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[AP Statistics] 12.2a Chi-Square test for Homogeneity

Last updated 5 months ago
27 questions
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.
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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?

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What are the sample(s) and variable(s) in this study?

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In general terms, what should be the null hypothesis for our significance test?

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In general terms, what should be the alternative hypothesis for our significance test?

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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

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What is the expected count for Students in period G doing best on Chapter 10?

Round to 1 decimal place

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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?

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Explain

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The degrees of freedom are calculated in a different way than last time. What are the degrees of freedom for this study?

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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

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You should also see the p-value. Type it below

Round to 2 places

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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

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Do we have convincing evidence that 2 classes differ in terms of which test they did best?

a=0.05

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Explain

SAMPLE STATE PLAN DO CONCLUDE



DO
X2=68.57, df = 6, p-value ~= 0

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What should be the expected value for the Red/Red cell?

Round to 1 place

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How many degrees of freedom?

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What is the chi-square test statistic?

Round to 2 places

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What is the p-value?

Round to three places

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What is your conclusion at the a=0.05 level?

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STATE

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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

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DO
Record P-Value, Degrees of Freedom, and the Chi Square Test Statistic

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CONCLUDE

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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.