Stats Question

[kemi]

Hi all

For a paired t-test, I understand the greater the magnitude of the t-value, the less likely it is to support the null hypothesis, and if it is closer to 0 it increases the chance of no mean difference. However, what exactly is considered a greater t-value? Is there some sort of scale or is it relative to the data? e.g, some results have yielded a t-value of 1.981. The p-value is 0.063. The sample size was 19. How would I interpret this? i.e. what is the degree of significance?

I'm not required to know the nitty gitty math stuff, just interpretation, any help would be greatly appreciated!

[RuiAce]

Well since you already have a \(p\)-value you can just work off that. If you assume the usual 95% cut-off (i.e. a 5%-level test), then you'd observe that \(0.063 > 0.05\) and thus not reject the null hypothesis.

If you don't need to know all the math stuff behind it then the \(p\)-value tells you all you need. You're correct in saying that "the greater the magnitude of the \(t\)-value, the less likely it is to support the null hypothesis" (i.e. reject). But the \(t\)-value (or really any test statistic) is directly linked to the \(p\)-value, and in general for the \(t\)-test, the higher the \(t\)-value is, the lower the \(p\)-value is.

In general, we assume the 95% cut-off to give us a concrete answer. If we did that in your case, we'd be inclined to accept the null. Alternatively, the \(p\)-value can be used in a vague sense like this:

- \( \ge 0.1\) - very little evidence against \(H_0\); you'd most likely accept
- \( \text{between 0.01 and 0.1} \) - some evidence against it, but it's really hard to say
- \( \text{between 0.001 and 0.01} \) - reasonable evidence against it
- \( < 0.001 \) - very strong against \(H_0\); you'd probably immediately reject \(H_0\)

(Apologies though, I'm reasonably rusty on this right now and also somewhat tired, so this might've read like garble. Feel free to ask more)

[kemi]

Thank you so much!!