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Hypothesis Test for Test of Independence

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)...

Introduction to Test of Independence

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:

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Testing different thresholds for risky episodic drinking--what's so special about five drinks?

Michael Livingston¹

¹Drug Policy Modelling Program, National Drug and Alcohol Research Centre, University of New South Wales, Australia; Centre for Alcohol Policy Research, Turning Point Alcohol and Drug Centre, Australia.

Drug and Alcohol Dependence

|June 4, 2013

Summary

This study suggests that lower thresholds for defining risky drinking, specifically seven or fewer drinks, better predict negative outcomes across the population. These findings support using lower thresholds to identify at-risk individuals and mitigate public health consequences.

Keywords:

Alcohol Drinking guidelines Drinking thresholds Episodic drinking Risky drinking

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Area of Science:

Public Health
Epidemiology
Substance Use Research

Background:

Episodic drinking studies often use a threshold of five or more standard drinks, but its appropriateness outside US college settings is under-researched.
Standard drink definitions vary, impacting the consistency of risky drinking measures.
Limited research exists on alternative thresholds for defining risky drinking and their predictive validity.

Purpose of the Study:

To evaluate fifteen different risky drinking thresholds.
To determine which definitions of risky drinking best predict negative outcomes.
To assess the appropriateness of varying risky drinking definitions in a national sample.

Main Methods:

Analysis of a national survey sample of 19,757 drinkers.
Assessment of threshold appropriateness using risk-curves, specificity, and sensitivity analyses.
Evaluation of threshold performance in multivariate logistic regression models predicting negative outcomes and risky behaviors.

Main Results:

The optimal risky drinking threshold varied depending on the analytical approach and outcome type.
Thresholds of seven or fewer drinks consistently outperformed higher thresholds across all analyses.
Lower thresholds demonstrated better predictive performance for population-level risk.

Conclusions:

Findings support the continued use of relatively low thresholds for defining risky drinking.
While individual risks may peak at higher consumption levels, population-level risk is highest at lower thresholds.
Lower thresholds are effective in identifying at-risk populations and informing public health strategies.