Evaluating if metric of one group is higher than the metric of another group when group sizes differ significantly

I am working with a dataset that contains data of applicant income, gender, and loan status (whether or not the person was approved for a loan). I've created the following plots from the data. The histogram plot is:

The kernel density estimate (KDE) plot is:

The KDE plots seem to indicate that the accepted to rejected ratio among men is higher for a given income than compared to women. I want to investigate this further. Note (!) there are more men in the dataset than women, so any conclusions will need to take the variance into account.

An idea: My initial idea was to bin the incomes and compute the ratio of accepted/rejected in each bin for each gender. We can then plot the ratio and the variance (using the counts of men/women in each bin) to see if there is a statistical significance in the dependence of accepted/rejected on gender.

Question: Is the above idea sound? Should I formulate this a hypothesis testing problem? If so, how would I go about doing this?

Topic hypothesis-testing data-analysis variance

Category Data Science

1
answered at

What you are describing is a contingency table, the Cartesian product of categorical variables with count values in the cells. The categorical variables are: gender, income bin, and loan status. Your contingency table will be a data cube.

One option for a statistical test on a contingency table is chi-squared test which compares expected vs. compared counts for categorical variables.

1
answered at

This can be framed as hypothesis testing problem and can be approached as follows using CHI SQUARE test.

Null Hypothesis : H0: The distribution of the outcome is independent of the groups. Loan Rejection/ approval is indepndent of age/income Bins

Test Statistic for Testing H0: Distribution of outcome is independent of groups

Chi sqaure = (O-E)**2/E

and we find the critical value in a table of probabilities for the chi-square distribution with df=(r-1)*(c-1).

Here O = observed frequency, E=expected frequency in each of the response categories in each group, r = the number of rows in the two-way table and c = the number of columns in the two-way table. r and c correspond to the number of comparison groups and the number of response options in the outcome.

You can create a table like this below and perform chi square test:

enter image description here

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