Statistical Consulting Blog

Sign Test

Posted May 11, 2009

There are non parametric tests or methods that are used in cases when the parametric test is not in use. One of the non parametric tests is the sign test. This non parametric test is used to test the null hypothesis that is assumed and says that the median of the distribution is equal to a particular fixed value.

The sign test can be used in the place of parametric tests, like one sample t-test, or in the place of the paired sample t test. It can be used to test that kind of data which is of ordered categorical type. The sign test is usually used in the kind of data where it is possible to rank the observations.

The researcher should keep in mind that the Wilcoxon Signed Rank Sum test is used in such situations, and is also more powerful than the sign test.

Let us discuss the procedure of carrying out the sign test. A sample consisting of ‘n’ number of observations is drawn. It is assumed that some s+ of the observations are greater than the population median. In the sign test, it is also assumed that some s- observations are smaller than the population median. The observations in the sample, which are absolutely equal to the population median, are ignored by the researcher. The value of the sum of s+ and s- are therefore less than the sample size ‘n’ in the sign test and therefore considered as ‘n/.’

According to the null hypothesis in the sign test, it is expected that half of the observations should be above the median and the other half of the observations should be below the median. Hence, under the null hypothesis in the sign test, both s+ and s- follow a binomial distribution with the probability of ‘0.5’ and the size n= n/.

The first step of conducting a sign test involves choosing the value of ‘s,’ which is nothing but the maximum value among the s+ and s- .

Then, the usage of the tables of the binomial distribution is done in the sign test. This table of binomial distribution is done in the sign test in order to find the probability of the value of ‘s’ or something higher than ‘s’ under the assumption that the probability is ‘0.5’ and the n= n/ .
If the sign test is two sided, then the probability obtained from the tables of binomial distribution is doubled.

The sign test can also be performed with the help of SPSS software. In SPSS software, the sign test can be performed by selecting “analyze” from the menu item. Then, the sign test is conducted in SPSS by clicking the “non parametric tests” in the analyze menu. From the non parametric tests, the researcher selects the “binomial test,” which is nothing but the sign test. Therefore, it should be noted by the researcher that due to the involvement of binomial distribution, the sign test is also called the binomial test.

In SPSS, after selecting the type of non parametric test, the researcher chooses the relevant variable, which is considered as the test variable on which the sign test is to be conducted.
In the case of a paired type of data in the sign test, the researcher specifies the null value of the paired data. The researcher also selects the cut point under “define dichotomy criteria” while conducting the sign test.After finishing all the specifications in SPSS, the researcher finally clicks on the “OK” button in order to the view the outcome obtained from the sign test.

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