Sign Test

Sign test is a non parametric test. The sign test is used to test the null hypothesis and whether or not two groups are equally sized. Sign test is based on the direction of the plus and minus sign of the observation, and not on their numerical magnitude. Sign test is also called the binominal sign test, with the null proportion of .5. Sign test is also used in the case of the paired sample, which is called the alternative test of the paired t-test.

Types of sign test:

The sign test can be of two types:

1. One sample sign test:In one sample sign test, we set up the hypothesis so that + and – signs are the values of random variables having equal size.
2. Paired sample sign test: This test is also called an alternative to the paired sample t-test. This test uses the + and – signs in paired sample tests or in before-after study. In paired sample sign test, null hypothesis is set up so that the sign of + and – are of equal size, or the population means are equal to the sample mean.

Procedure:

Sign test involves the following procedure:

1. Calculate the + and – sign for the given distribution. Put a + sign for a value greater than the mean value, and put a – sign for a value less than the mean value. Put 0 as the value is equal to the mean value.
2. Denote the total number of signs by ‘n’ (ignore the zero sign) and the number of less frequent signs by ‘S.’
3. Obtain the critical value (K) at 5% of the significance level by using the following formula in case of small samples:



Sign test in case of large sample:


Binominal distribution formula for sign test = with p =1/2

4. Compare the value of ‘S’ with the critical value (K). If the value of S is greater than the value of K, then the null hypothesis is accepted. If the value of the S is less than the critical value of K, then the null hypothesis is accepted. In the case of large samples, S is compared with the Z value.

Sign test in SPSS:

In most of the statistical packages, sign test is available. In SPSS, sign test is available in nonparametric tests. The following steps are involved in sign test in SPSS:

1. Click on the “SPSS” icon from the start menu. The following window will appear when we will click on the SPSS icon:



2. Click on the “open data” icon and select the data.
3. Select “nonparametric test” from the analysis menu and select “two related sample” from the nonparametric option. As we click on the two related samples, the following window will appear:

Select the first paired variable and drag it to the right side in variable 1, and select the second paired variable and drag it to the right side in variable 2. Select the “sign test” from the available test. Click on “option” and select the “descriptive statistic” from there. Now, click on the “ok” button. The result window for the sign test will appear.

In the result window, the first table will be of the descriptive statistics for sign test. These will include the number of observations per sample, the mean, the SD, the minimum and the maximum value for sign tests in both samples. The second table shows the frequency table for sign test. This will show the number of negative sign, the number of positive sign for the number of ties, and the total number of observations for sign test. In SPSS, the following table will appear for the descriptive table and frequency:

The third table will show the test statistics table for sign test. This table shows the value of Z statistic and the probability value. Based on this probability value, we can make our decision about the hypothesis. For example, if the probability value is less than the significance level at 5%, null hypothesis will be rejected for the sign test. If the probability value is greater than the significance level, then we will accept the null hypothesis for the sign test. The following table will appear for the test statistics of sign test: