P-Value

See: Schneiter, K. (2008). Two Applets for Teaching Hypothesis Testing. Journal of Statistics Education. 16(3).

Instructions

Overview

Use a p-value to make a decision about whether a coin is fair (i.e. the probability of tossing a head is 50%).

This tool consists of two 'views': the test view and the investigate view. The "Choose view" menu allows the user to move between them.

In each view, the p-value is displayed. In the test view, this enables the user to make a determination about whether or not the coin is fair, in the investigate view, the user can observe the behavior of the p-value when the probability of tossing heads with the coin is known. For a one-tailed test the p-value is the probability of getting the observed number of heads or fewer if the coin is fair. For a two-tailed test, the p-value is the probability that the absolute difference between the observed and expected numbers of heads is at least as big as observed, assuming the coin is fair.

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Options: The options allow the use to choose between conducting a one-tailed test or a two-tailed test. If a one-tailed test is chosen, an unfair coin will always be biased toward tails.

Test view

In the test view, the probability of heads is initially unknown. You are asked to either "accept" or "reject" the hypothesis that the coin is fair. To guide your decision, gather information about the coin by tossing it. The applet displays the results of the tosses and the probability of getting the observed number of heads or something more extreme if the coin is fair (the p-value). The actual probability of tossing heads is revealed once the user has made a decision regarding whether or not the coin is fair.

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Activity 1: Devise a plan to determine whether or not the coin is fair: Consider the following questions:
  1. For you to reject the hypothesis, how small must the given probabilty be?
  2. Do you always get the right answer when you make decisions based on this probability?
  3. Is it possible to get a very small p-value if the coin is fair?
  4. How are your decisions affected by increasing the number of times you flip the coin?
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Investigate view

Under the investigate view, use the radio buttons to choose to flip a fair coin or a biased coin. The probability of tossing heads is displayed. Using the buttons to flip the coin, you can observe the results of the coin tosses under the indicated probability of tossing a head.

Activity 2: Flip the coin 100 times then consider the following questions:
  1. If the coin is fair, how many heads do you expect to observe?
  2. If the probability of getting the observed number of heads or a more extreme number of heads (under the assumption that the coin is fair) is large, must the coin be fair?
  3. If the probability of getting the observed number of heads or a more extreme number of heads (under the assumption that the coin is fair) is very small, is it possible that the coin is fair?
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