Fit Y by X platform: how to check if a slope is something different than zero?

[#1]

The Fit Y by X platform has good options for doing linear regression. The resulting box shows the p-value of the intercept and slope compared to zero.

Is there a way to quickly assess whether the slope/intercept values are statistically close to a theoretical value that is non-zero? E.g. I know that the slope is supposed to be 15.0 and would like to see if the estimated value is close (enough) to that value.

(JMP 16)

[#2]

One approach could be to examine a confidence interval wrt to the parameter estimate in question. However your threshold for 'close enough' is up to you. A default value could be a 95% confidence interval...but ultimately the choice of alpha is up to you.

Note the above is not an equivalence test or hypothesis test wrt to some value other than zero. So it's not a foolproof way to determine if the parameter estimate in question is equal to some stated value...but it can give you an idea.

[#3]

Hi @robhanssen ,

not sure about the Fit Y by X platform. why not use the Fit model Platform instead? there, there are the "custom test" option. is that what you are looking for?

[#4]

The custom test only takes particular combinations of slope and intercept as parameters and calculates the p-value for the combo. In principle, this comes close but the intercept value doesn't come out of the theoretical expectation, so I don't have an estimate for it.

[#5 · Accepted solution]

The previous suggestions are appropriate when your goal is to claim that the slope is different than 15.0. That claim is represented by the alternative hypothesis. You reject the null hypothesis (slope = 15.0) if the evidence in your sample is strong enough (p-value less than alpha). Hypothesis tests are unidirectional. Failing to reject the null does not provide any evidence in favor of the null.

Your goal, in fact, is to claim that the slope is the same as 15.0, so that is your alternative hypothesis. (The null is that the slope is not 15.0.) You need a test for equivalence, not a test for difference. You need two one-sided t-tests. One test where the alternative is that the slope is greater than a lower bound and another test that the slope is less than an upper bound. The bounds are 15.0 plus or minus the margin in which you consider the slope practically equivalent to 15.0. Both tests must be significant to reject the null and claim equivalence.

JMP is adding equivalence tests. Unfortunately, there is no equivalence test for slope in Bivariate at this time.

[#6]

Thanks for the information. I'd certainly appreciate equivalence tests in newer versions.