Related Experiment Video
Updated: Mar 7, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
The likelihood ratio test for the Hill model
1a Department of Biostatistics , Pfizer , Cambridge , Massachusetts.
Abstract:
The Hill model is used to describe many biological phenomena to specify the dose-response relationship in clinical trials and other applications. When testing the null hypothesis of no curve versus the Hill model, the likelihood ratio test (LRT) does not exhibit the appropriate Type I error rate. We describe the reason for the failure of the LRT and then proceed to show that a chi-squared approximation with about 1.6 degrees of freedom works well. We then extend the results to analyses of data from published literature.
Related Concept Videos
Types of Hypothesis Testing
When the null and alternative hypotheses are stated, it is observed that the null hypothesis is a neutral statement against which the alternative hypothesis is tested. The alternative hypothesis is a claim that instead has a certain direction. If the null hypothesis claims that p = 0.5, the alternative hypothesis would be an opposing statement to this and can be put either p > 0.5, p < 0.5, or p...
Expected Frequencies in Goodness-of-Fit Tests
Goodness-of-Fit Test
Sign Test for Matched Pairs
To conduct the sign test, we first calculate the differences in...
Hypothesis Test for Test of Independence
H0: The two variables (factors)...
Hazard Ratio
For example, in a clinical trial...

