Testing for pairwise independence

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Updated: Aug 5, 2026

Combined Immunofluorescence and DNA FISH on 3D-preserved Interphase Nuclei to Study Changes in 3D Nuclear Organization
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Combined Immunofluorescence and DNA FISH on 3D-preserved Interphase Nuclei to Study Changes in 3D Nuclear Organization

Published on: February 3, 2013

M Haber

    Biometrics
    |June 1, 1986
    PubMed

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    Related Concept Videos

    Introduction to Test of Independence01:21

    Introduction to Test of Independence

    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:
    Hypothesis Test for Test of Independence01:16

    Hypothesis Test for Test of Independence

    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)...
    Test for Homogeneity01:23

    Test for Homogeneity

    The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to conclude whether two populations have the same distribution. To calculate the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. The hypotheses for the test for homogeneity can be stated as...
    Bonferroni Test01:10

    Bonferroni Test

    The Bonferroni test is a statistical test named after Carlo Emilio Bonferroni, an Italian mathematician best known for Bonferroni inequalities. This statistical test is a type of multiple comparison test to determine which means are different than the rest. Bonferroni test can minimize the Type 1 error by reducing the significance level alpha, which otherwise increases with sample pairs.
    The means of different samples are first paired in all possible combinations.
    The null hypothesis of the...
    Sign Test for Matched Pairs01:17

    Sign Test for Matched Pairs

    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 value between...
    Wilcoxon Signed-Ranks Test for Matched Pairs01:09

    Wilcoxon Signed-Ranks Test for Matched Pairs

    The Wilcoxon signed-rank test for matched pairs evaluates the null hypothesis by combining the ranks of differences with their signs. It essentially tests whether the median of the differences in a population of matched pairs is zero. Since the test incorporates more information than the sign test, it generally yields more trustable conclusions. This test also does not require the data to follow a normal distribution, but two conditions must be met for it to be applicable: (1) the data must...