# Favourite Experiments: An Addendum to What is the Use of Experiments Conducted by Statistics Students?

Margaret Mackisack
Queensland University of Technology

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.

# 1. The Squash Ball Experiment, by Grant Elliott

## 1.1. Background and description of design

"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."

## 1.2. Data

```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
```

## 1.3. Analysis

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

```

# 2. The Rose Experiment, by Jane Fennell and Kirsten Neish

## 2.1. Background and description of design

"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.

1. The roses tested should be identical. They should be the same size and colour, at the same stage of growth and picked at the same time from roughly the same area. We obtained our roses directly from the grower to enable us to be satisfied on this point.
2. The vases chosen for the experiment should also be identical; same size, shape, texture and translucency. For this experiment, (brown) beer bottles were chosen.
3. The water level in each vase should be the same. A water level of 1 inch from the top of the bottle was used.
4. The solution of water and citric acid should be consistent throughout. To achieve this, the solution should be mixed in one large jug, then poured into the vases.
5. The temperature each day should be noted. It may be needed if there is any dramatic drop or rise in temperature, that could have an effect on the results.
6. When can the rose be termed 'dead'? The point of death chosen for this experiment is when one would consider disposal of the rose under normal circumstances.
7. The roses were allocated randomly to the different treatments using a random number table.

"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."

## 2.2. Data

```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
```

## 2.3. Analysis

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.

# 3. The Meat-Ant Experiment, By Dominic Kelly

## 3.1. Background and description of design

"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:

1. Stop-watch set to zero.
2. Three centimetre square piece of sandwich was placed 10cm away from the main entrance to the nest.
3. After 5 minutes a drinking glass was placed over the portion of the sandwich. The glass covered an area of approximately 50.24 cm^2.
4. Stop-watch set to zero again.
5. Area outside the trap area was carefully swept in order to clear the area of other ants. The glass was then removed and the ants counted.
6. After five minutes the experiment was repeated using a portion of a different sandwich. The reason for the five minute break between observations was in order to allow the ant hill to 'settle down'.

"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."

## 3.2. Data

```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
```

## 3.3. Analysis

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.

# 4. A Corn-Popping Experiment, By Ying Ming Lee, Justine Nuttall and Yen Ching Wong

## 4.1. Background and description of design

"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."

## 4.2. Data

```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

```

## 4.3. Analysis

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.

# 5. A Paper Plane Experiment, By Stewart Fischer and David Tippetts

## 5.1. Background and description of design

"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."

## 5.2. Data

```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
```

## 5.3. Analysis

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
```

# 6. The Fishing Rod Experiment, By Peter Drew and Matt Seidemann

## 6.1. Background and description of design

"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."

## 6.2. Data

```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
```

## 6.3. Analysis

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
```

Margaret Mackisack
School of Mathematics
Queensland University of Technology
GPO Box 2434
Brisbane Q. 4001 Australia
mackisack@qut.edu.au