out at exactly the same speed, but it keeps variation to a minimum.
Criticism: Measuring the distance from the wall was done by my friend and I. We both would watch from different angles and would see where the ball landed. This means our figures are probably out by a couple of centimetres. When the balls were dropped into the water I forgot to take some of them out after 45 sec. Also with some I moved them around in the water to get the heat distributed evenly but others I forgot to move as I was collecting and organising the next ball. Another criticism is the temperature of the water. I put new boiling water into the cup after 4 balls had been in it. Therefore the last ball to go in wouldn't be the same temperature as the first ball.
|Order||Order in which runs were conducted|
|Ball||Yellow dot (Yellow) or Double x (Double)|
|Temp||Room temp (Room) or Playing temp (Playing)|
|Age||New or Old|
|Distance||Distance bounced by the ball in cm|
Data file (tab-delimited text file)
Mackisack, M. S. (1994). What is the use of experiments conducted by statistics students? Journal of Statistics Education, 2, no 1.
The following table summarises the most interesting result of this experiment. There was a very strong temperature effect, and a noticeable interaction with ball type: the double-x balls go from being slower than the yellow dot, to being faster than the yellow dot, as temperature increases. There was also a significant age effect, new balls being faster. This experiment is a good illustration of a two-way interaction present when one of the main effects is not at all significant.
Temp Playing (-) Room (+) Both Ball Double-x (-) 664.50 475.25 569.87 Yellow-dot (+) 624.25 531.25 577.75 Both 644.37 503.25 573.81