Python Lesson 2 - Testing moderation in the context of ANOVA

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Data Analysis Tools

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Wesleyan University

Data Analysis Tools

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Курс 2 из 5 — 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.

Из урока

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

Познакомьтесь с преподавателями

Jen Rose
Research Professor
Psychology
Lisa Dierker
Professor
Psychology

In statistics, moderation occurs when the relationship between two variables depends

on a third variable.

In this case, the third variable is referred to as the moderating variable or

simply the moderator.

The effect of the moderating variable is often characterized statistically

as an interaction.

That is, a third variable that effects the direction and or

strength of the relation between your explanatory and response variable.

So does type of exercise program effect the direction or

strength of the relationship between diet and weight loss?

The standard way of asking this question in the context of analysis of variance,

is to move to the use of a two-way or two factor analysis of variance,

rather than the one-way or one factor ANOVA that we've been using.

Instead, we're going to take a less standard approach

that can be consistently used across each of the inferential tolls.

That is, ANOVA, Chi Square, and Pearson Correlation.

In each of these contexts, we're actually gonna be asking the question

is our explanatory variable associated with our response variable, for

each population subgroup or each level of our third variable?

That is are diet type and weight loss associated for

those doing the cardio exercise program?

And are diet and weight loss associated for

those using the weight training program?

>> To accomplish this,

we are going to run two separate ANOVAS, one for each level of a third variable.

That is for each exercise program.

Syntax to be added to the program is listed here.

We need to first create new data frames with only the subsample of interest.

That is either cardio or weights separately.

When we run the analysis of variants, you'll see the following results.

The ANOVA table examining the relationship between diet and weight loss for

those in the cardio exercise group shows a large F value, and a significant p-value.

When examining the means table we see that for those involved in the cardio exercise

program, diet A is associated with greater weight loss,

20.5 pounds on average, than diet B, 7.1 pounds on average.

The association between diet and weight loss for

those involved in the weight training exercise program is also significant.

It has a large F value and a significant P value.

However, the means show that the association is in the opposite direction.

For those involved in weight training, diet B is associated with greater

weight loss, 11.5 pounds compared to diet A,

only 8.8 pounds.

>> Here, these results are shown graphically.

As you can see, the relationship between diet and

weight loss depends on which exercise program is being used.

When using cardio, diet A is significantly better for weight loss than diet B.

When using weights, diet B is significantly better for

weight loss than diet A.

Thus we can say there's a significant statistical interaction

between the variables diet and weight loss.

And the type of exercise, our third variable,

moderates the association between diet and weight loss.

>> Suppose that we did not evaluate exercise as a possible moderator.

And instead focused only on the association between diet and

weight loss for the entire population.

Based on this graph obviously we would have incorrectly concluded

that diet A is better than diet B.

As we now know that is only true if we're looking at the cardio group.

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