MATLAB: CoefTest and one tailed T-test

f-testgeneralizedlinearmodelone-tailed t testStatistics and Machine Learning Toolboxstatistics toolbox

Dear all,
I have fitted a linear model to my data as follows: Var6 ~ 1 + groupVar1 +groupVar2 + groupVar3 +Var4 + Var5
the first 3 variables are dummy variables for the three groups that I have, and I aim to compare groups using GeneralizedLinearModel.fit and adjusting for nuisance variables. Using coefTest with this contrast I get the f statistic of "any group different from zero" while controlling for Var4 and Var5: [0 1 0 0 0 0;0 0 1 0 0 0;0 0 0 1 0 0] and I get a p value, and so on. However, when it comes to one tail t tests for the following two contrasts I get the same significant p value for which does not make sense to me:
contrast 2:Group1 >Group2 coefTest(m, [0 1 -1 0 0 0]) contrast 3:Group2 >Group1 coefTest (m, [0 -1 1 0 0 0])
It would be great if someone could let me know where I'm getting this wrong, as there is no way for a group to be greater and lesser than another group at the same time.
-Arman

Best Answer

You are right that the result from coefTest is an F-test. There is no built-in way to carry out a one-sided t test.
Here are some commands to reproduce the calculations for the t statistic and its p-value as they appear int the coefficient table:
load carsmall
d = dataset(MPG,Weight);
d.Year = ordinal(Model_Year);
glm = GeneralizedLinearModel.fit(d,'MPG ~ Year + Weight + Weight^2')
glm.Coefficients.Estimate(3)
glm.Coefficients.Estimate(3)/sqrt(glm.CoefficientCovariance(3,3))
2*(1 - tcdf(glm.Coefficients.Estimate(3)/sqrt(glm.CoefficientCovariance(3,3)),glm.DFE))
You could compute a contrast among the coefficients (instead of just taking the third one as I did), use the covariance matrix to compute the variance of this contrast, and so on. Then you could pick the desired tail of the t distribution.
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