For question 14c, we are just looking for the p-value of the statistical test (t-test, in this case). Every test statistic has a corresponding probability or p-value. This value is the probability that the observed statistic occurred by chance alone.
To interpret this p-value, you would need to know what your pre-specified null hypothesis ("H0") and alpha (one-tailed or two-tailed tests, see below) are. The alpha value gives us the probability of a type I error, which occur when we reject a null hypothesis that is actually true.
- Pr(|T| > |t|)- This is the two-tailed p-value computed using the t distribution. It is the probability of observing a greater absolute value of t under the null hypothesis. If the p-value is less than the pre-specified alpha level (usually .05, but can theoretically be any number) we will conclude that mean difference in age between those with any calcification and those without calcification is statistically significantly different from zero.
- Pr(T < t), Pr(T > t)- These are the one-tailed p-values for evaluating the alternatives (mean diff < H0 value) and (mean diff > H0 value), respectively. Again, if the p-value is less than the pre-specified alpha level (usually .05) we will conclude that mean difference is statistically significantly greater than or less than zero. The mean difference in your Stata output is defined as diff = mean(0) - mean(1).
For question 16a, the probability for the association between "haircolor_fake" and age can be found in your Stata output under "Prob>F". This p-value is associated with the F-statistical test used in ANOVA to test the null hypothesis that the mean age across all hair color categories are the same.
The "Prob>chi2" is the p-value associated with the Bartlett's test, a test of the null hypothesis that the variance (SD) of age is the same across hair color categories.