Small+Samples

Consider the following:
The Gen Psych textbook has a TRY IT in Chapter 1 that says Sometimes students have a hard time believing that 1,000 people or so can represent the entire population of the United States. This activity will help you see that small samples can be representative. You probably know that when you flip a coin the chances of getting a head or tail is 50%. This probability is based on an infinite number of coin tosses. But how well does tossing the coin twice represent that whole population, what about a sample of 5 or 10 or 15 or 20? To answer such a question, you have to take repeated samples of the same size. Toss a coin twice (//n// = 2), and then write the numbers of heads and tails in the column labeled Sample 1. Repeat the process four more times, recording the results under sample 2 the second time, under Sample 3 the third time, and so on, until you have a total of five samples, each of which consists of two coin tosses. When the //n// = 2 row is completely filled in calculate the overall percentages of heads and tails. Next, use the same process to collect data on samples of //n// = 5, //n// = 10, //n// = 15, and //n// = 20, until you have filled the table with data.

You can see that, as //n// gets larger, the overall percentages of heads and tails become more balanced (closer to 50/50). However, notice also that //n// = 20 isn't much better than //n// = 15, and it took a lot longer to collect five samples of 20 coin tosses each. In other words, there wasn't much gain in representatives for the extra cost in time and energy. So, small samples can be representative, and increasing the size of a sample doesn't always pay off when costs are balanced against benefits.

Discuss:
Do the activity. Report results and discuss your experience below.

[Instructor may or may not add a Bonus section here]

References:
See TRY IT Gen Psych Chapter 1 page pp. 19 For more about Introduction see Gen Psych Chapter 1

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