# Power and Sample Size

### Two Types of Effect Size Statistic: Standardized and Unstandardized

June 26th, 2023 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

June 12th, 2023 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.

You will measure the effect size in question 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…)

### How the Population Distribution Influences the Confidence Interval

September 6th, 2022 by

Spoiler alert, real data are seldom normally distributed. How does the population distribution influence the estimate of the population mean and its confidence interval?

To figure this out, we randomly draw 100 observations 100 times from three distinct populations and plot the mean and corresponding 95% confidence interval of each sample.
(more…)

### Member Training: A Gentle Introduction to Bootstrapping

July 28th, 2022 by

Bootstrapping is a methodology derived by Bradley Efron in the 1980s that provides a reasonable approximation to the sampling distribution of various “difficult” statistics. Difficult statistics are those where there is no mathematical theory to establish a distribution.

### How Big of a Sample Size do you need for Factor Analysis?

August 21st, 2020 by

Most of the time when we plan a sample size for a data set, it’s based on obtaining reasonable statistical power for a key analysis of that data set. These power calculations figure out how big a sample you need so that a certain width of a confidence interval or p-value will coincide with a scientifically meaningful effect size.

But that’s not the only issue in sample size, and not every statistical analysis uses p-values.

### Member Training: Interpretation of Effect Size Statistics

August 30th, 2019 by

Effect size statistics are required by most journals and committees these days ⁠— for good reason.

They communicate just how big the effects are in your statistical results ⁠— something p-values can’t do.

But they’re only useful if you can choose the most appropriate one and if you can interpret it.

This can be hard in even simple statistical tests. But once you get into  complicated models, it’s a whole new story. (more…)