Hi: I had a question about how to interpret the t test statistic. For example, for question 6 in the homework (question 6, chapter 11 from pagano and gauvreau) it asks to test the null hypothesis that the mean blood levels of DDE are identical for women with breast cancer and for healthy controls. If you input the mean difference as 2.7 (and SD 15.9), you get a positive t statistic of 2.22. If you put in a mean difference of -2.7, you get a negative t statistic of -2.22. This makes sense to me. However, when you calculate the p values using a two-sided t test (i.e. 2*ttail) the p values are very different! If anyone has a straight forward explanation for why that is it would be much appreciated! (I am not very good at math :) )
Hi, good question. When you have a negative t statistic you have to either use:
1-ttail(df, tstat)
or
ttail(df,-tstat)
You are looking for the probability of getting a t-statistic as extreme (different from 0) as you did, so if the t-statistic is negative you are looking at the left tail. Of course if it is a 2-sided test you need to multiply your answer by 2.
In this question, the wording is that the difference for breast cancer patient and their matched control is +2.7. Doesn't this mean that levels are higher in the breast cancer patients? Therefore you would use the positive t-statistic?