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F-Test for Linear Relationship

abdulj

Community Trekker

Joined:

Jul 12, 2011

Hello

I'm trying to perform an f-test to check if there is a linear relationship between 2 continous variables at the 0.1 level. I've done Fit Y by X -> Fit Line and have my answer of Prob > F = < 0.001. However when I change the alpha level under the linear fit level none of the numbers change. Am I doing something wrong because I thought the ANOVA results should change as alpha changes.

Thanks

1 ACCEPTED SOLUTION

Accepted Solutions
Solution

Alpha does not influence the calculation of F and hence not the p-value. It is true that the critical F-value (used in a hypotheses test) changes with alpha but not the estimated F that is compared with the critical F. 

However, if you enable "Confid curve fit" you can see how the confidence bands narrow or widen as alpha is changed.

5 REPLIES
Solution

Alpha does not influence the calculation of F and hence not the p-value. It is true that the critical F-value (used in a hypotheses test) changes with alpha but not the estimated F that is compared with the critical F. 

However, if you enable "Confid curve fit" you can see how the confidence bands narrow or widen as alpha is changed.

abdulj

Community Trekker

Joined:

Jul 12, 2011

Thanks.

Quick question, how would I be able to find the critical F value in a hypothesis test?

ms

Super User

Joined:

Jun 23, 2011

The traditional way is to look it up in a table. In JMP there is a function F Quantile( ) that return F for a given p and the two-dimensional degrees of freedom.

For linear regression with two variables, 20 observations and alpha = 0.1 you use the formula

Fcrit = F quantile(0.9, 1, 18);

Show(Fcrit)

    

Fcrit = 3,00697659179545;

If your F exceeds this Fcrit you can reject the null hypotheses at a the chosen sign level. However you already knew that if you got p < 0,001. In these days with software that calculates the actual p-value for you, critical values is not used as much as before. At least not explicitly.

abdulj

Community Trekker

Joined:

Jul 12, 2011

Great thanks.

Just to double check I understand everything here, since p<0.001 we reject the null hypothesis that that data is not linear and accept the alternative hypothesis that there is in fact a linear relationship, right?

ms

Super User

Joined:

Jun 23, 2011

Well, we do actually not test if the relationship is linear. Linearity is our assumption when using this type of test. The relationship may still be nonlinear, even if p < 0.001. A quick way to identify nonlinearity is to look for any patterns in the residuals.

With a  p<0.001 we can with quite good certainty reject a null hypthesis of slope being zero, i.e. we have a strong (and statistically significant) indication of a positive relationship between x and y. But remember that linear regression by itself cannot "prove" anything in terms of causality. For that we use our scientific understanding of the process (x effects y?  y effects x? Or are there other factors that can influence both).