Sample Size Estimation and Power Analysis

Introduction of sample size estimation and power analysis

Sample size estimation is the process by which a researcher determines the number of observations they should include in a statistical sample. The sample size and sample size estimation are very important parts of empirical research in which the researcher selects a part of the population (sample) by which they will use to make inferences about the entire population. In other words, sample size and sample size estimation are the processes of selecting a certain number of observations from the entire population to use a representation of the entire population because in many cases, the data from an entire population is not feasible or even available.

The purpose of sample size estimation is usually to ensure that the margin of error is significantly small to make it informative. For example, to estimate the average height of university students, we will conduct a study and estimate the 95% confidence intervals which might be 150 ± 50 centimeters. This means that the actual average height of all students in the university will be between 100 and 200 centimeters. This is a very wide margin of error and to make it more informative, a researcher will want the margin of error to be smaller for instance 10 to 20 centimeters maybe. Therefore, to make the sample size informative, a researcher will select a desired margin of error and use it to estimate a sample size. The margin of error in a one sample confidence interval can be expressed as;

E= Z σ/ √n

With the above expression, the goal is to determine the sample size “n” sch that the margin of error “E” does not exceed a desired value. Other way of estimating sample sizes are;

• Using sample size experiences, small sample size while some time unavoidable have historically and consistently proved to provide very wide confidence intervals
• Utilizing a target for the power of a certain statistical test (power analysis) to be applied when a sample has been collected.
• Using confidence intervals, the narrower a required confidence interval the larger the sample size will be required.

A power analysis used when determining a sample size that utilizes a target for the power of a certain statistical test (power analysis) to be applied when a sample has been collected. Into perspective; when conducting a test of hypothesis, a researcher can commit a type I error or a type II error. Power analysis deal with the reduction of committing a type II error. A type II error is committed when the researcher accepts a null hypothesis when the null hypothesis should have been rejected. Facts about power analysis

• The larger the sample size, the easier it is to achieve a desired level of significance. As such, when the sample size is very small, the easier it is to commit a type II error due to insufficient power.
• The purpose of power analysis is to help the researcher determine the smallest sample size required to detect the effect of a certain test at a certain desired level of significance.
• In basic usage, the desired power is 0.8, a researcher can specify a higher power such as 0.9 which translates to 90% probability that the researcher will not commit a type II error.

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