Sample Size in Plain English

As a dissertation consultant for over 20 years, I consistently see confusion when it comes to answering a simple question—how many participants do in need? The confusion is reasonable because most programs do not even offer a class in sample size and leave it to the graduate student to figure it out on their own. This post will clear it up once and for all.

Two Types of Sample Sizes

There are two types of sample sizes to determine: one sample size determination is used to find the number to have enough participants to be representative of a population, and the other sample size determination is to achieve statistical power. Let’s talk about these two types.

Sample Size for a Population—what researchers and organizations need

This type of sample size determination is an effort to get a representation of the population, such as you see would see in election polling. To determine this sample size, you need to know the population size, confidence interval and confidence level (typically 95%). This is almost never the type of sample size that dissertation students need because you don’t have unlimited time, money, energy to get such as large sample. If you are a funded researcher or organization, and desire this type of sample size, you can view our free calculator at https://www.statisticssolutions.com/free-resources.

Sample Size for Statistical Power—what dissertation students need

Statistical power (also called a power analysis and typically set at .80) is the basically the probability of finding statistical differences in your data if in fact they are there. The .80 is saying that you have an 80% chance of finding difference in you data if differences exist. To assess this type of sample size you need to know a few things. First, you need to know what type of statistical analysis you are going to conduct. That is, the sample size calculation for an ANOVA is different than for a correlation or factor analysis. Second, you need to know the effect size, alpha, and desired statistical power. We decided on the conventional .80 power and alpha is usually set at .05 (you’ll recognize the p = .05 in the articles you’ve been reading for several years). Let’s talk about effect sizes and the three sizes they come in: small, medium, and large. Effect size is this context is the ability to detect differences in the data, so, a bit counter intuitively, a large, easily detected effect requires a small sample size to detect it, while a small, difficult to detect effect in the data requires a larger sample size.

How Do You Decide What Effect Size to Choose?

The next question you should be asking yourself is should I choose a small, medium, or large effect size? There are theoretical and practical considerations here. The theoretical answer is to look at the research previously conducted with your types of research questions, variables, and analyses, to see what effect size was found. The problem is that if a small effect size was found (thus requiring a large sample size) it may be impractical for you to find the 300+ participants! On the other hand, just picking a large effect size willy-nilly isn’t quite correct either. What I find is that most dissertation committees go along with are medium effect sizes. You can try to calculate it for free at G-Power or if you want to find the appropriate sample size with a simple write up and references, you can go here (while this one is not free—sorry—it’s cheaper than paying us or others $800 to calculate it).

Sample size note. Having said all of this, you should probably recruit as many participants as you can (hence boosting your statistical power).

If you have any sample size questions, or other questions about your methodology or results chapters, feel free to contact us. I hope this helps!

Happy Learning,

Statistics Solutions