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Two-Way ANOVA01:17

Two-Way ANOVA

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The two-way ANOVA is an extension of the one-way ANOVA. It is a statistical test performed on three or more samples categorized by two factors - a row factor and a column factor. Ronald Fischer mentioned it in 1925 in his book 'Statistical Methods for Researchers.'
The two-way ANOVA analysis initially begins by stating the null hypothesis that there is an interaction effect between the two factors of a dataset. This effect can be visualized using line segments formed by joining the...
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Sign Test for Matched Pairs01:17

Sign Test for Matched Pairs

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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.
To conduct the sign test, we first calculate the differences in...
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Goodness-of-Fit Test01:16

Goodness-of-Fit Test

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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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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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Hypothesis Test for Test of Independence01:16

Hypothesis Test for Test of Independence

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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:
H0: The two variables (factors)...
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Introduction to Test of Independence01:21

Introduction to Test of Independence

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In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their individual probabilities. Tests of independence are chi-square tests involving the use of a contingency table of observed (data) values.
The test statistic for a test of independence is similar to that of a goodness-of-fit test:
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Related Experiment Video

Updated: Sep 6, 2025

Author Spotlight: Validation of SICOLE-R for Assessing Cognitive and Reading Skills in Spanish-Speaking Children and Its Role in Personalized Education
09:00

Author Spotlight: Validation of SICOLE-R for Assessing Cognitive and Reading Skills in Spanish-Speaking Children and Its Role in Personalized Education

Published on: August 16, 2024

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Negligible interaction test for continuous predictors.

Yasaman Jabbari1, Robert Cribbie2

  • 1Department of Psychology, Neuroscience & Behaviour, McMaster University, Hamilton, Canada.

Journal of Applied Statistics
|June 27, 2022
PubMed
Summary
This summary is machine-generated.

Researchers can now test for negligible interactions between continuous predictors using equivalence testing. This method is more appropriate than traditional null hypothesis tests for demonstrating small, meaningful effects in behavioral science research.

Keywords:
Moderationinteractionlinear modelsmultiple regressionnegligible interaction

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Area of Science:

  • Behavioral Science
  • Psychology
  • Statistics

Background:

  • Researchers often need to test for negligible interactions between continuous predictors.
  • Traditional null hypothesis tests are ill-suited for demonstrating small, meaningful effects due to sample size sensitivity and hypothesis setup.

Purpose of the Study:

  • To investigate a method for testing negligible interaction effects between continuous predictors.
  • To compare equivalence testing with traditional association-based null hypothesis tests.

Main Methods:

  • Utilized unstandardized and standardized regression-based models.
  • Employed equivalence testing.
  • Conducted a Monte Carlo simulation study.

Main Results:

  • Equivalence testing demonstrated effectiveness in identifying negligible interaction effects.
  • The proposed method proved more suitable than traditional approaches for this research question.

Conclusions:

  • Equivalence testing offers a superior approach for assessing negligible interactions in behavioral science.
  • This method provides a more appropriate framework for researchers aiming to demonstrate consistency in predictor effects.