# t-Test:. t-value has to be greater than critical t-value to be statistically significant?

I have a doubt related to some calculation a statistician performed

I compared the increases in a Serum Hormone due to two different therapies X and Y. The results I got are in the table. The statistician who provided the data says there is a statistical difference between the two sample.

However, even if my P is < than 0.05. as far as I know the "critical t-value" is the minimum t-value I need in order to have P < 0.05. So If my t-value is smaller than my critical t-value, then my result will be not significant.

Am I right ?

• Your table doesn't show the sample size. This is important because it determines the degrees of freedom for the t test. – Michael R. Chernick Apr 11 '17 at 14:13
• @Michael The second and third lines of statistics show us the sample size is between $146$ and $167$, because those values (minus one) are the degrees of freedom for which a two-tailed $t$ statistic of $-2.7536$ yields a p-value of $0.0066$. The critical value of $1.9749$ strongly suggests the df is $160$, telling us the sample size is $161$. Regardless, all the information to answer this question is available: the sample size is not needed. – whuber Apr 11 '17 at 16:55

You then have $|-2.7536| = 2.7536 > 1.9749$, which would lead you to reject, just as you have with the p-value.