The Chi-Square Test for Multiple Categories
Instructions
Instructions
Objective: Investigate and implement the chi-square test to determine if a die is fair.
This tool consists of two 'views': the investigate view and the test view. Use "Choose view" menu to move
between views.
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Investigate view
Choose to roll either a fair die or a loaded die. The probabilities
of observing each of the faces are displayed. Check boxes at the bottom allow investigation of
- Expected counts: the number of times each face is expected to be rolled: if the die is fair.
- Observed counts: the actual number of times each face is rolled.
- Differences: the difference between expected and observed counts for each face.
- Scaled differences: for each face, the square differences divided by the expected counts.
The chi-square statistic and the p-value (both found assuming that the die is fair) can also be displayed.
Press the "New die" button or one of the radio buttons to begin again.
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Test view
The probabilities of rolling each of the die faces are unknown. Roll the die
to investigate whether the die is fair (all faces have the same probability). The number of times
each face is rolled (observed rolls) is shown, along with the number of times each face should turn
up if the die is fair (expected rolls). These are used to compute the chi-square statistic
(shown below the die) and the probability that the statistic is at least that big if the die is fair
(the p-value).
Use the p-value to decide whether the die is fair. A small probability signifies that it is unlikely
to get a chi-square value at least as large as the one observed if the die is fair.
The chi-square statistic
The chi-square statistic is the sum of the scaled differences of all die faces.
Options Menu
Use the options menu to change the appearance of the dice.
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