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Sign Test

The Sign test is a non-parametric test that is used to test whether or not two groups are equally sized.  The sign test is used when dependent samples are ordered in pairs, where the bivariate random variables are mutually independent  It is based on the direction of the plus and minus sign of the observation, and not on their numerical magnitude.  It is also called the binominal sign test, with p = .5.. The sign test is considered a weaker test, because it tests the pair value below or above the median and it does not measure the pair difference.  The sign test is available in SPSS: click “menu,” select “analysis,” then click on “nonparametric,” and choose “two related sample” and “sign test.”

Questions Answered:

Which product of soda (Pepsi vs. Coke) is preferred among a group of 10 consumers?

Assumptions:

  • Data distribution: The Sign test is a non–parametric (distribution free) test, so we do not assume that the data is normally distributed.
  • Two sample: Data should be from two samples.  The population may differ for the two samples.
  • Dependent sample: Dependent samples should be a paired sample or matched. Also known as ‘before–after’ sample.

Types of sign test:

  1. One sample: We set up the hypothesis so that + and – signs are the values of random variables having equal size.
  2. Paired sample: 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 this 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:

  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; pairs with 0 as the mean value are considered ties.
  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 .05 of the significance level by using the following formula in case of small samples:

Sign test in case of large sample:


Binominal distribution formula = with p =1/2

  1. 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.

SPSS:

Available in nonparametric tests, the following steps are involved in conducting a 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:

  1. Click on the “open data” icon and select the data.
  2. 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 “options” and select “descriptive” 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.  This will show the number of negative sign, the number of positive sign for the number of ties, and the total number of observations.  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 .05, null hypothesis will be rejected.  If the probability value is greater than the significance level, then cannot reject the null hypothesis.  The following table will appear for the test statistics:

*Click here for assistance with conducting the sign test or other quantitative analyses.

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