Python Lesson 3 - Testing moderation in the context of Chi-Square

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From the course by Wesleyan University

Data Analysis Tools

310 ratings

Wesleyan University

Data Analysis Tools

310 ratings

Course 2 of 5 in the Specialization Data Analysis and Interpretation

In this course, you will develop and test hypotheses about your data. You will learn a variety of statistical tests, as well as strategies to know how to apply the appropriate one to your specific data and question. Using your choice of two powerful statistical software packages (SAS or Python), you will explore ANOVA, Chi-Square, and Pearson correlation analysis. This course will guide you through basic statistical principles to give you the tools to answer questions you have developed. Throughout the course, you will share your progress with others to gain valuable feedback and provide insight to other learners about their work.

From the lesson

Exploring Statistical Interactions

In this session, we will discuss the basic concept of statistical interaction (also known as moderation). In statistics, moderation occurs when the relationship between two variables depends on a third variable. The effect of a moderating variable is often characterized statistically as an interaction; that is, a third variable that affects the direction and/or strength of the relation between your explanatory (X) and response (Y) variable. Your task will be to test your own research question in the context of one or more potential moderating variables.

Python Lesson 1 - Defining moderation, a.k.a. statistical interaction4:30

Python Lesson 2 - Testing moderation in the context of ANOVA3:49

Python Lesson 3 - Testing moderation in the context of Chi-Square4:39

Python Lesson 4 - Testing moderation in the context of correlation4:09

Meet the Instructors

Jen Rose
Research Professor
Psychology
Lisa Dierker
Professor
Psychology

Now lets evaluate third variables as potential moderators in the context of

Chi-Square Test of Independence.

For this, we're going to return to our original Python program using the NYSARC

data and asking the question, is smoking associated with nicotine dependence?

We're going to create another smoking variable for this purpose,

reflecting how many cigarettes each young adult smoker smokes per day.

Here is my code to create this secondary variable.

Where 0 will indicate non-daily smokers.

Three will indicate those smoking one to five cigarettes per day,

8 indicating six to ten cigarettes per day, 13 indicating 11 to

15 cigarettes per day, 18 indicating 16 to 20 cigarettes per day.

And 37 indicating greater then 20 cigarettes smoked per day.

Now, we're going to request a chi-squared test of independence

examining the association between nicotine dependence in the past 12 months and

this new smoking variable called USQUAN.

As we can see from the large chi-square value, and significant P value,

smoking quantity and nicotine dependence are significantly associated.

In examining the column percents here of each smoking group

with nicotine dependence,

we see generally higher rates of nicotine dependence among groups that smoke more.

So among non-daily smokers, only 25% Percent are nicotine dependent.

Among those smoking one to five cigarettes per day,

indicated by a code of three, about 48% meet the criteria for nicotine dependence.

These numbers increase with higher levels of smoking.

To graph these proportions, we use the following code.

And this gives us the graphic representation

of this positive linear relationship.

As smoking quantity increases, so

does the proportion of individuals with nicotine dependence.

This finding is accurate with regard to the larger population

of young adult smokers in the US.

But might a third variable moderate this significant association between

smoking quantity and nicotine dependence?

We are going to evaluate major depressive disorder as the third variable.

Our question will be, does major depression affect either the strength or

the direction of the relationship between smoking and nicotine dependence?

Put another way, does major depression moderate the signficant statistical

relationship between smoking and nicotine dependence?

Is smoking related to nicotine dependence for each level of this third variable?

That is for those with major depression and for those without major depression.

Similar to our ANOVA example, syntax to be added includes setting new data

frames that include either individuals with or without major depression.

Since we will look at these groups separately, the specific syntax for

the chi-square test of independence by major dep life levels is here.

Notice that I am using the appropriate data frames for each contingency table,

column percent table, and chi-square test, sub3, and sub4.

When this syntax is added to the Python program, here are the results.

You can see the cross-tabs or cross tabulation table

looking at usual quantity by tobacco dependence in the past twelve months.

First for major depression equal to zero which is those without major depression,

the chi-square value is large and the P value is quite small.

So we can say that this is a statistically significant relationship for

those without major depression.

For those with major depression, again we find a large chi-square value and

a small P value which is statistically significant.

Using a line graph to examine the rates of nicotine dependence by different levels

of smoking, we would use the following code changing only the data frame and

kind of graph.

Here we are asking for a point or line graph.

As you can see, it seems that both the direction and the size for

the relationship is similar for smoking and nicotine dependence.

For those with major depression and for those without.

Although those with major depression do show higher rates of

nicotine dependence at every level of smoking quantity.

Still, in this case, we would say that a diagnosis of major depression does not

moderate the relationship between smoking and nicotine dependence.

For both young adult smokers with major depression and for those without.

Higher levels of smoking behavior is associated with higher rates of

nicotine dependence.

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