This document discusses using the chi-square test for independence to analyze categorical data and determine if there is a relationship between two variables. It provides examples of chi-square test use cases, steps for implementing the test, requirements, hypothesis testing steps, and shows chi-square distribution plots. The document also includes sample code in R and analyzes a dataset on pricing plan sales across countries to determine if the number of sales is dependent on country.

1. Think stats: chi square test
in digital analytics
Chi-Square Test for independence FTW!!11one
Pawel Kapuscinski
pawel@databall.co
@aliendeg

2. Chi-square test use cases
Is gender a factor in color preference of a car?
Comparing the number of sales from the test experience vs the control
experience (A/B test or A/B/n)
Comparing sales revenues of each product before and after the change in
strategy
Is country a factor in pricing plan preference?
Is weather a factor in sales of different products?

3. Implementing the chi square test
1. Identify the two variables of interest from the data table
2. State hypothesis
3. Compute Margin summations
4. Build contingency table
5. Compute the observed chi-square value
6. Compare the observed value to critical value
IMPORTANT: Requirements for chi squared test
The variables under study are each categorical. If sample data are displayed in a

4. Hypothesis testing steps
1. State null (H0) and alternative (H1) hypothesis
2. Choose level of significance
3. Find critical values
4. Find test statistic
5. Draw your conclusion

5. Chi squared distribution plots

6. Dataset - pricing plans sold across world
Sold plans
Professional Team Business Enterprise
USA 1220 790 500 190
UK 950 590 200 120
Germany 880 420 320 70
Sweden 340 260 130 60
Belgium 290 190 110 80
Poland 910 290 190 40
Spain 250 320 220 50

7. Hypothesis
H0: Number of sales of each pricing plan is independent upon country
H1: Number of sales of each pricing plan is dependent upon country

8. Finding test statistics (manually, Excel and R)
Find critical value
(https://www.ma.utexas.edu/users/davis/375/popecol/tables/chisq.html)
Compute Margin summations
Summing rows and columns
Build contingency table
Compute the observed chi-square value

9. Finding test statistics - results

10. R code
df = data.frame(Prof= c(152,118,110,42,36,113,31),
Team = c(98,73,52,32,23,36,40),
Business = c(62,25,40,16,13,23,27),
Enterprise = c(23,15,8,7,10,6,6))
chisq.test(df)

11. Drawing conclusion
We can reject hypothesis zero (H0) and
accept H1. Number of sales of each pricing
plan is dependent upon country

12. Learn more
http://stats.stackexchange.com
www.analyticsvidhya.com
www.dartistics.com
Measure Slack - http://join.measure.chat

13. Assignment / homework
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14. Questions?