easy to confuse statistical concepts

One of those tricky, but necessary, concepts in statistics is the difference between crossed and nested factors.

As a reminder, a factor is any categorical independent variable. In experiments, or any randomized designs, these factors are often manipulated. Experimental manipulations (like Treatment vs. Control) are factors.

Observational categorical predictors, such as gender, time point, poverty status, etc., are also factors. Whether the factor is observational or manipulated won’t affect the analysis, but it will affect the conclusions you draw from the results.

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There are many statistical concepts that are easy to confuse.

Sometimes the problem is the terminology. We have a whole series of articles on Confusing Statistical Terms.

But in these cases, it’s the concepts themselves. Similar, but distinct concepts that are easy to confuse.

Some of these are quite high-level, and others are fundamental. For each article, I’ve noted the Stage of Statistical Skill at which you’d encounter it.

So in this series of articles, I hope to disentangle some of those similar, but distinct concepts in an intuitive way.

Stage 1 Statistical Concepts

The Difference Between:

• Association and Correlation
• A Chi-Square Test and a McNemar Test

Stage 2 Statistical Concepts

The Difference Between:

• Interaction and Association
• Crossed and Nested Factors
• Truncated and Censored Data
• Eta Squared and Partial Eta Squared
• Missing at Random and Missing Completely at Random Missing Data
• Model Assumptions, Inference Assumptions, and Data Issues
• Model Building in Explanatory and Predictive Models

Stage 3 Statistical Concepts

The Difference Between:

• Relative Risk and Odds Ratios
• Logistic and Probit Regression
• Link Functions and Data Transformations
• Clustered, Longitudinal, and Repeated Measures Data
• Random Factors and Random Effects
• Repeated Measures ANOVA and Linear Mixed Models
• Principal Component Analysis and Factor Analysis
• Confirmatory and Exploratory Factor Analysis
• Moderation and Mediation

Are there concepts you get mixed up? Please leave it in the comments and I’ll add to my list.

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It’s really easy to mix up the concepts of association (as measured by correlation) and interaction.  Or to assume if two variables interact, they must be associated.  But it’s not actually true.

In statistics, they have different implications for the relationships among your variables. This is especially true when the variables you’re talking about are predictors in a regression or ANOVA model.

Association

Association between two variables means the values of one variable relate in some way to the values of the other.  It is usually measured by correlation for two continuous variables and by cross tabulation and a Chi-square test for two categorical variables.

Unfortunately, there is no nice, descriptive measure for association between one (more…)

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