• Skip to primary navigation
  • Skip to main content
  • Skip to primary sidebar
The Analysis Factor

The Analysis Factor

Statistical Consulting, Resources, and Statistics Workshops for Researchers

  • Home
  • Our Programs
    • Membership
    • Online Workshops
    • Free Webinars
    • Consulting Services
  • About
    • Our Team
    • Our Core Values
    • Our Privacy Policy
    • Employment
    • Collaborate with Us
  • Statistical Resources
  • Contact
  • Blog
  • Login

ancova

Member Training: Confusing Statistical Terms

by guest contributer

Learning statistics is difficult enough; throw in some especially confusing terminology and it can feel impossible! There are many ways that statistical language can be confusing.

Some terms mean one thing in the English language, but have another (usually more specific) meaning in statistics.  [Read more…] about Member Training: Confusing Statistical Terms

Tagged With: ancova, association, confounding variable, confusing statistical terms, Correlation, Covariate, dependent variable, Error, factor, General Linear Model, generalized linear models, independent variable, learning statistics, levels, listwise deletion, multivariate, odds, pairwise deletion, random error, selection bias, significant

Related Posts

  • Series on Confusing Statistical Terms
  • Six terms that mean something different statistically and colloquially
  • Confusing Statistical Term #8: Odds
  • The Difference Between Association and Correlation

Member Training: ANCOVA (Analysis of Covariance)

by Karen Grace-Martin Leave a Comment

Analysis of Covariance (ANCOVA) is a type of linear model that combines the best abilities of linear regression with the best of Analysis of Variance.Stage 2

It allows you to test differences in group means and interactions, just like ANOVA, while covarying out the effect of a continuous covariate.

Through examples and graphs, we’ll talk about what it really means to covary out the effect of a continuous variable and how to interpret results.

Primary to the discussion will be when ANCOVA is and is not appropriate and how correlations and interactions between the covariate and the independent variables affect interpretation.


Note: This training is an exclusive benefit to members of the Statistically Speaking Membership Program and part of the Stat’s Amore Trainings Series. Each Stat’s Amore Training is approximately 90 minutes long.

Not a Member? Join!

About the Instructor

Karen Grace-Martin helps statistics practitioners gain an intuitive understanding of how statistics is applied to real data in research studies.

She has guided and trained researchers through their statistical analysis for over 15 years as a statistical consultant at Cornell University and through The Analysis Factor. She has master’s degrees in both applied statistics and social psychology and is an expert in SPSS and SAS.

Not a Member Yet?

It’s never too early to set yourself up for successful analysis with support and training from expert statisticians. Just head over and sign up for Statistically Speaking. You'll get access to this training webinar, 100+ other stats trainings, a pathway to work through the trainings that you need — plus the expert guidance you need to build statistical skill with live Q&A sessions and an ask-a-mentor forum.

Tagged With: ancova

Related Posts

  • Member Training: Statistical Contrasts
  • Member Training: Hierarchical Regressions
  • Member Training: Types of Regression Models and When to Use Them
  • The General Linear Model, Analysis of Covariance, and How ANOVA and Linear Regression Really are the Same Model Wearing Different Clothes

ANCOVA Assumptions: When Slopes are Unequal

by Karen Grace-Martin 21 Comments

There are two oft-cited assumptions for Analysis of Covariance (ANCOVA), which is used to assess the effect of a categorical independent variable on a numerical dependent variable while controlling for a numerical covariate:

1. The independent variable and the covariate are independent of each other.

2. There is no interaction between independent variable and the covariate.

In a previous post, I showed a detailed example for an observational study where the first assumption is irrelevant, but I have gotten a number of questions about the second.

So what does it mean, and what should you do, if you find an interaction between the categorical IV and the continuous covariate? [Read more…] about ANCOVA Assumptions: When Slopes are Unequal

Tagged With: ancova, Assumptions, slopes

Related Posts

  • When Assumptions of ANCOVA are Irrelevant
  • Assumptions of Linear Models are about Residuals, not the Response Variable
  • Using Adjusted Means to Interpret Moderators in Analysis of Covariance
  • Why ANOVA and Linear Regression are the Same Analysis

Member Training: Types of Regression Models and When to Use Them

by Karen Grace-Martin Leave a Comment

Linear, Logistic, Tobit, Cox, Poisson, Zero Inflated… The list of regression models goes on and on before you even get to things like ANCOVA or Linear Mixed Models.

In this webinar, we will explore types of regression models, how they differ, how they’re the same, and most importantly, when to use each one.


Note: This training is an exclusive benefit to members of the Statistically Speaking Membership Program and part of the Stat’s Amore Trainings Series. Each Stat’s Amore Training is approximately 90 minutes long.

Not a Member? Join!

About the Instructor

Karen Grace-Martin helps statistics practitioners gain an intuitive understanding of how statistics is applied to real data in research studies.

She has guided and trained researchers through their statistical analysis for over 15 years as a statistical consultant at Cornell University and through The Analysis Factor. She has master’s degrees in both applied statistics and social psychology and is an expert in SPSS and SAS.

Not a Member Yet?

It’s never too early to set yourself up for successful analysis with support and training from expert statisticians. Just head over and sign up for Statistically Speaking. You'll get access to this training webinar, 100+ other stats trainings, a pathway to work through the trainings that you need — plus the expert guidance you need to build statistical skill with live Q&A sessions and an ask-a-mentor forum.

Tagged With: ancova, Cox Regression, linear mixed model, linear regression, logistic regression, Poisson Regression, Tobit Regression, Zero Inflated

Related Posts

  • Member Training: Using Excel to Graph Predicted Values from Regression Models
  • Member Training: Hierarchical Regressions
  • How to Combine Complicated Models with Tricky Effects
  • When Dependent Variables Are Not Fit for Linear Models, Now What?

When Assumptions of ANCOVA are Irrelevant

by Karen Grace-Martin 44 Comments

Every once in a while, I work with a client who is stuck between a particular statistical rock and hard place.

It happens when they’re trying to run an analysis of covariance (ANCOVA) model because they have a categorical independent variable and a continuous covariate.

The problem arises when a coauthor, committee member, or reviewer insists that ANCOVA is inappropriate in this situation because one of the following ANCOVA assumptions are not met:

1. The independent variable and the covariate are independent of each other.

2. There is no interaction between independent variable and the covariate.

If you look them up in any design of experiments textbook, which is usually where you’ll find information about ANOVA and ANCOVA, you will indeed find these assumptions.  So the critic has nice references.

However, this is a case where it’s important to stop and think about whether the assumptions apply to your situation, and how dealing with the assumption will affect the analysis and the conclusions you can draw. [Read more...] about When Assumptions of ANCOVA are Irrelevant

Tagged With: analysis of covariance, ancova, Assumptions, experiments, General Linear Model

Related Posts

  • The General Linear Model, Analysis of Covariance, and How ANOVA and Linear Regression Really are the Same Model Wearing Different Clothes
  • 3 Reasons Psychology Researchers should Learn Regression
  • SPSS GLM: Choosing Fixed Factors and Covariates
  • ANCOVA Assumptions: When Slopes are Unequal

Using Adjusted Means to Interpret Moderators in Analysis of Covariance

by Karen Grace-Martin 1 Comment

If you’re like most researchers, your statistical training focused on Regression or ANOVA, but not both. It all depends on whether your field focuses more on experimental data (Biology, Psychology) or observed data (Sociology, Economics). Maybe one class covered a bit of the other, but most people are comfortable in one, but not the other.

This, in my opinion, is a shame. (Okay, I was going to say tragedy, but let’s be real.  Tsunami that kills thousands=tragedy.  Different scale here).

First of all, the distinction between ANOVA and linear regression is arbitrary. They’re really the same model with different outfits on.

Second, regardless of which one you normally use, you’re going to occasionally have to use the other kind of predictor variables–categorical or continuous. And we can come up with nice names for these models–a regression with dummy variables or an Analysis of Covariance.

But real understanding of the relationships among variables comes only when you dispense of the names and can focus on analyzing and interpreting the model using the kinds of variables you have.

There are other examples, but today I’m going to focus on an ANOVA model with a continuous covariate.

A common model is one in which one predictor is categorical (we’ll use 4 categories) and the other is continuous. Here is an example of a scatterplot of just such a model:

Scatterplot of Ancova
Scatterplot of Ancova

There are four groups, each of which received a different training.  The continuous moderator is Age, and the outcome is OverallPost, which is the post-training test score to see how well they learned the material in each training program.

As you can see, the effect of the training program is moderated by age.  Another way to say that is there is a significant interaction between Age and Training Group.  The effect of the training is depending on the trainee’s age.

One way to interpret this significant interaction is to compare the slopes of the four lines, which is easily done with any regression coefficient table.  (Okay, not always easily done, but easily found in…)

But this doesn’t make very much sense when Age is really a moderator–a predictor we want to control for, and see how it affects the relationship between the independent (IV) and dependent variables (DV), but not really the IV we’re interested in.

A better way to do it in this situation is to compare the means among groups at a low value of Age, say 20, and again at a high value of Age, say 50.  You can get p-values, adjusted for multiple comparisons, using either SAS or SPSS GLM.

SAS Proc GLM uses the LSMeans statement and SPSS GLM uses EMMeans.  They do the same thing–calculate the mean of Y for each group, at a specific value of the covariate.

If you use the menus in SPSS, you can only get those EMMeans at the Covariate’s mean, which in this example is about 25, where the vertical black line is.  This isn’t very useful for our purposes.  But we can change the value of the covariate at which to compare the means using syntax.

So it would tell us that at a young age of say 20, the three treatment groups (green, tan, and purple lines) all have means higher than the control (blue).  Young people learned more in all three treatment groups.

But at an older age, say 50, the means of the purple and tan groups were not significantly different from the control group’s (blue), and the green  (EIQ group) did worse!

In SPSS GLM, the syntax would be:

UNIANOVA OverallPost BY group WITH NEWAGE
/METHOD=SSTYPE(3)
/INTERCEPT=INCLUDE
/EMMEANS=TABLES(group) WITH(NEWAGE=MEAN) COMPARE ADJ(SIDAK)
/EMMEANS=TABLES(group) WITH(NEWAGE=45) COMPARE ADJ(SIDAK)
/EMMEANS=TABLES(group) WITH(NEWAGE=20) COMPARE ADJ(SIDAK)
/PRINT=PARAMETER
/CRITERIA=ALPHA(.05)
/DESIGN=NEWAGE group NEWAGE*group.

 


Bookmark and Share

Tagged With: analysis of covariance, ancova, EMMeans, moderating variable, Moderator, SPSS

Related Posts

  • Why ANOVA and Linear Regression are the Same Analysis
  • 3 Reasons Psychology Researchers should Learn Regression
  • SPSS GLM: Choosing Fixed Factors and Covariates
  • Same Statistical Models, Different (and Confusing) Output Terms

  • Go to page 1
  • Go to page 2
  • Go to Next Page »

Primary Sidebar

This Month’s Statistically Speaking Live Training

  • Member Training: Introduction to SPSS Software Tutorial

Upcoming Free Webinars

Poisson and Negative Binomial Regression Models for Count Data

Upcoming Workshops

  • Analyzing Count Data: Poisson, Negative Binomial, and Other Essential Models (Jul 2022)
  • Introduction to Generalized Linear Mixed Models (Jul 2022)

Copyright © 2008–2022 The Analysis Factor, LLC. All rights reserved.
877-272-8096   Contact Us

The Analysis Factor uses cookies to ensure that we give you the best experience of our website. If you continue we assume that you consent to receive cookies on all websites from The Analysis Factor.
Continue Privacy Policy
Privacy & Cookies Policy

Privacy Overview

This website uses cookies to improve your experience while you navigate through the website. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. We also use third-party cookies that help us analyze and understand how you use this website. These cookies will be stored in your browser only with your consent. You also have the option to opt-out of these cookies. But opting out of some of these cookies may affect your browsing experience.
Necessary
Always Enabled
Necessary cookies are absolutely essential for the website to function properly. This category only includes cookies that ensures basic functionalities and security features of the website. These cookies do not store any personal information.
Non-necessary
Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. It is mandatory to procure user consent prior to running these cookies on your website.
SAVE & ACCEPT