© Copyright 1998, Joel Levine and Thomas B. Roos
Truism: objects with the same name have the same properties (M & Ms)
Introduction
Mass production and sale of commodities promises a uniformity of product that it may or may not deliver. Everyone has heard of quality control and of objects whose performance fails to meet expectations. Everyone also knows that widely distributed commodities may appeal differently to people with different tastes and in diverse circumstances. Manufacturers know that the specific product that appeals to buyers in the Northeast may not sell well in Texas. It would be nice to test the truism that objects with the same name have the same properties by using automobiles, dolls or chickens, but the ubiquitous M&M^{®} candies are cheaper and easier to obtain, as well as more likely to be obtainable from great distances.
Materials Required
Procedure
Source of M&Ms 
Blue 
Brown 
Green 
Orange 
Red 
Yellow 
Other 
Total 
Home, plain: 








Source of M&Ms 
Blue 
Brown 
Green 
Orange 
Red 
Yellow 
Other 
Total 
Hanover, plain 








Source of M&Ms 
Blue 
Brown 
Green 
Orange 
Red 
Yellow 
Other 
Total 
Hanover, with nuts 








Stem and leaf diagrams or histograms.
Mean, median, and modal color distributions for the class.
Means, medians and variances for quantitative data (if collected).
Foreign (plain, without nuts)^{ *}
Source of M&Ms 
Blue 
Brown 
Green 
Orange 
Red 
Yellow 
Other 
Total 
Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








Home: 








N = _____ 








Local (plain, without nuts)^{*}
Source of M&Ms 
Blue 
Brown 
Green 
Orange 
Red 
Yellow 
Other 
Total 
Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








N = _____ 








Local (with nuts)^{ }*
Source of M&Ms 
Blue 
Brown 
Green 
Orange 
Red 
Yellow 
Other 
Total 
Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








Hanover 








N = _____ 








Report
Can you find evidence of differences in frequencies among the packages of candy from Hanover (with and without nuts)?
Compare the differences in variation between class results from Hanover and foreign packages (plain candies only).
Describe the distribution of colors between the bags of plain and peanut candies.
Consider whether the variations seen in one bag (in size and color) provide a good basis for describing the variation found in all the bags observed.
Aphorism: "Like as peas in a pod"
Introduction
Many annual varieties of the family Leguminosae have been cultivated in gardens for both personal and communal use for more than 6000 years. Their edible seeds include peas, beans, lentils, peanuts, groundnuts, and vetch that grow within a pod which may itself also be edible. They dry and keep well, serving as a major source of nutrition for people everywhere. Local varieties of peas or beans have been familiar for so long that their apparent uniformity has become part of language. This exercise explores whether the aphorism, "like as peas in a pod," reflects reality or just a perception of what reality ought to be. The "null" hypothesis (H_{0}) states that peas in a pod do not differ. We shall test it by collecting quantitative data. From this we can ascertain whether peas in the same pod differ or whether peas in one pod differ from other peas. Note that the expression refers to peas, not grain or other legumes. Why might it be more likely to have arisen than one about the similarity of beans or maize or lentils? What does it imply about the similarity of other legumes or seeds of grains?
The first questions to answer have to do with the nature of the data, but note that the "peas" will not be the data used, but only the objects from which the data will be gathered.
What (or who) are they?
Where, when, why and how were they collected?
Perhaps the most obvious way to evaluate the similarity of peas within a pod would be to weigh and compare the weights of peas from the same pod. This procedure becomes unwieldy, however, using even a small sample size. For example, given a sample of 25 pea pods with an average number of 5 peas per pod, requires 125 individual measurements and 25 computations of means and standard deviations a tedious process at best. Therefore, another, more efficient method should be sought for exploring the reliability of the aphorism.
One measurement of likeness is the variance, a statistic used to describe the spread of a set of values around the mean of those values. The standard deviation (square root of the variance) provides a more convenient descriptor, as it has the same units as the mean. If the aphorism holds true, the variance (or standard deviation) of the average weight of a pea within a pod would be small regardless of the number of peas in that pod. However, if the aphorism is false, that is if peas within a pod do not tend to be alike, then the variance (standard deviation) of the average weight of a pea in a pod would increase as the number of peas per pod increases. This conceptualization of variance allows measuring the contents of a pod all at once, computing the average weight per pea in that pod, and then comparing the computed variance (standard deviation) to test the aphorism.
Materials Required
Procedure  Part A (Preliminary)
Pod Number 
Number of Peas 
Weight of Peas 
Average Pea Weight 
1 



2 



3 



4 



5 



Preliminary Interpretation.
At this point you have selected a small sample of pea pods and sampled one quality (weight) of the contents. Note that in some pods the peas are fairly equal in size while in others the individual peas may differ dramatically in size. Is it possible that some of these peas should not be considered to be "peas" for this exercise? If you think this is the case, establish some criterion that would allow you to exclude these small ones (ovules) and count only the more developed seeds as peas. .
This process of looking at a small portion of your sample first is called "pretesting", a method which allows the experimenter to discover any factors that need refinement before embarking on the final analysis. Pretesting allows you to anticipate ambiguities and errors in judgement before they spoil your analysis.
Procedure  Part B (Descriptive)
Pod Number 
Number of Peas 
Weight of Peas 
Average Pea Weight 
6 



7 



8 



9 



10 



11 



12 



13 



14 



15 



16 



17 



18 



19 



20 



21 



22 



23 



24 



25 



Report
Germination of radish seeds
Introduction
Many seeds germinate differently in the light and the dark, in soil or in a moist chamber, under different conditions of temperature or pregermination treatment. This exercise tests the ability of a plant to germinate under defined, abnormal, and modestly different conditions. As a basis for study, germinate radish seeds in a moist chamber (petri dish with a water soaked substrate) under ambient conditions that are easy to maintain and measure (e.g., room temperature and normal illumination).
Materials Required
Procedure
Option 1: Growth in five days
Measure and record the length of each plant at the end of five days of growth.
Try to distinguish between growth of the root (that part below the old seed coat) and the shoot (that part above it).
Calculations
Compute the mean and median size for the six seedlings in each of the two or three dishes.
Get data from the entire class and compute the group mean, median, and spreads (variance and quartile) for each condition tested.
Option 2: Rate of growth for five days
Measure and record the length of each plant on each of the five days.
Calculations
Compute the mean and median size for the six seedlings for each day in each of the three dishes.
Compute the average growth rate in each dish.
Get data from the entire class and compute the group mean, median, and spreads (variance and quartile) of growth and growth rates.
Additional options
Compare different ways of measuring the length of germinating seeds:
Compare direct measurements (as above) with measurements of a length of thread carefully laid along the seedling and then measured separately.
Follow the procedures under Option 2 (above).
Compare the consequences of desiccation:
Compare the growth of seedlings in a continually damp chamber with that of seedlings in which the paper doesn’t remain visibly moist (be careful not to let it dry out completely).
Follow the procedures under Option 2 (above).
Compare the germination of seeds using paper from different sources:
Filter paper for coffee makers (you may want to compare differences between bleached and unbleached papers).
Paper towels from different manufacturers (e.g., recycled, untreated, "wetstrong").
Other absorbent papers and newsprint (with or without ink).
Follow the procedures under Option 2 (above).
Compare the germination of seeds pretreated under different conditions:
Quickly plunged into boiling water.
Chilled in a freezer for a day prior to germination.
Soaked in vinegar prior to germination.
Follow the procedures under Option 2 (above).
Compare with the germination of seeds in soil (following the procedures under Option 2, above).
Place the seeds in a pot with fine soil (you must wait until the end of the test period to measure their length, as removing and measuring them interferes with further development).
Be careful not to break the root when removing seeds from the soil.
Report
If necessary, transform the data to make the graph linear and describe the growth of the seedlings.
What kind of transformation gives the best result, i. e., closest approximation to a straight line on the graph and to heomoscedasticity in the variation?
What can infer from the transformation?
Data
Option 1: Germination of radish seeds and growth in five days, room (ambient light) conditions.
Seed Number 
Day 1 (mm) 
Day 2 (mm) 
Day 3 (mm) 
Day 4 (mm) 
1 




2 




3 




4 




5 




6 




Option 2: Germination of radish seeds and growth in five days, dark conditions.
Seed Number 
Day 1 (mm) 
Day 2 (mm) 
Day 3 (mm) 
Day 4 (mm) 
1 




2 




3 




4 




5 




6 




Additional Option (specify): .
Seed Number 
Day 1 (mm) 
Day 2 (mm) 
Day 3 (mm) 
Day 4 (mm) 

1 





2 





3 





4 





5 





6 




Body Parts
Introduction
Reason suggests that many physical (and mental) properties show a high level of association: that is, they reflect some underlying property of quality that distinguishes people from each other. Following this line of thought, the dimensions of various body parts might be expected to show a close relation so that a small person would have shorter arms and legs than a taller one. But how far might these expectations extend? Would the same be true for the relative size of ear lobes, the width of shoulders, the circumference of biceps, or the length of their nose? And what of less concrete associations, such as disease resistance, spatial or odor perception, and musicality. Some of these dimensions and properties must have a greater susceptibility to environmental modification than others, even if they all show an underlying association with some index of "general size," "general quality," or "general intelligence."
Test your hypotheses (assumptions, preconceptions) by first stating them and then collecting data that measure them. Although not as controversial (interesting) as properties such as intelligence, beauty, or creativity, body parts have the advantage of easy accessibility and measurement. Use some easily measured anatomical elements to examine whether the general truism holds, that body parts reflect body size. Measure the lengths of your thumb (terminal joint), middle digit (proximal joint), forearm (ulna), and foot (heel to tip of longest toe) to give yourself data to test the general hypothesis and your particular notions of which parts vary together.
Materials Required
Procedure
Write a brief hypothesis incorporating your anticipated results. Keep the discussion simple, but include reasons for your expectations. Don’t modify this document as you continue, but keep it as a record of your preconceptions and as a basis for possible hypothesis testing.
Mark the distance between the middle knuckle and the thumb tip on the string and then measure that distance with the ruler.
Report
Compute an appropriate average and estimate of variation for each variable: mean ± standard deviation or median ± step.
On what basis do you choose the least square or minimum absolute difference values?
How would you compare these differences to see whether the different parts have different amounts of variability?
Discuss how these correlations support or contradict your initial hypothesis (as recorded before you began your work).
Assumptions
Body Part 
Expected Correlation (circle one) 

Body 
+ 
0 
— 

Thumb (terminal joint) 
+ 
0 
— 

3rd Finger (proximal joint) 
+ 
0 
— 

Forearm (ulna) 
+ 
0 
— 

Foot 
+ 
0 
— 

Biceps (circumference) 
+ 
0 
— 
Data (all measurements in cm estimated to the nearest tenth)
Body Part 
Body (height) 
Thumb 
3rd Finger 
Forearm 
Foot (length) 
Longest toe (length) 
Biceps 

You 








Classmate 








Classmate 








Classmate 








Classmate 








Classmate 








Classmate 








Classmate 








Classmate 








Classmate 








Classmate 








Classmate 








Classmate 








Classmate 








Classmate 








Classmate 








Classmate 








Classmate 








Classmate 








Classmate 








Classmate 








Classmate 








Classmate 








Classmate 








Classmate 








Classmate 








N = 






