Chi-square: Life Dice Statistics

Life Dice Statistics is a site where the results from thousands of rolls of dice has been recorded. The frequency of each number that occurs is recorded in a chart that includes the individual statistics. There are several other charts on the site that are more complex, but for this activity you will just focus on the individual results.

 In this activity you will perform a chi-squared test for goodness of fit using a DIG Stats Online Chi-Squared Calculator. In order to use the DIG Stats Online Chi-Squared Calculator, just download either format, open the calculator, and enter the data by hand.  A lot of dice have been rolled and recorded since November 2000. Many of these rolls have been recorded, and have been conveniently placed in a table with the frequency of each result. A test for goodness of fit will be used to determine whether the die is fair or not-- in other words it will determine if there is an appropriate margin between the amount of numbers that is not so different that one will occur more than any other in probability. The reason this study uses a chi-squared test is to determine if there is an equal amount of occurrences of each number. Naturally there will not be exactly an equal amount, but it will determine if the amount is close enough. Since there is only one variable, the test for goodness of fit will be used.
The data in the table given is the actual data. The expected data is given at the bottom of it. You will have to copy the data from the chart to the java applet, putting the actual data in the row it is supposed to go in, and the same expected number in each cell for the corresponding row. The data is in Excel Format.

1. What is the c2 value, and what is the df value?
2. Is the frequency for each number equal?
3. Does this mean that you accept the null hypothesis or the alternate hypothesis?

You can find an online chi-squared table at

Page created by Central Virginia Governor's School Students Matthew James and Kyle Nenninger
Copyright 2011 Central Virginia Governor's School