Keywords: Three-Way Analysis of Variance, Interaction, Experimental Design, Learning Effect.
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)
Mackisack, M. S. (1994). What is the use of experiments conducted by statistics students? Journal of Statistics Education, 2, no 1.
Factor Levels Values rod 2 1 2 line 2 1 2 sinker 2 1 2 Analysis of Variance for distance Source DF Seq SS Adj SS Adj MS F P 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