P-Value, Degrees of Freedom, and Test Statistic: Differences

The difference between the P-Value, Degrees of Freedom, and Test Statistic value.

Is the Test value different in T-Test of equal variance to that of unequal variance?

• The tests statistic is the t score itself.
• The Degrees of Freedom is a characteristic of the sample.
• Degrees of Freedom = n - 1
• The P-Value is the Probability.

Here ya go...

If my Degrees of Freedom were 10, and the P-Value, let’s assume is 0.55,  and Test value statistic was 0.65, using a T-Test assuming equal variances, shouldn’t these figures also be the same in a T-Test assuming unequal variances? Hmmm...let's see.

Using the same exact data on one T-Test (of equal variances) on the other T-Test (of unequal variances), the formulas for both T-Tests are identically the same for Degrees of Freedom, P-Value, and test value, except for the pooled variance in (equal variances).

So, why are the figures for Degrees of Freedom, P-Value, and test value different in T-Test of equal variance from a T-Test of unequal variance? And why do the Degrees of Freedom change, and the P-Values different by about 0.004 through 0.020 (not much but it is still a difference), and test values different by about 0.01.

• The uncertainty is always greater when the “variances are not equal,” therefore resulting in why these variances see different results.

Are you still confused as to which calculation you should run for the various differences?

Okay, to be on the safe side, always run both methods, the Critical Value and the P-Value.

• It helps by checking to see if your initial intent to reject or fail to reject the null is supported by both methods.
• If one method rejects and the other method fails to reject on the same problem, there's an error with the original computation or an error with the computation for one of the methods.
• It's ideal that both methods (critical value and P-Value), on the same problem, perform the same type of action, reject or fail to reject the null.
• The only type of problem where I don't see the P-Value being used is the Hypothesis Test for the Difference of Population Means with Paired Comparisons.

One issue that use to confuse me most was what type of P-Value Formula to use with the different types of Problems when the Test Statistic Value is either positive or negative.

To end my confusion, I developed a simple cheat sheet that has been a rather nifty tool in the world of statistics. It's pretty self explanatory, listing the different types of problems, and if your Test Statistic Value is either negative or positive in a T or Z test, it shows the type of formula to use. Hope it works for you. Here you go.