Statistical Assumptions

What Makes a Statistical Analysis Wrong?

January 21st, 2010 by

One of the most anxiety-laden questions I get from researchers is whether their analysis is “right.”

I’m always slightly uncomfortable with that word. Often there is no one right analysis.

It’s like finding Mr. or Ms. Right. Most of the time, there is not just one Right. But there are many that are clearly Wrong.

What Makes an Analysis Right?

Luckily, what makes an analysis right is easier to define than what makes a person right for you. It pretty much comes down to two things: whether the assumptions of the statistical method are being met and whether the analysis answers the research question.

Assumptions are very important. A test needs to reflect the measurement scale of the variables, the study design, and issues in the data. A repeated measures study design requires a repeated measures analysis. A binary dependent variable requires a categorical analysis method.

But within those general categories, there are often many analyses that meet assumptions. A logistic regression or a chi-square test both handle a binary dependent variable with a single categorical predictor. But a logistic regression can answer more research questions. It can incorporate covariates, directly test interactions, and calculate predicted probabilities. A chi-square test can do none of these.

So you get different information from different tests. They answer different research questions.

An analysis that is correct from an assumptions point of view is useless if it doesn’t answer the research question. A data set can spawn an endless number of statistical tests that don’t answer the research question. And you can spend an endless number of days running them.

When to Think about the Analysis

The real bummer is it’s not always clear that the analyses aren’t relevant until you  write up the research paper.

That’s why writing out the research questions in theoretical and operational terms is the first step of any statistical analysis. It’s absolutely fundamental. And I mean writing them in minute detail. Issues of mediation, interaction, subsetting, control variables, et cetera, should all be blatantly obvious in the research questions.

Thinking about how to analyze the data before collecting the data can help you from hitting a dead end. It can be very obvious, once you think through the details, that the analysis available to you based on the data won’t answer the research question.

Whether the answer is what you expected or not is a different issue.

So when you are concerned about getting an analysis “right,” clearly define the design, variables, and data issues, but most importantly, get explicitly clear about what you want to learn from this analysis.

Once you’ve done this, it’s much easier to find the statistical method that answers the research questions and meets assumptions. Even if you don’t know the right method, you can narrow your search with clear guidance.