Python Lesson 4 - Testing moderation in the context of correlation

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From the course by Wesleyan University

Data Analysis Tools

311 оценки

Wesleyan University

Data Analysis Tools

311 оценки

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

So, now let's test for moderation within the context of our final inferential test,

the correlation coefficient.

You might remember this scatter plot and correlation based on the gap minder data

between rate of urban dwellers in each country and the Internet use rate.

We found that this was a significant association with correlation of 0.61.

But might this relationship, this correlation between urban rate and

Internet use rate differ based on countries with different income levels.

>> To explore this question, we create a third variable that is categorical.

For this new variable, the income-per-person variable,

which is quantitative, will be categorized as high income countries,

middle income countries, and low income countries.

The adjustments we made to our program are very similar to the adjustments we made to

our Nova syntax, and to our chi square syntax when testing moderation.

We'll start our program calling in our libraries and loading the gap minder data.

Next, we set our three variables of interest to numeric, and

set blank data on our third variable to NAN.

Then I create a new data frame I am calling data_clean that drops all missing,

that is NAN values for each of the variables in the data set.

Now, I create my income group variable which splits the sample of countries into

low, middle, and high income groups using the dummy codes 1, 2, and 3.

Next I create three different data frames that include only one income group each.

Here, called sub1 for low income countries, sub2 for

middle income countries, and sub3 for high income countries.

Then we request a Pearson correlation measuring the association between

urban rate and Internet use rate as well as its associated P value for

each of our new data frames.

We use the Pearson R function from the scipy.stats library and

include our variables urban rate and Internet user rates.

When we examine the correlation coefficients between urban rate and

Internet user rate for each of the income groups, we find the following.

For the low income group the correlation between urban rate and

Internet use rate is 0.11 and the P value is not significant.

For the middle income countries, the association between Internet use rate and

urban rate is 0.32.

With a significant P value of 0.001 and finally among high income

countries the correlation coefficient is 0.089, with a large P value.

Suggesting that the association between urban rate and

Internet use rate is not significant for high income countries.

When we map these findings onto the associated scatter plots for

each income group, we are better able to visualize the significant and

non-significant relationships.

Estimating a line of best fit within each scatter plot

shows the positive association between urban rate and

Internet use rate among the middle income countries.

And almost no relationship between these variables in both the low income and

high income countries.

>> Asking questions about statistical interactions can an interesting way to

explore your data and your associations of interest.

This is not difficult to do using the skills you've acquired this far.

There are more advanced topics that we can cover here such as

multivariate techniques that can be very powerful.

But even without these techniques, we can still use bivariate inferential

tools of ANOVA, Chi Square in correlation to describe our sample,

make inferences about the larger population.

And really begin to understand understand what relationships these associations

hold, under what conditions, or at what levels of our third variable.

Now that we've found associations, can we assume that association implies causation?

We'll answer that question soon.

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