Section 4.5 Chi-Squared Test of Independence

• Explain the null and alternative hypothesis without using the words from the book.

Scatterplots with two measures

Finish the following sentences for comparing two measures

• Positive Correlation: As x increases y ________.
• Negative Correlation: As x increases y ________.
• No Correlation: As x increases y _________.
• If there is a relationship between x and y then knowing x gives us information about y.

Tables with two dimensions

Let’s think about our counts of birth by month and sport data.

• Does being in a professional sport provide information about what month they were born in?
• If yes, they are correlated or their is a relationship. They are not independent
• if no, then birthday months are independent of what sport a professional plays.

Building our data tables (Tableau)

1. Build a table that shows the sum of all births for each group and each month.
2. Build a table that shows the percentage of births by month within each sport. A. Edit table calculations
3. Build a table that has the counts for the US and Baseball for July and August. A. Filter

Cut off dates

• Baseball: July 31st
• Football: July 31st (but it has weight limits and other dates)
• Basketball: August 31st (but it has other dates)
• Hockey: December 31st

Comparing with two group proportions?

1. How could we compare US births to Hockey births to see if there is a Matthew effect?
2. What are some other ways we could compare the two groups?
3. Which is better?
4. What concerns do you have?

Comparing multiple variables over two populations?

• If the Matthew effect is real, why would it only happen in certain months. Should we see a trend?
• What are the benefits of comparing the entire trend?
• Now that we see a difference, what would we want to do?

Why does Basketball not have a Mathew effect?

Can’t coach height

Why does US Football not have a Matthew effect?