Journal of Statistics Education v.2, n.1 (1994)
Copyright (c) 1994 by Margaret Mackisack, all rights reserved. This text may be freely shared among individuals, but it may not be republished in any medium without express written consent from the author and advance notification of the editor.
Below are descriptions of six additional experiments conducted by students. The background information and descriptions of the designs were written by the students, the summary analyses by the author.
"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 centimeters. 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."
Data codes: Ball Yellow dot/Double x +/- Temp Room temp/Playing temp +/- Age New/old +/-
Order Ball Temp Age Distance (cm) 7 + + + 540 13 + + + 567 11 + + - 553 8 + + - 465 14 + - - 637 12 + - - 562 4 + - + 613 2 + - + 685 16 - + - 467 6 - + - 412 1 - + + 497 5 - + + 525 3 - - - 647 10 - - - 619 15 - - + 719 9 - - + 673
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
"The experiment conducted here was to test the effect certain factors such as refrigeration, stem length and water content have on the life of a rose. The outcome of such an experiment would prove to be extremely useful in the running of rose farms and florists.
"During the course of the experiment we jotted down the temperature for each day just in case we had to account for any particular pattern in the residual plots.
"One topic of particular interest was the length of time taken for the refrigerated roses to die. This took much longer than we anticipated, and due to time restrictions the roses had to be taken out of the refrigerator after 15 and a half days. By this time we knew in any case that there was an enormous difference between life in and out of refrigeration.
"Three factors, each consisting of two levels, are considered:
Stem length, 15cm or 25cm
Water content: tap water or tap water and citric acid (supposed to extend the life of cut flowers)
Refrigerated or at room temperature.
"The experiment was replicated so that 16 responses were obtained, the response variable being time (in days) taken for the rose to die.
"In order to remove biases from our results, caution should be taken to be consistent while conducting the experiment. The following were considered important points.
"We expected the rose to last longer if the stem was shorter as the water would not have as far to travel; and there is a smaller probability of the rose dying if the rose was in a citric acid solution rather than water according to the advice of the rose farmer, and also if the rose was refrigerated, as we noted most florists and rose farms do try to keep their roses in a cold room."
Data Codes: Refrigerated yes/no 1/2 Citric acid no/yes 1/2 Length 15cm/25cm 1/2 Days citric length refrig 6.5 1 2 2 23.0 1 1 1 11.0 1 1 2 9.5 2 1 2 9.5 2 1 2 23.5 2 1 1 24.0 1 2 1 21.5 2 2 1 10.0 2 2 2 23.5 2 1 1 11.0 1 1 2 9.0 1 2 2 22.0 1 2 1 24.0 1 1 1 21.5 2 2 1 8.0 2 2 2
There is the potential here to use the 'refrigerated' factor as a time-varying covariate for a more advanced analysis. However, if we accept that refrigeration does extend the life of roses and pool both temperature groups the results show that there is a difference in life due to stem length, in the expected direction, and that the citric acid appears to have no consistent effect, contrary to the rose-farmer's advice.
"When I was in Grade 7 at St Joseph's Primary School, North Ipswich, my two best friends and myself would usually have the same type of sandwiches each day:
Daniel Jones: Vegemite
Greg Smith: Peanut Butter
Myself: Ham and Pickles.
Dan, Greg and I would spend many a lunch hour discussing which of our sandwiches the meat ants preferred. We would carry out experiments by dropping a portion of our sandwich on the ground and then after a predetermined number of minutes we would count how many ants were on the sandwich. Eleven years later I have decided to reconstruct that experiment by using the meat ant hills situated in the park adjacent to my house.
"The experiment has been expanded somewhat, in the following manner:
Four types of bread: Rye, wholemeal, multi-grain and white;
Three types of filling: Vegemite, Peanut Butter, ham-and-pickles;
Each combination with or without Butter. "
In the park I counted 17 meat ant nests which were quite prominent. Of these seventeen, six were extremely similar in size. Out of the six I chose two which were almost identical and which had a distance of four metres between them. I wanted to do two replicates so in order to save time I used the two ant hills.
"I assigned one of my two sisters to each ant hill in order to carry out the experiment in a predetermined random fashion whilst I recorded the results. Each result was determined by the following steps:
"Criticism: Two results are large outliers. A reading of 97 was due to one of my sisters leaving a portion of sandwich behind from the previous observation (i.e., there were already ants there); and one of 2 was due to one of my sisters placing her portion too far away from the entrance to the hill. In one observation there were 67.5 ants recorded. This was due to my sister slicing one ant in half when placing the glass over the area in question. To maintain the credibility of my experiment I decided to include this half."
Data Codes Bread Type: Rye 1 Wholemeal 2 Multi-grain 3 White 4 Filling: Vegemite 1 Peanut Butter 2 Ham and Pickles 3 Butter: with butter 1 no butter -1 Bread Filling Butter Ant count Order 1 1 1 22 27 1 1 -1 18 10 1 2 1 27 45 1 2 -1 43 26 1 3 1 67.5 3 1 3 -1 44 39 2 1 1 57 17 2 1 -1 29 25 2 2 1 42 48 2 2 -1 59 35 2 3 1 58 6 2 3 -1 34 1 3 1 1 26 15 3 1 -1 42 44 3 2 1 60 24 3 2 -1 22 36 3 3 1 63 4 3 3 -1 36 32 4 1 1 2 42 4 1 -1 42 33 4 2 1 57 11 4 2 -1 24 34 4 3 1 66 37 4 3 -1 48 13 1 1 1 45 30 1 1 -1 31 14 1 2 1 50 29 1 2 -1 36 31 1 3 1 65 9 1 3 -1 54 20 2 1 1 42 40 2 1 -1 21 19 2 2 1 36 28 2 2 -1 47 38 2 3 1 97 43 2 3 -1 65 5 3 1 1 28 18 3 1 -1 38 21 3 2 1 47 2 3 2 -1 19 22 3 3 1 76 12 3 3 -1 59 8 4 1 1 40 46 4 1 -1 25 41 4 2 1 51 7 4 2 -1 21 16 4 3 1 59 47 4 3 -1 53 23
This experiment is a good basis for discussions about what to do with outliers, whether we can use Normal-theory analysis for these count data, and dealing with noise variation in experiments with animals.
The ants show a definite preference for ham-and-pickle sandwiches; having butter greatly increases the appeal of ham-and-pickle, slightly increases the appeal of peanut butter, and has little effect on the attractiveness of vegemite. The formal analysis is not very tidy, but the residual plots indicate that using the Normal distribution seems justifiable.
"As an avid movie-watcher, it is essential that not one minute of the movie is unseen. Therefore to replenish the popcorn bowl during commercial breaks it became essential to find the minimum course of action so as not to miss the movie. Thus an experiment was designed so as to enable us to find the method of making the maximum number of popcorns in a given time span.
"In particular we were interested in the effects of different oil substances used and the effect of these in different size pots. Three pots were chosen for the experiment, large (26.5cm in diameter), medium (22.5cm diameter) and small (18cm diameter). The diameters of the pots are all approximately equally spaced. We expected some amount of variability so the experiment was replicated 3 times. To minimise error the following procedures were carried out.
"To minimise any errors that might have occurred in heating each of the different size pots, a tablespoon of water was added to each pot and then heated until all of the water evaporated. This would approximately give the same temperature in each pot. Different hot plate sizes were matched to the appropriate sized pots, so as to ensure that the entire base of each pot was in contact with uniform heat. The hotplates were set to the highest setting, giving identical temperatures for each pot so as to reduce any difference between pots.
"To ensure that kernels did not pop after the time limit was up, the contents of each pot was poured into a bowl when the time limit had elapsed. For each popping sample, we used pots with lids to prevent the loss of any popping corn.
"Since our oil substances came in two different states, solid (margarine) and liquid (oil), we melted the margarine and let it set until it reached room temperature. This was done to avoid any errors that might occur due to the differing states of the oils.
"We assumed that all grains of corn here are of the same weight. Taking this into consideration we removed any kernels that were half or were defective. To achieve identical sample sizes we counted 100 kernels for each sample. The response measured was the number of corns that popped in one minute.
"Because we used all of the pots more than once, we decided to wash and clean each pot after we popped each sample so as to reduce errors and to treat all samples equally; i.e., the initial state of each experiment was identical.
"During each popping sample each of us had a one task to carry out so as to avoid any differing performances if we were to rotate our duties. Justine poured the water, oil and the popped corn into the bowl; Yen poured the counted corn sample and counted the number of popped corns, and Ying timed the corn and cleaned the pots.
"Randomisation of the experiment was done by pulling numbers out of a random number table."
Data Codes: Pot size large/medium/small 1/2/3 Oil margarine/oil 1/2 Pot Oil Count Order 3 2 23 1 2 2 77 2 3 2 20 3 3 1 12 4 3 1 19 5 2 1 54 6 3 2 15 7 2 2 44 8 2 2 41 9 2 1 15 10 1 2 73 11 3 1 31 12 1 1 41 13 2 1 31 14 1 1 79 15 1 2 70 16 1 1 80 17 1 2 69 18
There is a strong difference between pots, the number of corns popped increasing in a linear manner as diameter increases. There is no apparent difference in number of corns popped in oil or margarine, but an extra observation made was that: "From this experiment it was also found that the popcorn tastes much better when salted margarine is used instead of oil. But it was also seen that the corn burns very easily when margarine is used instead of oil."
This experiment also lends itself to discussion of whether the results should be analysed as binomial instead of using Normal theory, and also to designing further experiments to investigate the taste/burning influence of a wider variety of oils.
"The experiment decided upon was to see if by using two different designs of paper aeroplane, how far the plane would travel. In considering this, the question arose, whether different types of paper and different angles of release would have any effect on the distance travelled. Knowing that paper aeroplanes are greatly influenced by wind, we had to find a way to eliminate this factor. We decided to perform the experiment in a hallway of the University, where the effects of wind can be controlled to some extent by closing doors.
"In order to make the experimental units as homogeneous as possible we allocated one person to a task, so person 1 folded and threw all planes, person 2 calculated the random order assignment, measured all the distances, checked that the angles of flight were right, and checked that the plane release was the same each time.
"The factors that we considered each had two levels as follows:
Paper: A4 size, 80gms and 50gms
Design: High Performance Dual Glider, and Incredibly Simple Glider (patterns attached to original report)
Angle of release: Horizontal, or 45 degrees upward.
"The random order assignment was calculated using the random number function of a calculator. Each combination of factors was assigned a number from one to eight, the random numbers were generated and accordingly the order of the experiment was found."
Data Codes: Paper 80gms 1 50gms 2 Plane High-Performance 1 Incredibly Simple 2 Angle horizontal 1 45 degrees 2 Distance(mm) Paper Angle Plane Order 2160 1 1 1 12 1511 1 1 1 11 4596 1 1 2 8 3706 1 1 2 6 3854 1 2 1 4 1690 1 2 1 2 5088 1 2 2 1 4255 1 2 2 7 6520 2 1 1 3 4091 2 1 1 9 2130 2 1 2 14 3150 2 1 2 5 6348 2 2 1 16 4550 2 2 1 15 2730 2 2 2 13 2585 2 2 2 10
The results are dominated by the two-way interaction between paper weight and design; the high-performance design flies much better when made with the lighter weight paper, while the incredibly simple design flies better when made with the heavier paper. The table of means summarises the result:
Design High-perform Simple Both Paper 80gms 2303.7 4411.3 3357.5 50gms 5377.2 2648.8 4013.0 Both 3840.5 3530.0 3685.2
"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 adjacent to the RSL, 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 -1 Line 1kg 1 2kg -1 Sinker 8oz 1 12oz -1 Rod Line Sinker Distance (m) 1 1 1 28.0 1 1 1 30.5 1 -1 1 31.0 1 -1 1 30.0 -1 1 1 33.5 -1 1 1 35.0 -1 -1 -1 38.0 -1 -1 -1 37.5 -1 1 -1 42.0 -1 1 -1 40.5 1 -1 -1 33.0 1 -1 -1 34.0 -1 -1 1 36.0 -1 -1 1 38.5 1 1 -1 38.0 1 1 -1 37.5
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 summarised 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