The hypotheses that we have been working on for t-tests where there are two sample means drawn from two independent populations have all been two-tailed. It is perfectly possible to have a one-tailed test, but we haven’t learned that. So, when you look at the Excel output, you are interested only in the result for the two-tailed test. Excel provides a p value, as shown here.
| t-Test: Paired Two Sample for Means | ||
| | Current | Previous |
| Mean | 0.5468 | 0.3404 |
| Variance | 0.305139 | 0.276987 |
| Observations | 25 | 25 |
| Pearson Correlation | 0.880067 | |
| Hypothesized Mean Difference | 0 | |
| df | 24 | |
| t Stat | 3.889064 | |
| P(T<=t) one-tail | 0.000349 | |
| t Critical one-tail | 1.710882 | |
| P(T<=t) two-tail | 0.000697 | |
| t Critical two-tail | 2.063899 | |
This output was found by using a paired t-test, using the Earnings2005 data (you have the file). Because the p value for two-tailed is 0.000697, we reject the null hypothesis: p is smaller than 0.05. If we reject the null, we are saying that the two population means are not the same. So look at the top line of means, and you can see that ‘current’ is larger than ‘previous’.
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