How to Make a Chi Square
To test differences between groups of data, use a chi-square. The test compares obtained proportions in each group to what chance would obtain. You can apply this test to nominal, ordinal, interval and ratio data. For example, if you were selling tickets in front of three different types of stores and you wanted to see if the type of store was associated with ticket sales, then a chi-square test would be ideal.
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Instructions
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Count the data. In this example, you tried to sell tickets to 100 people in front of three different stores. You want to know if the type of store made a statistically significant difference in the amount of successful sales made.
You will have rows as follows:
Store one = 80 tickets bought and 20 tickets refused
Store two = 60 tickets bought and 40 tickets refused
Store three = 71 tickets bought and 29 tickets refused
You will have two columns as follows:
Bought Tickets
Refused Tickets.
You will have six cells in your table:
Store one/Bought
Store Two Bought
Store Three/Bought
Store one/Refused
Store Two/Refused
Store Three/Refused
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Calculate the expected amounts for each cell if the store did not have any effect. Take the total amount offered for each row and multiple it by the column total. Divide this figure by the total number of observations in the table.
For the Bought Tickets column:
100*211/300 = 70.3
For the Refused Tickets column:
100*89/300 = 29.67
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3
Calculate a chi-square value for each of the six cells by using the formula observed-expected)^2/(expected).
Store One/Bought:
80-70.3 = 9.7
9.7*9.7 = 94.09
94.09/70.3 = 1.338
Store Two Bought:
60-70.3 = (-10.3)
(-10.3) x (-10.3) = 106.9
106.9/70.3 = 1.509
Store Three Bought:
71 - 70.3 = 0.7
0.7 x 0.7 = 0.49
.49/70.3 = 0.007
Store One Refused:
20 -- 29.67 = (-9.67)
(-9.67) x (-9.67) = 93.5089
93.5089/29.67 = 3.152
Store Two Refused:
40 -- 29.67 = 10.33
10.33 x 10.33 = 106.7089
106.7089/29.67 = 3.597
Store Three Refused:
29 -- 29.67 = (-0.67)
(-0.67) (-(0.67) = .4489
.4489/29.67 = 0.015
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4
Add all the individual chi-values together to get the total chi-squared value. In this example:
1.338 + 1.509 + 0.007 + 3.152 + 3.597 + 0.015 = 9.618
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Tips & Warnings
Look up the chi-square value in a chi-square table which you find in the back of most statistics textbooks.
References
Resources
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