The 2-Sample t conducts a hypothesis test of the difference between two population means when the population standard deviation, s is unknown. It also calculates a confidence interval of the mean.
This procedure is based on the t-distribution which is derived from a normal distribution. The samples should be drawn independently from each other. For dependent samples, use the Paired t-test.
|
Test |
Null Hypothesis, H0 |
Alternate Hypothesis, H1 |
|
One-tailed |
m1 - m2 = d |
m1 - m2 < d or m1 - m2 > d |
|
Two-tailed |
m1 - m2 = d |
m1 - m2 ¹ d |
where m1 and m2 are the population means and d is the hypothesised difference between the population means.
1. Choose ProcessMA > Basic Statistics > 2-Sample t.
2. In Data in, choose how your data is stored.
· If your data in stored in a single column:
- In Variable, select the column containing the sample.
- In Category, select the column containing subgroup codes.
· If your data in stored in different columns:
- In Sample 1, select the column containing the first sample.
- In Sample 2, select the column containing the second sample.
3. In Test mean difference, enter the hypothesised difference between the population means.
4. Click OK.
Optional
5. In Alternate, select the type of test.
6. In Confidence level, enter the desired confidence level for the confidence interval.
7. Check Assume equal variances, if you want to assume that both populations have equal variances.
8. Check Plot dotplot, if you want to display a Dotplot of the data and the hypothesis test parameters.
Note To select a column of data into a textbox, double-click on any of the column names shown in the list on the left of the dialog box while in the textbox.
Variable: Numeric.
Category: Text or Numeric; Must have the same number of data points as the Variable; Must contain 2 distinct categories.
Sample 1: Numeric.
Sample 2: Numeric.
Test mean difference: Numeric.
Confidence level: Numeric; Between 0 and 100.
Two call centres were involved in a study to evaluate the impact of a new system. The new system was deployed in call centre 2 while call centre 1 continues to use the existing system. You collected data on time (in minutes) to resolve a customer enquiry from these two call centres. Suppose you know that the variance between both call centres is different. You want to determine if there is any evidence that the difference in time resolve a customer enquiry between the two call centres is different from zero.
1. Open worksheet ProcessMA > Tools > Data Files > Sample.xls.
2. Choose ProcessMA > Basic Statistics > 2-Sample t.
3. In Data in, select a single column.
4. In Variable, select A – Time.
5. In Category, select B – Call Centre.
6. In Test mean difference, enter 0.
7. In Alternate, select Not equals.
8. In Confidence level, enter 95.
9. Uncheck Assume equal variances.
10. Check Plot boxplot.
11. Click OK.
Interpretation
For a desired a = 0.05, since p = 0 < a, we will reject H0. Therefore, we conclude that there is significant evidence that the difference in time to resolve a customer enquiry between the two call centres is not equals to 0.