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T-test question

I have the following queries on the t-test,

1) Why with sample correlation the t-test formula is different from what we saw in Level-1 t-test formula? As we know, in Level-1 the t-test formula was (estimated value - hyphotesized values)/ std. error

2) Why with sample correlation the DF is n-2 here, while in Level-1 formula it was n-1?

3) Why DF is included in the formula itself here while in Level-1 we had to look up DF in the t Table?

Apprecite if someone can clarify. Many thanks in advance.

I don't think the formula is different....and I'm not clear on your DF question. Do you have a problem you can reference?

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The t-test you're referring to for level 2 is for testing the significance of the correlation coefficient. You obtain the t statistic through a different formula.

DF is n-2 instead of n-1 because you're estimating 2 parameters: the intercept (b0) and the slope coefficient (b1).

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