Question

Question 14 5 pts Describe how to conduct a sign test. HTML Editora BIVAAIX EEx X, DE 12pt O words

Answer 1

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

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:

K= n-1 -0.98.10 2

Sign test in case of large sample:

(d-1)du II du-s

Binominal distribution formula =
x d " x - R
with p =1/2

Compare the value‘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

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