Re: interpreting sign of t-value

On 10/15/2006 10:39 AM, nymphnode wrote:
Hi,

If you did a t-test against the null hypothesis involving the beta
coefficients from a multilinear regression analysis, how would you
interpret the sign of the t-value?

The t-value is the statistic used to test whether or not the regression coefficient (I think that's what you mean by beta coefficient) is equal to the hypothesized value. A negative t-value indicates the regression coefficient is LESS THAN the hypothesized value.

We usually run a t-test against the null hypothesis on another measure
and interpret the sign of the t-value as whether the measure
positively/negatively correlated with our variable. However, if the
sign of the beta coefficients already tell us whether the correlation
is negative/positive, what does the sign of the t-value from a t-test
involving it mean?

Under certain assumptions, your statement about "the sign of the t-value as whether the measure positively/negatively correlated with our variable" is correct. Under other assumptions, this would be incorrect.

The standard regression output from statistical packages WHEN THERE IS ONLY ONE PREDICTOR VARIABLE tests the null hypothesis that the regression coefficient is equal to zero. If that is what you are testing, then this is an equivalent way to test that the correlations are positive or negative. If you are testing a null hypothesis that the regression coefficient is equal to some other value (a non-zero value), OR IF YOU HAVE MULTIPLE PREDICTOR VARIABLES (which is what I think you mean by "multilinear"), then your statement is incorrect, and the interpretation would be as I explained in my first paragraph at the top of this reply.

Don't use t-test values to tell you about correlation. Use them to tell you if the regression coefficient is statistically different from (and above or below) the hypothesized value.

--
Paige Miller
pmiller5@xxxxxxxxxxxxxxxx

It's nothing until I call it -- Bill Klem, NL Umpire
If you get the choice to sit it out or dance,
I hope you dance -- Lee Ann Womack
.

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