Chi-square goodness of fit tests
1. Chi-square goodness of fit tests
Last time, we used a chi-square test to compare proportions in two categorical variables. This time, we'll use another variant of the chi-square test to compare a single categorical variable to a hypothesized distribution.2. Purple links
The Stack Overflow survey contains a fun question about how users feel when they discover that they already visited the top resource, also called a purple link, when trying to solve a coding problem. We can use the dot-value-counts method to get the counts of each group in the purple_link column. We also do a little bit of manipulation here to get a nicely structured DataFrame that we can work with later. First, we rename the leftmost column to be purple_link, assign the counts to n, and finally sort by purple_link, so the responses are in alphabetical order. There are four possible answers stored in the purple_link column.3. Declaring the hypotheses
Let's hypothesize that half of the users in the population would respond "Hello, old friend", and the other three responses would get one sixth each. We can create a DataFrame for these hypothesized results from a dictionary of key-value pairs for each response. We specify the hypotheses as whether or not the sample matches this hypothesized distribution. The test statistic, chi-squared, measures how far the observed sample distribution of proportions is from the hypothesized distribution. Let's set the significance level of point-zero-one.4. Hypothesized counts by category
To visualize the purple_link distribution, it will help to have the hypothesized counts for each answer, which are calculated by multiplying the hypothesized proportions by the total number of observations in the sample.5. Visualizing counts
Let's create a visualization to see how well the hypothesized counts appear to model the observed counts. The natural way to visualize the counts of a categorical variable is with a bar plot. First, we use plt-dot-bar to plot the observed purple_link counts, setting the horizontal axis to purple_link and the vertical axis to n. We set the color of the bars and add a label for a legend. We do the same again for the hypothesized counts, but also add transparency with the alpha argument.6. Visualizing counts
We can see that two of the responses are reasonably well-modeled by the hypothesized distribution and another two appear quite different, but we'll need to run a hypothesis test to see if the difference is statistically significant.7. chi-square goodness of fit test
The one-sample chi-square test is called a goodness of fit test, as we're testing how well our hypothesized data fits the observed data. To run the test, we use the chisquare method from scipy-dot-stats. There are two required arguments to chisquare: an array-like object for the observed counts, f_obs, and one for the expected counts, f_exp. The p-value returned by the function is very small, much lower than the significance level of point-zero-one, so we conclude that the sample distribution of proportions is different from the hypothesized distribution.8. Let's practice!
Let's perform some chi-square goodness of fit tests.Create Your Free Account
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