The ART and SCIENCE of Good Sampling

 

Overview:

         In this activity students will explore the need for sampling in order to understand how diverse life is on their study site. They undertake two sampling exercises, one of heads and tails in a coin toss and the other of eye color. They then prepare for their trip back to their study site, in which they will perform sampling exercises with transects and quadrats.

Goals and Objectives:

         The goal of the activity is to enhance student understanding of the complexity of gathering information and the need for sampling, under certain circumstances.

         Students will be able to:

         - define a sample

         - discuss difficulties of making a good sample      

         - explain how a transect and quadrat used in the field are sampling

 

Time:  One- two class period(s)

Background:

Field scientists collect information, but sometimes there is just too much information to collect completely.  So they collect samples that they hope will represent much of the nature of the larger group they want to find out about.

 

For example, field scientists might want to find out the percentage of trees affected by a fungus, sociologists might wonder who are more likely to adopt children, and laboratory scientists might want to investigate the viruses that cause mice to develop cancer.  But counting ALL trees, surveying all people or testing all mice would be too hard.

 

 Sometime scientists don't have the time or money to collect lots of data. Sometimes they settle for a few samples.  But they hope the samples will be representative of the whole group in which they are interested.

 

How are samples collected?

Sociologists interested in who adopts children might interview people who have been chosen randomly from a larger group (say, every 14th page from a phone book.)

 

Field scientists interested in the tree fungus might collect some samples by laying out random transects – lines across a natural area with counting places spaced evenly throughout the sample. 

 

Lab scientists interested in viruses that cause cancer might design experiments using randomly selected samples of mice.

 

How can samples be unrepresentative?

Samples can be quite biased, quite unrepresentative of the whole population being questioned.  A lab scientist, for example, could select only those mice that look sick, or healthy.  This is why scientists take more than one sample, at random (without order).

 

If the question is:  How serious is the tree blight in Karelia, and if one knew that a particular region of Karelia had many diseased trees, you might not want to sample ONLY in that region.

 

What about the sociologists who wanted to find out about a connection between growing up in a large family and likelihood of adopting children in later life?  How could their sample be biased?

 

Random numbers help

Often scientists use random (completely unordered) numbers to help them decide which tree, which transect, which mouse or group of mice, or which set of people to sample.  That way they aren't biased, deciding to sample and get results that are unrepresentative but results they would LIKE.

 

See a random number generator on the web: http://www.random.org/integers/

 

The power of multiple samples.

The more times you take a handful of candy from a jar and get no chocolates, the less likely there is much chocolate in the whole candy jar. The more samples are added together, the closer the numbers are to the true values of a population.  Scientists can use different teams and average the samples to make the data from the sample more representative of the problem you are studying.

 

STEPS

A. SAMPLING EXERCISE 1: COIN TOSS

Ask students to do the Coin Toss Exercise.

B. SAMPLING EXERCISE 2: EYE COLOR

 

Question: What fraction of the class has brown eyes?

In exercise one, you knew that half the coins should come up heads. This time, you don't know what to expect. If you looked at only some of the students, how close would you come to the actual fraction of brown-eyed students in your class? In the entire country?

 

1. Divide the class into two equal groups at random. What is a good way to be sure there is no bias? Call one group A, the other B.

 

2. Count the number of brown-eyed students in group A.

 

3. Use the data for group A to PREDICT the number of brown-eyed students in group B. Every student should write down a prediction.

 

4. Count the number of brown-eyed students in group B. How good were the predictions? What was the best prediction?

 

5. Suppose this was repeated for every class in the country. You go to every class and bet on its B group. How would you bet? How often do you think you would be right?

 

6. Discus whether your data would predict the fraction of people in the whole country with brown eyes.

 

C. SAMPLING WORK 3:  QUADRATS AND TRANSECTS

Explain to your students that in the next field trip they will be taking samples of the plants in the study site, and that they will try to decide how diverse plant life is on the site.

 

Ask them how they might sample the vegetation. Hopefully your students will develop ideas somewhat like the approaches embodied in quadrats and transects.

 

Have student teams construct any needed quadrats and tie knots every meter in 10 meter ropes for the transects.

 

The quadrat frame is a simple square usually constructed from wood. Alternatively, you can cut out a cardboard template and have students create a string or rope quadrat frame at the study  site. If your study site has small plants and dense vegetation, use a 10 by 10 centimeters quadrat, but if your site has larger plants  (predominantly shrubs or trees) use a 1 by 1 meter quadrat.