# PAIRED SAMPLE t-TEST

## PAIRED SAMPLE t-TEST

A paired t-test is used to compare two population means where the observations in one sample can be paired with observations in the other sample. It is generally used when:

1. The measurements are taken from the same subject before and after a particular course of action.
2. The number of observations in each data set is the same, and they are related in pairs.

We are interested in testing the equality of two population means (μ1 and μ2). The hypotheses for the comparison of the means in a two-sample paired t-test are as follows:

H0: μ1 = μ2

H1: μ1 ≠ μ2 (Two tailed test) or H1: μ2 > or (<) μ1 (One tailed test)

##### PROBLEM

The marketing head of company wants to compare the performance of two sales executives based on their average sales in last 6 weeks before and after they were trained. The average sales of salesmen A and B are given in the following table.

Table-1: Sample Data

The hypotheses for the analysis are:

Null hypothesis-H0: There is no significant difference between the average sales of A and B.

1 = μ2)

Alternative Hypothesis- H1: There is a significant difference between the average sales of A and B. (μ1  μ2)

Input Data

Table-2: Input Data

Performing the Analysis with SPSS

For SPSS Version 11, click on Analyze ⇒ Compare Means ⇒ Paired-Samples T Test .This will bring up the SPSS screen dialogue box as shown below

After clicking Paired-Samples T test, this will bring up the following SPSS screen dialogue box

the variables and move them to Paired variables box.

Click Option and select confidence interval 95% (5% level of significance) and then Continue.

This will bring the Paired-Samples T Test dialogue box. Finally click OK.

SPSS Output

The SPSS outputs of the analysis are depicted in table-3 and table-5

T-test

Table-3: Paired Samples Statistics

The average sales by the salesman A is 22.5 units and 22 units by B.

Table-4: Paired Samples Correlations

The correlation between A and B is 0.624

Table-5: Paired Samples Test

From the output, t = 0.165 with 5 degrees of freedom

DECISION

Reject the null hypothesis if p-value (Sig. value) ≤ 0.05

INTERPRETATION

The p-value is 0.875 and it is more than 0.05 (5% level of significance), so we accept the null hypothesis and reject the alternative hypothesis at 5% level of significance. It is concluded that the average sales by two salesmen are equal.

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