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Related Concept Videos

Statistical Hypothesis Testing01:16

Statistical Hypothesis Testing

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.
Statistical significance measures the probability that an observed result occurred by chance. If this probability, known as...
Types of Hypothesis Testing01:11

Types of Hypothesis Testing

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 ≠ 0.5.
Accuracy and Errors in Hypothesis Testing01:13

Accuracy and Errors in Hypothesis Testing

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.
In hypothesis testing, the probability of making a Type I error, denoted as α, is commonly set at 0.05. This significance level indicates a 5% chance...
What is a Hypothesis?01:14

What is a Hypothesis?

A hypothesis can be a simple sentence or statement about a property or any phenomenon observed or predicted for a population. It is usually a claim about a  property of the population. It can be stated for any field observations or experiments. A hypothesis statement cannot be said to be right or wrong as it is merely a statement. It needs to be tested through an elaborate data collection process and an appropriate statistical test. A hypothesis should be a general but not a vague statement. It...
Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data01:16

Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data

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, comparing...
Errors In Hypothesis Tests01:14

Errors In Hypothesis Tests

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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Related Experiment Video

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A User-friendly and Powerful R Analysis of Large-scale Datasets
10:56

A User-friendly and Powerful R Analysis of Large-scale Datasets

Published on: November 4, 2025

Repeated hypothesis testing on a growing data set.

G V Trunk1, J O Coleman

  • 1Radar Analysis Branch, Radar Division, Naval Research Laboratory, Washington, DC 20375.

IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 27, 2011
PubMed
Summary

Repeatedly testing hypotheses with accumulating data increases the risk of falsely rejecting the true null hypothesis. This occurs even when the hypothesis is correct, especially with an infinite number of tests.

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Area of Science:

  • Statistics
  • Statistical inference
  • Hypothesis testing

Background:

  • Hypothesis testing is frequently performed as new data become available over extended periods.
  • Sequential analysis and repeated significance testing are common in longitudinal studies.

Purpose of the Study:

  • To investigate the behavior of hypothesis testing when conducted repeatedly on accumulating data.
  • To determine the probability of rejecting a true null hypothesis in sequential testing scenarios.

Main Methods:

  • Mathematical analysis of hypothesis testing procedures.
  • Demonstration for a specific case and generalization to a broader class of problems.

Main Results:

  • It is proven that the true simple null hypothesis will eventually be rejected if testing continues indefinitely on all accumulated data.
  • This rejection occurs even when the null hypothesis is true.

Conclusions:

  • Repeated hypothesis testing on cumulative data, as the number of tests approaches infinity, leads to the rejection of a true simple null hypothesis.
  • This conclusion is conjectured to apply to most relevant problems involving simple null hypotheses.