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When performing a hypothesis test, there are four possible outcomes depending on the actual truth (or falseness) of the null hypothesis and the decision to reject or not.
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Accuracy and Errors in Hypothesis Testing01:13

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Hypothesis testing is a fundamental statistical tool that begins with the assumption that the null hypothesis H0 is true. During this process, two types of errors can occur: Type I and Type II. A Type I error refers to the incorrect rejection of a true null hypothesis, while a Type II error involves the failure to reject a false null hypothesis.
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Statistical inference techniques, paramount in hypothesis testing, differentiate into two broad categories: parametric and nonparametric statistics.
Parametric statistics, as the name suggests, assumes that data follow a specific distribution, often a normal distribution. This assumption enables robust hypothesis testing and estimation. Parametric methods, like the Student's t-test or Goodness-of-fit test, are frequently employed in biostatistics due to their robustness. For instance,...
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When one or more data points appear far from the rest of the data, there is a need to determine whether they are outliers and whether they should be eliminated from the data set to ensure an accurate representation of the measured value. In many cases, outliers arise from gross errors (or human errors) and do not accurately reflect the underlying phenomenon. In some cases, however, these apparent outliers reflect true phenomenological differences. In these cases, we can use statistical methods...
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Once data is collected from both the experimental and the control groups, a statistical analysis is conducted to find out if there are meaningful differences between the two groups. A statistical analysis determines how likely any difference found is due to chance (and thus not meaningful). In psychology, group differences are considered meaningful, or significant, if the odds that these differences occurred by chance alone are 5 percent or less. Stated another way, if we repeated this...
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Hypothesis testing is a critical statistical procedure facilitating informed, evidence-based decisions. It begins with a hypothesis, which is a tentative explanation, or a prediction about a population parameter. This hypothesis can be either a null hypothesis (H0), indicating no effect or difference, or an alternative hypothesis (Ha), suggesting an effect or difference.
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Related Experiment Video

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The Power of Interstimulus Interval for the Assessment of Temporal Processing in Rodents
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Inappropriate use of statistical power.

Raphael A Fraser1

  • 1Medical College of Wisconsin, Milwaukee, WI, USA. raphael.fraser@gmail.com.

Bone Marrow Transplantation
|March 3, 2023
PubMed
Summary

This article warns against misusing statistical power calculations after studies conclude. Post hoc power analysis is discouraged, as p-values already account for study power, preventing misinterpretation of null hypothesis results.

Area of Science:

  • Statistics in Medicine
  • Clinical Trial Methodology
  • Biostatistics

Background:

  • Discusses the inappropriate use of statistical analyses, particularly post hoc power calculations, after study completion.
  • Highlights the common misinterpretation of negative study conclusions and the incorrect belief that high observed power supports the null hypothesis.

Discussion:

  • Explains that failure to reject the null hypothesis does not equate to its truth, emphasizing insufficient evidence.
  • Uses analogies like jury trials and boxing to illustrate hypothesis testing principles.
  • Addresses the distinction between frequentist confidence intervals and Bayesian credibility limits, noting common misinterpretations of confidence intervals.

Key Insights:

  • Post hoc power calculations should not be used to interpret negative study results.

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  • Observed power is inherently incorporated within the p-value calculation.
  • Misinterpretation of confidence intervals is prevalent; they do not represent the probability of containing the true parameter.

    • Outlook:

    • Aims to eliminate imprecise statements like 'trend towards' or 'failed to detect benefit due to small sample size' from scientific publications.
    • Encourages rigorous statistical interpretation and reporting in medical research.
    • Promotes a clearer understanding of statistical concepts among researchers and reviewers.