Example of a 2-Sample t with the Samples in one Columnmain topic interpreting results session command see also
Example of a 2-Sample t with the Samples in one ColumnA study was performed in order to evaluate the effectiveness of two devices for improving the efficiency of gas home-heating systems. Energy consumption in houses was measured after one of the two devices was installed. The two devices were an electric vent damper (Damper=1) and a thermally activated vent damper (Damper=2). The energy consumption data (BTU.In) are stacked in one column with a grouping column (Damper) containing identifiers or subscripts to denote the population. Suppose that you performed a variance test and found no evidence for variances being unequal (see Example of 2 Variances). Now you want to compare the effectiveness of these two devices by determining whether or not there is any evidence that the difference between the devices is different from zero.
1 Open the worksheet FURNACE.MTW.
2 Choose Stat > Basic Statistics > 2-Sample T.
3 Choose Both samples are in one column.
4 In Samples, enter 'BTU.In'.
5 In Sample IDs, enter Damper.
6 Click Options.
7 Check Assume equal variances.
8 Click OK in each dialog box.
Session window output
Two-Sample T-Test and CI: BTU.In, Damper
Two-sample T for BTU.In
Damper N Mean StDev SE Mean 1 40 9.91 3.02 0.48 2 50 10.14 2.77 0.39
Difference = μ (1) - μ (2) Estimate for difference: -0.235 95% CI for difference: (-1.450, 0.980) T-Test of difference = 0 (vs ≠): T-Value = -0.38 P-Value = 0.701 DF = 88 Both use Pooled StDev = 2.8818 |
Minitab displays a table of the sample sizes, sample means, standard deviations, and standard errors for the two samples.
Since we previously found no evidence for variances being unequal, we chose to use the pooled standard deviation by choosing Assume equal variances. The pooled standard deviation, 2.8818, is used to calculate the test statistic and the confidence intervals.
A second table gives a confidence interval for the difference in population means. For this example, a 95% confidence interval is (-1.450, 0.980) which includes zero, thus suggesting that there is no difference. Next is the hypothesis test result. The test statistic is -0.38, with p-value of 0.701, and 88 degrees of freedom.
Since the p-value is greater than commonly chosen a-levels, there is no evidence for a difference in energy use when using an electric vent damper versus a thermally activated vent damper.