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# Sample Size Estimation as Exemplified in Job Satisfaction Survey

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Sample size determination is an important step in the survey conceptualization process. Various considerations must be taken into account prior and subsequent to the calculation of the survey sample size. One prior consideration to consider is the type of variable being measured. For example, job satisfaction is usually measured using a Likert scale made up of five to ten points, which is a continuous variable. However, the researcher may also be interested in determining if the employees differ by categorical variables such as job position, gender, tenure etc.

If so, the researcher must determine which type of variables must be used in the calculation of sample size. As Bartlett et al. (2001) points out, this is an important question since the use of a dichotomous variable such as gender will result in a larger sample size than when the point scale is used as the primary variable of measure (p. 44). Cochran (1977) suggests the specification of a margin of error as one method to be used in calculating sample size. Sample size using this margin of error is then estimated for each of the important variables of interest (p. 1) leaving the researcher to decide which combination of variable and sample size fits his or her needs.

The equation that Cochran refers to is well-known and appears as equation 1 in Shiffler et al. (1987, p. 319). As the authors state, a problem with using this equation is the need for the variance term, which is often an unknown value. In answer to this, researchers often make use of a sample variance estimate from a previous pilot study. Of course this would mean that the estimator used is a random variable and would vary from the actual population variance.

Using this in equation 1 would then mean that the sample size as well as the precision of the accompanying confidence interval for the sample size will also be random variables (Shiffler et al. ,1987, p. 319). Given certain assumptions, Shiffler et al. computed for the mean, the variance, and the skewness of an estimate sample size ( ) that makes use of a pilot sample variance for single variable from a normally distributed population of simple random sampling design.

This is not a huge setback since most sampling designs build on the concepts used in simple random sampling and in the case of the example SRS is a popular and logical choice for estimating overall employee job satisfaction. Shiffler et al. (1987) were able to conclude that 1) is an unbiased estimator of the n, 2) E[ ] is independent of the pilot sample size, 3) Var[ ] decreases as pilot sample size increases and finally 4) that for a pilot sample size of less than 60, is negatively skewed (p. 320).

Thus, for a unique sample, there is greater chance of underachieving rather than overachieving the desired sample size when using a pilot study with sample size (p. 320). As we all know, a larger sample size is advantageous for inference as it increases the probability that the estimate equals the actual value. In the case of job satisfaction, this would be problematic for small companies with small number of employees rendering an unsatisfactory estimate of job satisfaction.

Luckily, Shiffler et al. ere able to compute for correction factors applicable to balance the probabilities of the under and overachievement of n using pilot sample sizes less than 60. Table 1 of their paper facilitates the choice of an appropriate sample size using pilot studies with sample sizes less than 60 by providing the pilot sample sizes and the probabilities of underachievement of the true n as well as the corresponding correction factor. They observed that at a pilot sample size equal to 60, the bias from using small pilot samples is small enough to be ignored and when greater than 60, correction is no longer even necessary (p. 19).

As Shiffler et al. (1987) states, Equation 1 (p. 319) is significant in computing sample size because it ascertains that the confidence interval has a desirable sampling error of at most e. According to Shiffler et al. , once a pilot study is completed, the probability that the sampling error is at most e is a function of the previous pilot study variance and the full sample variance that is based on independent observations. The correction factors presented in their study increases the probability of the occurrence of e (p. 21).

Another quantitative criterion is proposed by this study, but ultimately, the final choice for the appropriate sample size relies solely of the researcher. As mentioned, this study can be directly applied when doing a Job Satisfaction Survey as SRS is often the sampling scheme used. This paper is important in that it banishes the fear of researchers in relying on pilot studies, particularly those with small sample sizes, when computing for sample sizes to use in their own surveys.

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