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Related Concept Videos

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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Hypothesis Test for Test of Independence01:16

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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:
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Contingency Table01:29

Contingency Table

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A contingency table provides a way of portraying data that can facilitate calculating probabilities. It is a method of displaying a frequency distribution as a table with rows and columns to show how two variables may be dependent (contingent) upon each other; The table helps determine conditional probabilities quite quickly and can help systematically organize, analyze and quantify data. The table displays sample values concerning two variables that may be dependent or contingent on one...
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Determination of Expected Frequency01:08

Determination of Expected Frequency

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Suppose one wants to test independence between the two variables of a contingency table. The values in the table constitute the observed frequencies of the dataset. But how does one determine the expected frequency of the dataset? One of the important assumptions is that the two variables are independent, which means the variables do not influence each other. For independent variables, the statistical probability of any event involving both variables is calculated by multiplying the individual...
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Test for Homogeneity01:23

Test for Homogeneity

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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...
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Friedman Two-way Analysis of Variance by Ranks01:21

Friedman Two-way Analysis of Variance by Ranks

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Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures...
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Testing for independence in J×K contingency tables with complex sample survey data.

Stuart R Lipsitz1, Garrett M Fitzmaurice2, Debajyoti Sinha3

  • 1Brigham and Women's Hospital, Boston, Massachusetts 02115, U.S.A.

Biometrics
|March 13, 2015
PubMed
Summary
This summary is machine-generated.

New statistical tests for independence in contingency tables overcome limitations of existing methods, especially for complex survey data. These novel Wald and score tests always exist, unlike the Rao-Scott test, and show promise for analyzing real-world health data.

Keywords:
Chi-squared testNationwide Inpatient SampleScore statisticWald statisticWeighted estimating equations

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Area of Science:

  • Statistics
  • Survey Methodology
  • Biostatistics

Background:

  • The independence test for contingency tables is crucial in various fields.
  • Standard Pearson chi-squared tests are unsuitable for complex survey samples due to intra-cluster correlation.
  • The Rao-Scott test adjusts for complex survey designs but fails with zero cell counts.

Purpose of the Study:

  • To propose novel Wald and score test statistics for assessing independence in contingency tables.
  • To address the limitation of the Rao-Scott test which fails when observed cell counts are zero.
  • To provide robust statistical methods for analyzing complex survey data, particularly in healthcare.

Main Methods:

  • Development of Wald and score test statistics using weighted least squares estimating equations.
  • Comparison of proposed methods with the Rao-Scott test through simulations.
  • Application of the proposed methods to post-surgical complication data from the Nationwide Inpatient Sample (NIS).

Main Results:

  • The proposed Wald and score test statistics for independence are always defined, even with zero cell counts.
  • Simulation studies indicate the score test exhibits superior performance regarding type I error control.
  • The methods are successfully applied to analyze complex hospital survey data on post-surgical complications.

Conclusions:

  • The proposed Wald and score tests offer a reliable alternative to the Rao-Scott test for independence in contingency tables with complex survey data.
  • The score test demonstrates excellent performance in simulations, making it a valuable tool for statistical analysis.
  • These new methods enhance the analysis of health-related survey data, addressing limitations of previous approaches.