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# Fishing Rod Experiment

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

## Description

The data was collected by Peter Drew and Matt Seidemann, statistics students at the Queensland University of Technology, in a subject taught by Dr Margaret Mackisack. Here is their description of the data and its collection:

"As keen fishermen out and about on a fairly regular basis, the common arguments arise between anglers on the best rigging set up for various conditions. We decided that upon our next group outing that we would back up our opinions with hard statistical facts. Our interest led us to test the most obvious variables in the fishing rig.

"Of interest were firstly the rod length, as between fisherman there always tends to be a variety of rods of different sizes; secondly the type of line, in that the larger the line it would be logical that the weight would increase; thirdly the sinker weight and how it affected the casting distance.

"In deciding on the three variables a 2^3 factorial design seemed obvious and for our purposes seemed to be quite adequate. So the question was placed as to whether or not the above variables in any combination made any difference to the overall distance the line was cast. The rods used were 6ft and 7ft two piece boat rods, fitted with the same type of spinning reel. The variable sinkers were 8oz and 12oz round ball sinkers and the line used was either the 1kg or 2kg line of the same make.

"The experiment was carried out on a day that was close to windless thus lowering the relative influence of the wind. The series of casts was conducted by the same person as were the measurements thus giving uniformity to the total experiment. A break of five minutes was timed between casts so as to allow the caster to allocate the same amount of energy to each cast. The rods were not rigged by the caster; a rigger would set the rod up with a combination of sinker, line and rod, and an effort was made to keep the caster oblivious to the changes in the rig.

"The experiment was conducted on the rugby ovals on Oleria St, Brookside (a western surburb of Brisbane) adjacent to the RSL (Returned Serviceman League club), which for all intents and purposes would be classified as a level surface. A line was placed at one end of the field and from it the caster would cast the rod as he would given normal fishing conditions. A spotter who was also the measurer would mark the point of impact of the sinker and from it measure back to the line from which it was cast. The distance observed was subsequently rounded up to the nearest 0.5 of a metre. Two runs were made of each combination.

"Possible improvements: Because of the time the rigging took, both casts with each rig were done at the same time. If we did it again it would be better to use random numbers to decide the order of all sixteen casts."

```Data Codes:
Rod           6ft   1
7ft   2
Line          1kg   1
2kg   2
Sinker        8oz   1
12oz   2
Distance     Distance line cast in metres
Order        Order in which observations were recorded```

Data file (tab-delimited text)

## Source

Mackisack, M. S. (1994). What is the use of experiments conducted by statistics students? Journal of Statistics Education, 2, no 1.

## Analysis

• Two-way interaction between sinker and line.
• Discernible learning effect of observations versus order.
``` Factor   Levels Values
rod           2     1     2
line          2     1     2
sinker        2     1     2

Analysis of Variance for distance

rod                1     95.063     95.063     95.063   78.00  0.000
line               1      3.063      3.063      3.063    2.51  0.152
sinker             1     90.250     90.250     90.250   74.05  0.000
rod*line           1      1.563      1.563      1.563    1.28  0.290
rod*sinker         1      4.000      4.000      4.000    3.28  0.108
line*sinker        1     36.000     36.000     36.000   29.54  0.000
rod*line*sinker    1      0.250      0.250      0.250    0.21  0.663
Error              8      9.750      9.750      1.219
Total             15    239.937```

There is a big difference between the two rods (37.625m vs 32.75m average cast for 7ft and 6ft rods), and a similar difference between sinkers, casting further with heavier sinker. There is also a considerable interaction between the sinker weight and line weight, the best casts being made with heavy sinker and lighter line, and the worst casts with the light sinker on the light line, as summarized in the following table.

```Sinker    12oz     8oz    Both
Line
2kg     35.625  33.875  34.750
1kg     39.500  31.750  35.625
Both    37.563  32,813  35.187```