Determining Sample Size in Research

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Introduction

Estimating the correct sample size is an important, but often overlooked, step in the research process. Obtaining a sufficient number of participants is critical for achieving the level of statistical power needed to minimize the chance or error or falsely rejecting a null hypothesis when interpreting results. Unfortunately, numerous studies rely on convenience or purposeful sampling methods, which may or may not generate the correct number of participants. The purpose of this paper is to report on methods for determining sample size for research in the field of nursing. Quantitative methods will first be described, followed by qualitative methods. This paper will conclude with a brief summary and outline of key points. 

Quantitative Methods

Quantitative research is designed to empirically determine the relationship between one or more independent variables and their subsequent impact on any number of predetermined research outcomes (Johanson & Brooks, 2010). All research variables are objectively measured and statistically analyzed to determine the significance of these relationships (Johanson & Brooks, 2010). However, because there is always some degree of chance or error associated with any empirical study, particularly when measuring phenomena related to people, obtaining a sufficient sample size is critical to producing accurate and generalizable results (Johanson & Brooks, 2010). As with all components of quantitative research, there are very accurate and well-established steps for ensuring that minimum sampling requirements are met.

While there are some small discrepancies between quantitative researchers as to the precise and most accurate methods for determining sample size in a true random sample, there are some universal factors that always apply. First, the study population must be considered (Johanson & Brooks, 2010). The study population represents all the people for which the results of the study will apply. For example, a study intended to determine the impact of burnout on attrition in newly hired nursing professionals in the United States would include all newly hired nurses within this region for a given year. As of 2012, approximately 50,000 new nurses were hired, making the population for this study 50,000 (American College of Nursing, 2012). The next factor to consider when estimating sample size is the degree of accuracy, or statistical power, desired for the study (Dillman, Smyth & Christian, 2009). This degree of accuracy is referred to as "confidence", and most research related to human participants accepts a 95% confidence level (Dillman et al., 2009). In other words, researchers are willing to accept a 5% chance that the findings related to a particular study are based on purely chance. The variance for this population must then be determined, which is calculated by generating a z-score. A z-score informs researchers of the number of standard deviations a particular data point falls above or below the population mean (Dillman et al., 2009). While obtaining this score requires its own statistical formula, charts are available for determining the z-score for various confidence levels (Dillman et al., 2009).  For a confidence level of 95% and a standard deviation of 20, the z-score is 1.96 (Dillman et al., 2009). Finally, once the study population and confidence level are determined, the sample size can be estimated. The general formula (Dillman et al., 2009) used to estimate sample size is:

(Formula omitted for preview. Available via download) 

In this formula:   = the final sample size;   = the size of the population;  = the distribution of the population (usually 50%);  = margin of error; and  = z-score associated with desired confidence level. For the study described above, the formula would be:

(Formula omitted for preview. Available via download) 

Therefore, it can be determined that the sample size needed for the current study would be approximately 104 participants.  

Qualitative Methods

Unlike quantitative studies, qualitative research does not attempt to manipulate an independent variable to detect change in some predetermined study outcome (Mason, 2010). Qualitative research also does not attempt to calculate the significance of relationships that exist between certain variables (Dillman et al., 2009). Instead, this research design and methodology aims to merely describe the nature and existence of certain phenomena (Dillman et al., 2009). Due to its lack of statistical methodology, many researchers believe that qualitative research is not associated with error or bias. However, obtaining the correct sample size for qualitative research is equally, if not more, important than that of quantitative research (Mason, 2010). Relying on the responses of just one or a few individuals is not always sufficient for externally generalizing study findings. Therefore, researchers must still make an attempt to properly estimate and obtain enough participants to reduce the risk of response biases and produce valid results related to a particular topic. While there is no widely agreed upon method for determining sample sizes for qualitative research, several researchers have proposed guidelines based on the study methodology. The important factor to consider when determining sample size in qualitative research is saturation, or the point at which further interviews no longer yield novel information (Mason, 2010). Once again, there is no well-established method for calculating saturation in qualitative research, as this concept depends largely on the nature of the study. However, studies seeking to generalize their results to larger populations will generally require greater sample sizes, and vice versa (Mason, 2010). Thirty interviews is a common standard for many qualitative studies, with most qualitative researchers agreeing that 15 are the minimum number of acceptable participants (Mason, 2010). 

Conclusion

The purpose of this study was to discuss common methods for determining sample size in both quantitative and qualitative research. While numerous formulas exist for determining sample size in quantitative studies, guidelines for estimating sampling needs in qualitative research are much less clear. Nevertheless, making efforts to generate a sufficient number of participants helps reduce the chances of statistical or methodological errors in both research designs, and is a critical step for strengthening the results of a particular study. 

References

American College of Nursing (2012). Nursing shortage. Retrieved from http://www.aacn.nche.edu/media-relations/fact-sheets/nursing-shortage. 

Dillman, D. A., Smyth, J. D. & Christian, L. M. (2009). Internet, mail, and mixed-mode surveys (3rd ed.). Hoboken, NJ: John Wiley & Sons. 

Johanson, G. A. & Brooks, G. P. (2010). Initial scale development: Sample size for pilot studies. Educational and Psychological Measurement, 70(3), 394-400.

Mason, M. (2010). Sample size and saturation in PhD studies using qualitative interviews. Forum: Qualitative Social Research, 11(3). Retrieved from http://www.qualitative-research.net/index.php/fqs/article/view/1428/3027.