What it’s for:
The sign test is a simple way to compare two central tendencies. It is non-parametric, but less powerful than the Kruskal-Wallis test. However, it has one advantage — it can be used on data collected in pairs. The KW test assumes all data points are independent. The sign test reduces all measurements to a plus or minus, and then asks if the pluses outweigh the minuses more than would be expected by random chance (or vice versa).
Assumptions/Cautions:
Data points must be independent or collected in pairs.
The null hypothesis must be of no difference between pluses and minuses.
How to use it:
1) Each measurement must be assigned a plus or minus value. Typically, the test is used for data collected in pairs, and if the first measurement of the pair is greater than the second, we assign a plus. For example, we could measure the right and left index fingers of a sample of people to see if the right-hand fingers tended to be longer. We would assign a plus to each person with a right-hand finger longer than the left. (Reversing plus and minus would make no difference.) Measurements which are equal are assigned a value of 0, and are excluded from calculations. Sample size should also be adjusted to exclude these measurements.
2) Count up the pluses and minuses.
3) Estimate the p-value using a computer program, or by comparing your pluses and minuses, along with sample size, to a table of critical values. (No test statistic is calculated with this extremely simple test).
4) Draw a conclusion based on your p-value. See also Types of Error.
MS Excel Tips:
MS Excel will not directly perform a sign test. However, a spreadsheet can be very useful in counting up pluses and minuses. You can also use the BINOMDIST function to calculate the exact probability associated with your results. In the first box in the dialogue window enter the number of pluses in your data (or the number of minuses), in the second box enter the total sample size (remembering to adjust for 0’s), in the third box enter 0.5, and in the fourth box enter FALSE.
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