# Analysis of Chi-squared and logistic Regression Tests

Review the article "Prevalence and Characteristics of Hazardous Drinkers: Results of the Greater Milwaukee Survey" by Lisa K. Berger, PhD; Michael Fendrich, PhD; and Adam Lippert, MA found in the Wisconsin Medical Journal 2007, Volume 106, Number 7.

1. Were the chi-square and regression tests presented and used correctly?

2. Could the authors' analysis be recreated?

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#### Solution Preview

The Chi squared test (X2 test) for independence (sometimes called the Pearson chi squared test) tests the association (connection) between two categorical variables.

The Null hypothesis H0 is that the one categorical variable does not affect the other categorical variable and thus they are independent (not associated).

With the alternative hypothesis Ha being that the one categorical variable affects the other categorical variable and thus they are dependent (associated).

In the case of this article drinking habits i.e. Hazardous and non hazardous drinkers are the one categorical data and various demographic characteristics (one demographic characteristic each time) formed the second categorical variable. In other words the association between drinking habits and a certain demographic characteristic was tested. Please note that one or both of the categorical variables can take more than two values e.g. the age or education demographic characteristics in the article.

If the calculated chi squared value is "small" it indicates that the observed frequencies are close to the expected frequencies assuming the two categorical variables were independent which in turn gives a "large" probability (p value) for independence.

If the calculated chi squared value is "large" it indicates that the observed frequencies are far from the expected frequencies assuming the two categorical variables were independent which in turn gives a "small" probability (p value) for independence.

In other words the chi squared statistic gives a probability that the two categorical variables are independent from each other or not.

Now in the case of this article no calculations of the ...

#### Solution Summary

Over 1000 words of step by step explanation of chi squared test for independence and logistic regression with a critical review and evaluation of how these were calculated, presented and interpreted in an academic journal.