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# Time to Swim 25m

Keywords: Three-Way Analysis of Variance, Interaction, Experimental Design, Learning Effect.

## Description

This experiment was conducted by Kim Horsfall, Sue Hall and Simone Golik, statistics students at the Queensland University of Technology in a subject taught by Dr Margaret Mackisack. The students designed and conducted an experiment to determine the factors affecting the time to swim one lap of a 25m pool.

The experiment was inspired by the subtropical climate of Brisbane, which makes swimming a popular activity to experiment with in late Spring. (The swimming pool is also immediately adjacent to the building which houses the School of Mathematics.) The students who carried out one swimming experiment used a friend to actually do the swimming, measuring her time to swim one lap as the response, and included as additional information in their report a note from the swimmer explaining her view of the experience:

``The first thing I remember is trying to concentrate on a set rhythm more than anything else as I was looking to keep the lap times as consistent as possible. On the first lap I shot out of the gate and suddenly realised that I would be doing a number of laps and I needed to concentrate on rhythm rather than speed. As the laps continued I slowly began to realise that I was getting more tired. At about lap 20 I took a break for a couple of minutes as I felt that I had reached the stage where it would begin to affect the lap times.

``When I was swimming without the goggles I found it more difficult to swim straight and would occasionally bump into things (lane rope, people). It mostly felt as thought I was going slower when swimming from the shallow to the deep end. After taking the flippers off, the first few kick beats felt funny.''

Armed with this information, and the data about order of runs and which end of the pool they were made from, students can be asked to consider revising the design of the experiment, taking the end of pool into account and possibly breaking the runs up into blocks to minimise the tiredness effect. The role of serial correlation can be investigated, and the effect of incorporating time as an extra covariate.

```Data codes:
Wearing flippers     Yes/No  1/0
Wearing goggles      Yes/No  1/0
Wearing shirt        Yes/No  1/0
Start from deep end  Yes/No  1/0

Order   Time  Shirt  Goggles  Flippers  End
5      16.55    1       1         1      0
12     17.22    1       1         1      1
18     17.70    1       1         1      1
9      21.53    1       1         0      0
14     22.49    1       1         0      1
17     22.50    1       1         0      0
7      17.77    1       0         1      0
11     17.43    1       0         1      0
21     18.70    1       0         1      0
2      23.78    1       0         0      1
19     24.29    1       0         0      0
22     24.89    1       0         0      1
4      16.14    0       1         1      1
20     16.39    0       1         1      1
24     16.40    0       1         1      1
1      19.97    0       1         0      0
3      19.95    0       1         0      0
6      20.32    0       1         0      1
10     16.85    0       0         1      1
13     17.80    0       0         1      0
15     16.81    0       0         1      0
8      22.63    0       0         0      1
16     22.81    0       0         0      1
23     22.31    0       0         0      0```