Sample Size Formula
The Formula Gets You a Number. The Justification Gets You Approved.
Every doctoral student needs a sample size. Most Google a formula, plug in numbers, and paste the result into Chapter 3. But your committee doesn’t care about the number. They care about the reasoning. Why that effect size? Why that alpha level? Why that power target? Where did you get the population estimate? What happens if you fall short? The formula is the easy part. The narrative around it is what separates a methodology chapter that moves forward from one that gets returned.
The tipping point isn’t n = 128. It’s the paragraph that explains why n = 128. The formula produces a number. Your justification produces committee confidence.
Anyone can run a formula. Not everyone can defend the inputs. That defense is the tipping point between a proposal that stalls and one that gets approved.
Get Expert Help with Your Results. Schedule Your free Consultation.
20 minutes with Dr. Lani. No obligation. No pressure.
Sample is the part of the population that helps us to draw inferences about the population. Collecting research of the complete information about the population is not possible and it is time consuming and expensive. Thus, we need an appropriate sample size so that we can make inferences about the population based on that sample.
One of the most frequent problems in statistical analysis is the determination of the appropriate sample size. One may ask why sample size is so important. The answer to this is that an appropriate sample size is required for validity. If the sample size it too small, it will not yield valid results. An appropriate sample size can produce accuracy of results.
Moreover, the results from the small sample size will be questionable. A sample size that is too large will result in wasting money and time. It is also unethical to choose too large a sample size. There is no certain rule of thumb to determine the sample size. Some researchers do, however, support a rule of thumb when using the sample size. For example, in regression analysis, many researchers say that there should be at least 10 observations per variable. If we are using three independent variables, then a clear rule would be to have a minimum sample size of 30. Some researchers follow a statistical formula to calculate the sample size.
Calculation of the Sample Size
Sample size based on confidence intervals: In calculating the sample size, we are interested in calculating the population parameter. Thus, we should determine the confidence intervals, so that all the values of the sample lie within that interval range.
Sample Size Calculation Based on Effect Size
An alternative approach of calculating the sample size is effect size. Effect size is known as the difference between the sample statistics divided by the standard error. More efficiently it is as follows:
Once an effect size has been estimated, the following table can be used to estimate a sample:
|
Alpha (α) = .05 |
Alpha (α) = .01 | |||
|
Effect Size (ES) |
Effect Size (ES) | |||
|
Sample size |
Small (.2) |
Moderate (.5) |
Small (.2) |
Moderate(.5) |
|
20 |
0.10 |
0.34 |
0.03 |
0.14 |
|
40 |
0.14 |
0.60 |
0.05 |
0.35 |
|
60 |
0.19 |
0.78 |
0.07 |
0.55 |
|
80 |
0.24 |
0.88 |
0.09 |
0.71 |
|
100 |
0.29 |
0.94 |
0.12 |
0.82 |
|
150 |
0.41 |
0.99 |
0.20 |
0.96 |
|
200 |
0.52 |
1.00 |
0.28 |
0.99 |
As mentioned above, the alpha is equal to the acceptable probability of the type I error and beta is the acceptable probability of type two errors and 1-beta equal to the power. As the power will increase with different levels of alpha, sample size will also increase.
Take the course: Sample Size and Power Analysis