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:
- The measurements are taken from the same subject before and after a particular course of action.
- 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)
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.
(μ1 = μ2)
Alternative Hypothesis- H1: There is a significant difference between the average sales of A and B. (μ1 μ2)
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.
The SPSS outputs of the analysis are depicted in table-3 and table-5
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
Reject the null hypothesis if p-value (Sig. value) ≤ 0.05
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.