A chi-square tests if two variables are associated by comparing data you collect with what would be expected if the variables were not related. By learning the specific terms and phrases used when reporting the outcome of a chi-square test, you can write the results of your study in a clear way that will be easily understood. If you want to know if the kind of fruit in your smoothies influences buying preference, for example, you can conduct a taste test with smoothies flavoured with blueberry, apple and pineapple, complete a chi-square analysis and report the results according to scientific convention.
Arrange your data into rows and columns. In this example, you conducted a taste test on 60 different people, 20 in each group. Make two columns, labelled Buy and Not Buy, and three rows, one for each fruit. Enter the sample data in the six cells as follows:
Blueberries = 10 Buy / 10 Not Buy
Apples = 5 Buy / 15 Not Buy
Pineapples = 2 Buy / 18 Not Buy
Compute the results expected for the taste test if chance alone were operating. Multiply the row totals by the column totals for each cell and divide this number by the total number of observations in the table. For example:
Buy column: (20 x 17)/60 = 5.67
Not Buy column: (20 x 43)/60 = 14.33
Compute a chi-square value for each of the six cells. Subtract the expected value from the observed value, square the result and divide that figure by the expected value. For example:
Blueberry Buy: (10 -- 5.66)^2/5.67 = 3.33
Apples Buy: (5 -- 5.66)^2/5.67 = 0.08
Pineapples Buy: (2 -- 5.66)^2/5.67 = 2.37
Blueberry Not Buy: (10 -- 14.33)^2/14.33 = 1.31
Apple Not Buy: (15 -- 14.33)^2/14.33 = 0.03
Pineapples Not Buy: (18 -- 14.33)^2/14.33 = 0.94
Add each individual chi-square value to obtain a total chi-value. In this example, you get 8.06. Calculate the degrees of freedom. This is the number of total groups less one, which in this example is 2. Select an alpha-level, or amount of error you can tolerate. A common alpha-level is .05.
Use a chi-square table to look up the intersection between the degrees of freedom in the rows on the left and the alpha-level in the columns across the top. At the intersection of 2 degrees of freedom and alpha-level .05 is the value 5.99. If the actual chi-value from step 4 is equal to or greater than 5.99, as in our example, chi-square is said to be significant at the .05 level.
Report that you conducted a chi-square test to assess the relationship between your variables, which in this example is fruit flavour and smoothie-buying preference. State whether or not your results were significant. Follow this by the degrees of freedom, a comma, the letter "n," an equal sign and the total number of observations, all in parentheses, followed by an equal sign, the actual chi-square value you calculated, a comma, the letter "p," a less-than sign and the p-value used. For this example: The association between fruit flavour and smoothie-buying preference was examined using a chi-square test. The relationship between the two variables was significant, (3, n=60) = 8.06, p < .05.
Make a statement about which group had the highest chi-square value. In this example, you would say that people were significantly more likely to buy the shake with the blueberry flavour.