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Related Concept Videos

Types of Hypothesis Testing01:11

Types of Hypothesis Testing

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There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed.
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...
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A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n)  to the number of categories (k).
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The goodness-of-fit test is a type of hypothesis test which determines whether the data "fits" a particular distribution. For example, one may suspect that some anonymous data may fit a binomial distribution. A chi-square test (meaning the distribution for the hypothesis test is chi-square) can be used to determine if there is a fit. The null and alternative hypotheses may be written in sentences or stated as equations or inequalities. The test statistic for a goodness-of-fit test is given as...
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The sign test for matched pairs offers a robust method for comparing two paired samples, often for the effects of an intervention in one of them. This method is very useful in situations where the underlying distribution of the data is unknown. The test compares two related samples—often pre- and post-treatment measurements on the same subjects—to determine if there are significant differences in their median values.
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The test of independence is a chi-square-based test used to determine whether two variables or factors are independent or dependent. This hypothesis test is used to examine the independence of the variables. One can construct two qualitative survey questions or experiments based on the variables in a contingency table. The goal is to see if the two variables are unrelated (independent) or related (dependent). The null and alternative hypotheses for this test are:
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The hazard ratio (HR) is a widely used measure in clinical trials to compare the risk of events, such as death or disease recurrence, between two groups over time. It reflects the ratio of hazard rates—the instantaneous risk of the event occurring—between a treatment group and a control group. This measure provides valuable insights into the relative effectiveness of a treatment by assessing how the risk of an event differs between the two groups.
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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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The likelihood ratio test for the Hill model.

Yifang Li1, Russell Reeve2

  • 1a Department of Biostatistics , Pfizer , Cambridge , Massachusetts.

Journal of Biopharmaceutical Statistics
|February 7, 2017
PubMed
Summary
This summary is machine-generated.

The likelihood ratio test (LRT) has issues with Type I error rates when assessing the Hill model for dose-response relationships. A chi-squared approximation with 1.6 degrees of freedom offers a more accurate solution for clinical trial data analysis.

Keywords:
Chi-squared processEmax modelMichaelis-Mentendose responselogistic modelmeta-analysisnonstandard conditionspsoriasis

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Area of Science:

  • Pharmacology and Toxicology
  • Biostatistics
  • Clinical Trial Design

Background:

  • The Hill model is a standard for characterizing dose-response relationships in biological and clinical studies.
  • Accurate statistical testing is crucial for reliable interpretation of dose-response data in clinical trials.
  • The likelihood ratio test (LRT) is commonly applied but may have limitations in specific contexts.

Purpose of the Study:

  • To identify the reasons for the failure of the likelihood ratio test (LRT) in the context of the Hill model.
  • To propose and validate a more accurate statistical method for testing the Hill model.
  • To evaluate the performance of the proposed method using existing literature data.

Main Methods:

  • Theoretical analysis to explain the LRT's Type I error rate issues with the Hill model.
  • Development and application of a chi-squared approximation with approximately 1.6 degrees of freedom.
  • Validation of the chi-squared approximation by analyzing published dose-response data.

Main Results:

  • The LRT demonstrates an inappropriate Type I error rate when testing the null hypothesis against the Hill model.
  • A chi-squared approximation with approximately 1.6 degrees of freedom provides a well-performing alternative.
  • The proposed method shows good performance when applied to real-world data from published studies.

Conclusions:

  • The standard LRT is unreliable for assessing the Hill model due to incorrect Type I error rates.
  • The chi-squared approximation with ~1.6 degrees of freedom is a statistically sound and practical alternative.
  • This improved statistical approach enhances the analysis of dose-response data in various scientific applications.