[AP Statistics] 12.2a Chi-Square test for Homogeneity
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Last time, we learned the Chi-Square test for Goodness of Fit. This test is used when you have 1 sample (Harvard Applicants in 2019) and 1 variable (Racial Identity).
Today we will learn the Chi-Square test for Homogeneity, which is used when you have 2 samples and 1 variable.
Question 1
1.
One thing I've been curious about: does the AP Statistics class period you are in affect which test you did best at this semester? My lessons always end up playing out slightly differently, and students in each class ask different questions.
There are 4 graded tests so far this semester (Chapters 7, 8, 9, and 10). For each person in each class period, I looked in my grade book and noted the test they did best on out of the 4. Turns out no one did best on Chapter 9 so we will ignore it for convenience!
Observed Counts for best test:
Just looking at the data, do you think the difference between the periods could be due to random chance?
Question 2
2.
What are the sample(s) and variable(s) in this study?
Question 3
3.
In general terms, what should be the null hypothesis for our significance test?
Question 4
4.
In general terms, what should be the alternative hypothesis for our significance test?
Question 5
5.
Like our other Chi-Square test, we will need to calculate the expect count
Observed:
What is the expected count for Students in Period E doing best on Chapter 7?
Round to 1 decimal place
Question 6
6.
What is the expected count for Students in period G doing best on Chapter 10?
Round to 1 decimal place
Question 7
7.
I'm only going to make you calculate two of those since it is tedious. Your calculator will take care of the rest soon.
Now we need to check our conditions, which are the same as for the other Chi-Square test
Do we meet the Large Counts condition?
Question 8
8.
Explain
Question 9
9.
The degrees of freedom are calculated in a different way than last time. What are the degrees of freedom for this study?
Question 10
10.
The Chi-Square test statistic is calculated the same way as we did last time. We will let our calculator do the heavy lifting.
Because our data is in a 2 way table, we need to enter it into a matrix instead of a list.
Enter the OBSERVED data into matrix A: 2nd->Matrix->Edit->[A]
Stat->Test-X^2-Test shows the following, indicating that it will read the observed in Matrix [A] and output the expected values into Matrix [B]
When you hit enter, you should see the X^2 test statistic. Type it below.
Round to 1 place
Question 11
11.
You should also see the p-value. Type it below
Round to 2 places
Question 12
12.
If you hit 2nd->Matrix->[B] and hit enter, you can see the expected values that your calculator calculated.
Note: It might actually be easier to see the values if you go 2nd->Matrix->Edit->[B]
What is the expected value for Period G students who did best on Chapter 7 (2nd row first column)?
Round to 1 place
Question 13
13.
Do we have convincing evidence that 2 classes differ in terms of which test they did best?
a=0.05
Question 14
14.
Explain
SAMPLE STATE PLAN DO CONCLUDE
DO
X2=68.57, df = 6, p-value ~= 0
Question 15
15.
Question 16
16.
Question 17
17.
What should be the expected value for the Red/Red cell?
Round to 1 place
Question 18
18.
How many degrees of freedom?
Question 19
19.
What is the chi-square test statistic?
Round to 2 places
Question 20
20.
What is the p-value?
Round to three places
Question 21
21.
What is your conclusion at the a=0.05 level?
Question 22
22.
Question 23
23.
STATE
Question 24
24.
PLAN (You probably want to complete the Do step first to get the table of expected values)
For my class, you don't need to recreate the table for the plan step like they do in the sample. If this comes up on the AP exam, you SHOULD recreate the table
Question 25
25.
DO
Record P-Value, Degrees of Freedom, and the Chi Square Test Statistic
Question 26
26.
CONCLUDE
Question 27
27.
Are there any problems above that you would like to go over in class? Indicate the question numbers below (Numbers refer to the Formative question number). I'll try to cover anything that is highly requested.