Intro To Stats 11.2 Part 1

Lesson 11.2
Chi-Square Tests for Goodness of Fit

Starnes/Tabor/Wilcox, Statistics and Probability with Applications, 4e

© 2021 BFW Publishers

11

Starnes/Tabor/Wilcox, Statistics and Probability with Applications, 4e

© 2021 BFW Publishers

A significance test about the distribution of a categorical variable is called
a chi-square test for goodness of fit.

Chi-Square Tests for Goodness of Fit

How to Check the Conditions for a Chi-Square Test for Goodness of Fit

•Random: The data come from a random sample from the population of interest.

•Large Counts: All expected counts are at least 5.

Multiple Select

Did you catch that? What were the conditions for a Chi-Square test?

• All expected counts are at least 10

• Data is from a random sample

• All expected counts are at least 30

• All expected counts are at least 5

• Data is from a normally distributed sample

Multiple Choice

Did Andre's class from our example yesterday meet the Chi-Square conditions?

• Yes

• No

• Not enough information

Starnes/Tabor/Wilcox, Statistics and Probability with Applications, 4e

© 2021 BFW Publishers

For Andre’s class data, given in Lesson 11.1, the conditions for a chi-square test for goodness of fit are met:

Andre’s teacher selected a random sample of M&M’S® Milk Chocolate
Candies from the large bag and all the expected counts were at least 5:

Chi-Square Tests for Goodness of Fit

Starnes/Tabor/Wilcox, Statistics and Probability with Applications, 4e

© 2021 BFW Publishers

To see if birth date is uniformly distributed across
the four quarters of the year for NHL players, a
random sample of 80 NHL players from a recent
season was selected and their birthdays were
recorded. The table shows the observed and
expected counts for a test of the null hypothesis
that the true proportions of NHL players born in
each quarter are the same.

Check if the conditions for performing a chi-square test for goodness of fit are met.

Example: Can we test the distribution of NHL birthdays?

Multiple Choice

How about our randomly selected NHL players, did that sample meet the Chi-Square conditions?

• Yes

• No

• Not enough information

Starnes/Tabor/Wilcox, Statistics and Probability with Applications, 4e

© 2021 BFW Publishers

SOLUTION:

Random?

The data come from a random sample of NHL players. P

Large Counts?

All expected counts (20, 20, 20, 20) are at least 5. P

Example: Can we test the distribution of NHL birthdays?

Starnes/Tabor/Wilcox, Statistics and Probability with Applications, 4e

© 2021 BFW Publishers

Andre’s class did “The Color of Candy” activity
in Lesson 11.1 and got a chi-square test statistic
of 𝝌𝟐 = 9.8.

Is this an unusually large value?

Or is this a value that is likely to happen by
chance alone when the distribution of color
in the bag is the same as the company claims?

Chi-Square Tests for Goodness of Fit

Poll

Andre’s class did “The Color of Candy” activity
in Lesson 11.1 and got a chi-square test statistic
of 𝝌𝟐 = 9.8.

Is this an unusually large value?

• No

• Yes

• I have no idea

• I have no idea, but I'm still gonna trust my gut and say Yes

• I have no idea, but I'm still gonna trust my gut and say No

Multiple Choice

Wait a minute. Stop right there. Degrees of Freedom? How do we find that for Chi-Square?

• df = number of data values in the sample - 1

• df = number of categories -1

• df = the higher the degree the more financial freedom I will have in life.

• df = number of boxes in the chart - 1

Pages 675 - 676
# 1, 2, 3, 7, 9, 11 (Use table T3 in the back of your book to find a range)

​

Homework

Starnes/Tabor/Wilcox, Statistics and Probability with Applications, 4e

© 2021 BFW Publishers

You can use technology to perform the calculations for a chi-square test for goodness of
fit. We’ll illustrate using the hockey data from the preceding example.

TECH
CO R N E RChi-Square Test for Goodness of Fit

Applet

1.

Launch the One Categorical
Variable, Single Group applet at
bfwpub.com/spa4e.

2.

Enter “Birthday” as the variable name.
Then input each of the different
quarters of the year along with the
observed frequencies. Press the +
button in the lower right to get more
rows in the table.