OptinMon 25 - Effect Size Statistics

Two Types of Effect Size Statistic: Standardized and Unstandardized

October 25th, 2016 by

Effect size statistics are all the rage these days.

Journal editors are demanding them. Committees won’t pass dissertations without them.

But the reason to compute them is not just that someone wants them — they can truly help you understand your data analysis.

What Is an Effect Size Statistic?

When many of us hear “Effect Size Statistic,” we immediately think we need one of a few statistics: Eta-squared, Cohen’s d, R-squared.
And yes, these definitely qualify. But the concept of an effect size statistic is actually much broader. Here’s a description from a nice article on effect size statistics:

“… information about the magnitude and direction of the difference between two groups or the relationship between two variables.

– Joseph A. Durlak, “How to Select, Calculate, and Interpret Effect Sizes”

If you think about it, many familiar statistics fit this description. Regression coefficients give information about the magnitude and direction of the relationship between two variables. So do correlation coefficients. (more…)

The Effect Size: The Most Difficult Step in Calculating Sample Size Estimates

March 25th, 2013 by

One of the most difficult steps in calculating sample size estimates is determining the smallest scientifically meaningful effect size.

Here’s the logic:

The power of every significance test is based on four things: the alpha level, the size of the effect, the amount of variation in the data, and the sample size.

The effect size in question will be measured differently, depending on which statistical test you’re performing. It could be a mean difference, a difference in proportions, a correlation, regression slope, odds ratio, etc.

When you’re planning a study and estimating the sample size needed for (more…)

The Difference Between Eta Squared and Partial Eta Squared

December 16th, 2011 by

It seems every editor and her brother these days wants to see standardized effect size statistics reported in journal articles.

For ANOVAs, two of the most popular are Eta-squared and partial Eta-squared.  In one way ANOVAs, they come out the same, but in more complicated models, their values, and their meanings differ.

SPSS only reports partial Eta-squared, and in earlier versions of the software it was (unfortunately) labeled Eta-squared.  More recent versions have fixed the label, but still don’t offer Eta-squared as an option.

Luckily Eta-squared is very simple to calculate yourself based on the sums of squares in your ANOVA table. I’ve written another blog post with all the formulas. You can (more…)

5 Reasons to Run Sample Size Calculations Before Collecting Data

September 9th, 2011 by

Most of us run sample size calculations when a granting agency or committee requires it.  That’s reason 1.

That is a very good reason.  But there are others, and it can be helpful to keep these in mind when you’re tempted to skip this step or are grumbling through the calculations you’re required to do.

It’s easy to base your sample size on what is customary in your field (“I’ll use 20 subjects per condition”) or to just use the number of subjects in a similar study (“They used 150, so I will too”).

Sometimes you can get away with doing that.

However, there really are some good reasons beyond funding to do some sample size estimates. And since they’re not especially time-consuming, it’s worth doing them. (more…)

A Comparison of Effect Size Statistics

January 13th, 2011 by

If you’re in a field that uses Analysis of Variance, you have surely heard that p-values alone don’t indicate the size of an effect. You also need to give some sort of effect size measure.

Why? Because with a big enough sample size, any difference in means, no matter how small, can be statistically significant. P-values are designed to tell you if your result is a fluke, not if it’s big.

Truly the simplest and most straightforward effect size measure is the difference between two means. And you’re probably already reporting that. But the limitation of this measure as an effect size is not inaccuracy. It’s just hard to evaluate.

If you’re familiar with an area of research and the variables used in that area, you should know if a 3-point difference is big or small, although your readers may not. And if you’re evaluating a (more…)

How to Calculate Effect Size Statistics

January 13th, 2011 by

There are many effect size statistics for ANOVA and regression, and as you may have noticed, journal editors are now requiring you include one.

Unfortunately, the one your editor wants or is the one most appropriate to your research may not be the one your software makes available (SPSS, for example, reports Partial Eta Squared only, although it labels it Eta Squared in early versions).

Luckily, all the effect size measures are relatively easy to calculate from information in the ANOVA table on your output.  Here are a few common ones: (more…)