Question

The numerator and denominator of a t-test (and z-test) have interpretable meanings. Thus, the ratio of these two numbers – the t-

statistic – has a meaning. If my t-statistic equals three, what does the three mean? [ I know it means reject the null hypothesis. Rather,

what is three times the size of what?] We are not looking for anything complex.

Answer 1

let me short it down for you.

The numerator of a t-test is which indicates the strength where is the mean of the sample and is the hypothesized mean. That is, if mean is 6 and the hypothesized mean is 3 then the strength is 3.

The denominator means the variation which is where s tells us how much the data variates and basically helps us to tell the average of the variations where n is the sample size. And together this denominator tells us the standard error.

Now let us come to your question i.e. what does the ratio mean ?

Taking your example if t-statistic value comes out to be 3 then it means the difference i.e. the numerator is 3 times the size of the standard error.