Sample Size

• How do I determine the sample size I need for my study? 
• How does it impact my research if my sample size is smaller (or larger) than recommended?
• How does sample size influence how I interpret my results and conclusions?
• What is G-Power and how can it help determine sample size?
  

 Determining Sample Size  

 The sample size needed for a particular research project depends, in part, on the type of research and the experimental design.  There are numerous textbooks and websites that give specific instructions regarding how to calculate the appropriate sample size.  Quantitative studies make use of statistical techniques for determining sample size.  The statistics usually take into account the size of the target population and the confidence level desired in the results. There are relatively simple ways for researchers to use these statistical calculations, such as calculators or tables.  Follow this link for an example:  Sample Size Calculator.  In qualitative studies, sampling typically continues until information redundancy or saturation occurs. This is the point at which no new information is emerging in the data.  Therefore, in qualitative studies is it critical that data collection and analysis are occurring simultaneously so that the researcher will know when the saturation point is reached.  Regardless of the type of research, most researchers are able to ascertain the needed sample size. However, in the real world, research rarely goes as planned and obtaining the correct sample size is no exception. This module explains the impact of a smaller (or larger) sample size and how that may influence the results, and ultimately, the conclusions.

Impact and Influence of Smaller (or larger sample) Sizes

 If the sample size is smaller (or larger) than recommended, it can create limitations and have detrimental effects.  Determining the correct sample size and following through to collect data from a sample population reflecting that size is one of the most important steps in conducting meaningful research.  Following is a list of ways small sample size may impact a research study:

• Reduces Statistical Power – The statistical power is the ability of statistical test to measure or demonstrate traits that exist in the target population. As the sample size declines, the statistical power of the data also declines and the results become less reliable because they may not truly represent the entire population.
• Type II Error – As sample size decrease, the probably of a Type II Error increases. A Type II Error is when a “false negative” occurs. The occurrence of a trait in the small sample may not occur at the same rate in the overall population. This may lead to errors in accepting or rejecting the hypothesis.
• Significance – This refers to the “significance” of differences in data points. For example, if examining student test scores, the researcher may need to know if the difference between two sets of scores from different classrooms is significant.  If each class only has two students, the results may not accurately represent a larger student body and it would be difficult to determine if the difference in test scores was significant.
• Distribution – It is helpful to subdivide the data collected into groups so that the researcher can see the distribution of data points along a continuum. Placing the data points into groups becomes very difficult if the sample size is too small.  It is possible that some groups or categories may not even have any data points.
• Wasteful Research – Small sample sizes may lead to research that is unreliable and therefore, not valuable. This may result in a waste of financial and human resources because the study is essentially not valid.
• Reproducibility – Good research is reproducible. Small sample sizes may lead to results that are skewed or inaccurate, and therefore, not reproducible.  For example, perhaps a researcher is looking at disease prevalence of a very rare disease among a certain population.  If the sample size is too small and the researcher, by chance, has a higher number of these patients in the sample, the results will show that the prevalence of the disease is much higher in the general population than it really is.  Not only are the results inaccurate, another researcher would not get this same result because the data is skewed.

While researchers believe that large sample sizes are always ideal, they can present challenges as well.  The first of those concerns is an ethical one.  Should a study be conducted or performed with more participants than necessary?  For example, if it is medical study, it may not be in the subjects best interest to participate in the study and therefore, it is unethical to subject more people to the treatment or therapy than necessary.  Overly large sample sizes may also involve additional financial and human resources than necessary.  Finally, a large sample size may increase the statistical power and exaggerate the results to points where something that is insignificant becomes significant.

As discussed above, the correct sample size is important for statistical, methodological, and ethical reasons.  It may also have practical impacts on financial and human resources.  For the results of a study to reliable and valid, collecting data from an appropriate sample size is critical to the study if the results are going to be generalized to the larger population.  Therefore, planning the sampling phase of the research and including a large enough number of samples from the beginning will produce the best results and most accurate conclusions.

G Power & Sample Size:

Fortunately, there is help for researchers trying to determine sample size and statistical software is one of the most resources that researchers utilize.  

G-Power is a free statistical software that can be  used for power analysis and sample size calculations. It is available  for both Windows and Mac and it is relatively easy to learn and use.   The software is used to assist in minimizing type II errors or false  negatives and ensuring an appropriate sample size is an important part  of the process. If the sample size is too small, the study will lack  precision and will not provide reliable data that can be used to answer  the research question. If the sample size is larger than necessary,  resources and time will be wasted.

Researchers can use Power Analysis software to gain access to a number of graphical and analytical tools  that will enable them to evaluate the factors that affect the power of a  study and consider the statistical tests planned for the data analyses.   The G-Power software can then be used to calculate the sample size  necessary for the desired power levels and the type of statistical  analysis that will be performed.  Before using this software,  researchers should become familiar with basic statistical terminology  and commonly used methods of data analysis.

The following video  offers step-by-step instructions on how to use G-power to calculate the  sample size appropriate for the study and the desired statistical  analysis: