Question

A. Compare the Goodness of Fit Test and the Test for Independence in terms of the number of variables and levels of those that can be compared. In what ways are they similar or different?

B. Describe how the Test for Independence and correlation are similar yet different.

Answer #1

A. The Goodness of Fit Test compares the distribution of one categorical variable with a specified distribution and the Test for Independence checks the association between two categorical variables. In Goodness of Fit Test, the levels of the categorical variable are same as the levels given for the specified distribution but in case of Test for Independence, the levels may vary.

B. The Test for Independence and correlation both are used to find the relationship between two variables but the Test for Independence helps us to identify the relationship or association between two categorical variables on the other hand correlation measures the linear relationship between two continuous variables.

The Goodness of Fit Test and Test for Independence both use the
same formula to calculate chi-square. Why? I.e., explain the logic
of the test.

why does the goodness of fit test and test of independence use
the same formula? What's the logic behind it?

For each of the following examples, state whether the chi-square
goodness-of-fit test or the chi-square test for independence is
appropriate, and state the degrees of freedom (df) for the
test.
Part (a)
A student tests whether the professor's speaking style (monotone,
dynamic) and student interest (low, average, high) are
independent.
State whether the chi-square goodness-of-fit test or the chi-square
test for independence is appropriate.
chi-square goodness-of-fitchi-square test for
independence
State the degrees of freedom for the test.
df =
Part...

How is the chi-square independence test similar to the
goodness-of-fit test? How is it different?
What is the difference between McMemar’s Test and the
Chi-squared test for 2 by 2 table.
Question 2
A clinic administers two drugs to two groups of randomly
assigned patients to cure the same disease: 70 patients received
Drug 1 and 80 patients received Drug 2. The following table gives
the information about the number of patients cured and the once not
cured by each...

Practice finding degrees of freedom for a Chi-square test.
Goodness of fit
categories - 1
Independence
(rows -1)( columns -1)
Homogeneity
categories -1
Variance
n-1
To look up a p-value for Chi-Square test you need to know the
degrees of freedom.
A goodness of fit test has 7 categories. What degrees of freedom
do you use?
A test for homogeneity has 9 categories. What is the degrees of
freedom, d.f.?
A test for independence has 3 rows and 9 columns....

*4.) For each of the following examples, state whether the
chi-square goodness-of-fit test or the chi-square test for
independence is appropriate, and state the degrees of freedom
(df) for the test.
Part (a)
An instructor tests whether class attendance (low, average, high)
and grade point average (low, average, high) are independent.
State whether the chi-square goodness-of-fit test or the chi-square
test for independence is appropriate.
chi-square goodness-of-fitchi-square test for
independence
State the degrees of freedom for the test.
df =...

test for multiple population
proportions
test for independence
Goodness of fit test
1. A person in a city observes a sample of 500 cars and wants to
know whether the car make distribution in the city is different
from the car make distribution in the Unites States.
2. A customer wants to compare the percentages of customer
satisfaction among three hotels.
3. A survey asks adults the following questions: What is your
age? 18-50 Above 50 How many cups of...

A chi-square test for goodness of fit is used to examine the
distribution of individuals across four categories, and a
chi-square test for independence is used to examine the
distribution of individuals across the six categories in a 2×3
matrix of categories. Which test has the larger value for df?
a. The test for goodness of fit
b. Both tests have the same df value.
c. The test for independence
d. The df value depends on the sizes of...

What is evaluated by the chi-square test for goodness of
fit?
a. If proportions of a sample distribution match those of a
population specified by the null hypothesis
b. If the frequencies found within an individual category match
a certain shape
c. Whether the means of two or more categories differ from one
another
d. Whether two variables are related to each other or
independent

When evaluating a chi-square test, describe the importance of
the goodness of fit test. Provide an example and explain how the
test is used to evaluate the data.

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