WarmUp

1
Warm-Up

• Here are the number of births in each zodiac sign
  for the CEO of 256 of the Fortune 400.
• Is there evidence that some zodiac signs are more
  likely than others?

2
Chi-Square Testing for Homogeneity

• Thursday 10 April 2008

3
Goodness of Fit

• The chi-square goodness of fit test tells us
  whether a given set of observations fits with an
  underlyling probability distribution.

4
Homogeneity

• Having similar components
• Uniform
• Undifferentiated

5
Chi Square Test for Homogeneity
6
Testing for Homogeneity

• Determine overall for each category.
• Determine expected number for each cell.
• Use degrees of freedom to find a critical value.
• Figure out chi-square test values and sum.
• Compare and decide.

7
Homogeneity DF

• Subtract 1 from each of the horizontal and
  vertical.
• Multiply.

8
Chi-Square Goodness of Fit Test

• This is our test statistic.
• For each outcome, E is the expected value, and O
  is the observed value.
• Compute and sum.

9
Chi Square Test for Homogeneity
10
AP Test Scores
11
Stats Grades