How to Calculate P Values for Ordinal Data

Make a table to organize ordinal data.

The Friedman test is a non-parametric statistical test for determining the p-value of ordinal data (ranking data). The Friedman test uses a formula to calculate the variance of the ordinal data between groups. Calculate the p-value for the data by comparing this number to the critical value of a chi-square test with the same degrees of freedom, rows and columns.

Instructions

1. Construct a table with columns representing the groups to be compared and rows representing a single data set for the group. For example, if you are comparing ordinal poll results for four candidates over five days, make one column for each candidate and write a 1, 2, 3 or 4 at the header of each row to represent each candidate's position in each of the five days.

2. Calculate the sum of the ordinal rankings in each column. Write the sums in a row below the data rows.

3. Calculate the degrees of freedom by subtracting one from the number of groups. In the example, there are four groups so the degrees of freedom is three.

4. Look up the critical value on a Chi-Square table for the value of alpha you have chosen and the degrees of freedom. With a standard alpha of 0.05 and 3 degrees of freedom, the critical value is 7.815.

5. Calculate the chi-square value using the formula Chi-Square = (12 / (nk(k + 1))) * Sum(R^2) - 3n(k + 1), where n = the number of rows, k = the number of columns and R = the sum for each column. In the example, if the sums of the five rows are 7, 11, 12 and 20, then Sum(R^2) is equal to 49 + 121 + 144 + 400, so the formula is (12 / (5*4*5)) * 714 - 3*5*5. This simplifies to 10.68.

6. Compare the chi-square value to the critical values on the chi-square table. If the chi-square value exceeds the critical value for that alpha, then p is less than the alpha. In the example, the chi-square value is 10.68 and the critical value for alpha 0.05 is 7.815, so p < 0.05. The critical value for alpha 0.01 is 11.345, so p > 0.01.

References

• Vassar College Department of Statistics: Friedman Test; Richard Lowry

Resources

• Statisticslectures.com: Chi-Square Table