Saturday, December 18, 2010

Finding the p value in t-tests


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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