In: Statistics and Probability

Provide a simple research example to illustrate how chi-square could be used in an analysis.

It must discuss how the frequency distribution should be set up.

For example, you have to make categories of the data in order to run a chi-square.

**Introduction:**

Consider that a researcher wants to test the effectiveness of a vaccine in treating a disease.

Two categories of vaccination are considered- vaccinated and non-vaccinated. Again, two categories of the status of the disease are considered- diseased and non-diseased.

The null and alternative hypotheses for the test are:

*H*_{0}: Vaccination
and disease status are independent.

*H*_{1}: Vaccination
and disease status are not independent, but related.

A chi-squared is suitable to be used in this situation. It would be a chi-square test of independence.

**Explanation:**

Data must be collected on a total four classes- diseased and vaccinated, diseased and non-vaccinated, non-diseased and vaccinated, and non-diseased and non-vaccinated. Consider that the observed frequencies of these four classes are respectively, a, b, c, and d.

The frequency distribution of the data would be of the form:

Consider the observation in the
*i*^{th} row and *j*^{th} column of
the table, that is, in the cell (*i*, *j*). Then, the
expected frequency of the cell (*i*, *j*), if it is
assumed that the two categories are independent, is [(total of row
*i*) ∙ (total of column *j*)] / (grand total).

For example, for the 1^{st}
cell, that is, row 1 and column 1, the expected frequency will
be:

Similarly, the expected frequencies of all the cells are calculated below:

Now, the formula for the chi square test statistic is:

In general, for *r*
categories of the row variable and *c* categories of the
column variable, the degrees of freedom for the test would be df =
(*r* – 1) ∙ (*c* – 1).

It can be observed that there are
*r* = 2 rows, indicating the 2 statuses of vaccination-
Vaccinated, and Non-vaccinated, and there are *c* = 2
columns, indicating 2 statuses of disease- Diseased, and
Non-diseased.

Thus, the degrees of freedom for the test would be:

df

= (*r* – 1) ∙ (*c* –
1)

= (2 – 1) ∙ (2 – 1)

= 1 ∙ 1

= 1.

Thus, the degree of freedom is 1.

The p-value is, p-value = *P*
(*χ*_{df}^{2} ≥ *χ*^{2}).

Decision rule using
p-value for level of significance, *α*:

Reject
*H*_{0} at significance level *α*, if
p-value ≤ *α*.
Otherwise, fail to reject *H*_{0}.

explain how experimental design, analysis of variance,
and chi square test are used in research.

Learning Objectives
Understand when and how Chi-square testing is
used.
Become proficient with the Chi-square analysis in
SPSS.
Gain more experience with customizing statistical
calculations in Excel.
Perform a basic interpretation of a Chi-Square
analysis.
Using Chi Square
Using a statistical test without having a good idea of what it
can and cannot do means that you may misuse the test. This also
means that you won't have a clear grasp of what your results really
mean. We know that...

cite and explain how chi square is utilized in stat
analysis by giving an example including constructing a 2x2
table

List the characteristics of the chi-square distribution, and
provide an example. What are the limitations of the chi-square?
What is the difference between the goodness-of-fit test for equal
expected frequencies and unequal expected frequencies? Provide an
example of each. Kindly no pictures and no handwritten materials.
Thank you.

For this discussion, you will create an example to which the
chi-square test of independence could be applied. Develop a main
response in which you address the following:
Identify two categorical variables for which a chi-square test
of independence could be conducted.
Describe the categories of each.
Explain why these would be appropriate for this test.
Predict whether or not the chi-square test result would be
significant, and what this would imply about the variables.

In a research article, the authors said that they used a
chi-square test for independence for testing whether there is
statistically significant correlation between two categorical
variables. Each of categorical variables has two categories of
outcomes. So, the contingency table for crossclassifying these two
variables is a 2x2 table. They reported the chi-square statstic
value for this test of independence and it is 5.21. Please mark all
statements that are correct.
A
The correlation between the two categorical variables is...

Devise and describe an experiment based on a chi-square (simple
preference) analysis investigating a phenomenon of mate choice. Be
sure to clearly state what it is you are trying to find out, how
you will do that, and how the chi-square analysis will help you do
that. Show a data table of sample data and be sure
to indicate the expected values (Hint: these are NOT what YOU
expect; they are the expectations based on
probabilities)

Chi Square Test
We will now use Excel to run an example of a chi square test.
Chi square test is checking the independence of two variables. Our
example will test if taking hormonal pills and being overweight are
related. We will test the independence on 200 random patients.
Thus, N=200. They will be divided first into two groups, those who
take hormonal pills and those who do not. Second, they will be
divided into three groups based on weight,...

Describe, through an example or two, the use of a contingency
table analysis (Chi Square test) in a business research project.
What conclusion(s) could we draw from a Chi Square test?

Describe, through an example or two, the use of a contingency
table analysis (Chi Square test) in a business research project.
What conclusion(s) could we draw from a Chi Square test?

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