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Related Concept Videos

Fisher's Exact Test01:08

Fisher's Exact Test

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Fisher's exact test is a statistical significance test widely used to analyze 2x2 contingency tables, particularly in situations where sample sizes are small. Unlike the chi-squared test, which approximates P-values and assumes minimum expected frequencies of at least five in each cell, Fisher's exact test calculates the exact probability (P-value) of observing the data or more extreme results under the null hypothesis. This feature makes it especially valuable when the assumptions of...
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P-value01:10

P-value

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P-value is one of the most crucial concepts in statistics.
P-value stands for the probability value.  P-value is the probability that, if the null hypothesis is true, the results from another randomly selected sample will be as extreme or more extreme as the results obtained from the given sample.
A large P-value calculated from the data indicates to  not reject the null hypothesis. But a higher P-value does not mean that the null hypothesis is true. The smaller the P-value, the more...
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Behrens–Fisher Test00:57

Behrens–Fisher Test

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The Behrens-Fisher test is a statistical method designed to address the Behrens-Fisher problem, which arises when comparing the means of two normally distributed populations with unequal variances. Unlike the Student's t-test, which assumes equal variances, the Behrens-Fisher test allows for mean comparison without this restrictive assumption. This flexibility makes it particularly valuable in scenarios where two independent samples exhibit normality but lack variance homogeneity.
This test...
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Decision Making: P-value Method01:09

Decision Making: P-value Method

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The process of hypothesis testing based on the P-value method includes calculating the P- value using the sample data and interpreting it.
First, a specific claim about the population parameter is proposed. The claim is based on the research question and is stated in a simple form. Further, an opposing statement to the claim  is also stated. These statements can act as null and alternative hypotheses:  a null hypothesis would be a neutral statement while the alternative hypothesis can...
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F Distribution01:19

F Distribution

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The F distribution was named after Sir Ronald Fisher, an English statistician. The F statistic is a ratio (a fraction) with two sets of degrees of freedom; one for the numerator and one for the denominator. The F distribution is derived from the Student's t distribution. The values of the F distribution are squares of the corresponding values of the t distribution. One-Way ANOVA expands the t test for comparing more than two groups. The scope of that derivation is beyond the level of this...
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Wald-Wolfowitz Runs Test II01:17

Wald-Wolfowitz Runs Test II

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The Wald-Wolfowitz runs test, commonly referred to as the runs test, is a nonparametric test used to assess the randomness of ordered data. The test evaluates the number of runs, which are consecutive sequences of similar elements within the data. If the number of runs is significantly higher or lower than expected, the data is considered non-random, indicating a detectable pattern or structure.
For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and 0s. In...
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Updated: Dec 14, 2025

Combined Immunofluorescence and DNA FISH on 3D-preserved Interphase Nuclei to Study Changes in 3D Nuclear Organization
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When possible, report a Fisher-exact P value and display its underlying null randomization distribution.

M-A C Bind1, D B Rubin2,3

  • 1Department of Statistics, Faculty of Arts and Sciences, Harvard University, Cambridge, MA 02138; ma.bind@mail.harvard.edu.

Proceedings of the National Academy of Sciences of the United States of America
|July 25, 2020
PubMed
Summary
This summary is machine-generated.

Fisher-exact P values are recommended over asymptotic P values in randomized experiments. They use the actual randomization procedure, avoiding irrelevant assumptions and revealing deeper scientific insights, especially in small studies.

Keywords:
Fisher-exact P valuesasymptotic P valuescrossover randomized experimentsrandomization-based inferencesensitivity analyses

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Area of Science:

  • Statistics
  • Biostatistics
  • Experimental Design

Background:

  • Asymptotic P values are commonly reported in randomized experiments.
  • Asymptotic P values can introduce irrelevant distributional assumptions, altering the research question.
  • The Fisherian framework offers an alternative P value calculation based on the randomization procedure.

Purpose of the Study:

  • To illustrate the Fisherian statistical framework in a crossover randomized experiment.
  • To compare Fisher-exact P values with asymptotic P values for evaluating experimental results.
  • To highlight the importance of the null randomization distribution in interpreting study outcomes.

Main Methods:

  • Analysis of a crossover randomized experiment, considering the first period independently and then both periods.
  • Focus on 10 outcomes to demonstrate differences between asymptotic and Fisher tests.
  • Application of the Fisherian framework using the actual randomization procedure.

Main Results:

  • For some outcomes, asymptotic P values were substantially lower than minimum attainable Fisher-exact P values.
  • For other outcomes, the Fisher-exact null randomization distribution significantly differed from the assumed bell-shaped distribution.
  • Differences highlight the impact of distributional assumptions in traditional P value calculations.

Conclusions:

  • Fisher-exact P values should be preferred in randomized experiments, particularly for small sample sizes.
  • Examining the shape of the null randomization distribution can yield valuable scientific insights.
  • Using Fisher-exact P values ensures the P value directly addresses the question posed by the randomization procedure.