Sample Size Estimation

Sample size estimation:

This paper discusses the estimation of sample size for a study with reference to a Journal article by Chadwick (2001) “organization research”, according to Chadwick (2001) inadequate and inappropriate sample size influence the accuracy and quality of research. In this journal article he highlights the factors to consider when determining the sample size using Cochran (1977) formula. He states that bias may arise when sampling error and non response bias is disregarded. The following is a discussion of some of these factors to consider when determining sample size including the primary variable, margin of error, variance and the alpha value.

Primary variable:

The primary variable according to Cochran (1977) is the variable that is crucial in the study, in the AIU data the primary variable is job satisfaction, according to Chadwick (2001) using a variable like gender as the primary variable will result into a large sample size. The importance of this variable is the scale, in our case the scale is 1 to 7.

Margin of error:

According to Chadwick (2001) a researcher should decide on the margin of error a researcher is willing to accept, in previous studies researcher have identified the acceptable margin of error whereby for categorical data the acceptable margin is 5% while for continuous data the acceptable margin of error is 3%. In the AIU example job satisfaction is continuous and therefore the acceptable margin of error is 3%.

Sample Size Estimation

Alpha:

the alpha value is the risk a researcher is willing to accept in a case where the actual margin of error exceed the acceptable margin of error, in most studies the alpha value is usually 0.01 or 0.05, after deciding on the alpha value the T value of the alpha value is incorporated in the formula. In the AIU data set case the alpha value is assumed to be 0.01 and therefore the T value is 2.3164.

Variance:

According to Cochran (1977) the variance of the primary variable is also used in the sample size determination formula, this variance can be determined in a number of ways, one way to determine the variance is to use the scale of the primary variable and the structure of the population, for example in the AIU data set the primary variable scale is 7 and the assumption is that 98% of data is captured in either side of the mean, then the variance or standard deviation is determined as

S = scale points/ number of standard deviation

In this case according to the normal distribution assumption 98% of the data values are contained within 3 standard deviations, therefore standard deviations are 3 in each side of the mean, therefore

S=7/6

S = 1.166667

Sample Size Estimation

The formula:

The sample size determination formula as stated by Cochran (1977) is as follows:

N=(T2XS2)/D2

Where d2 = scale points multiplied by the acceptable error, T is the T value and S is the estimated variance

In the AIU data set the value are as follows:

T =2.3164, S =  1.166667, Scale points = 7, Acceptable error = 3%

Therefore the required sample size is:

N = ([2.3164]2 X [1.166667]2) / [7*3%] 2

N =340.9142

Therefore the required sample size is 341.

Sample Size Estimation

Population:

Assuming that the population is 1000, then the sample size estimated above is greater than 5%, according to Cochran’s (1977) stated that in such a case the correction formula should be used, this formula is stated as follows:

N’ = estimated sample/ (1+estimated sample/population)

In our case therefore the correctional formula should be used:

N’ = estimated sample/ (1+estimated sample/population)

N’ = 341/ (1+ (341/1000))

N’ = 254.2878

Therefore sample size should be 254

Response rate:

When a researcher estimates that the response rate will be certain percentage then the sample size should be increased, for example if response rate is expected to be 99% in the AIU study then the appropriate sample size will be the N’ estimated above divided by this percentage. As follows:

Sample Size Estimation

N = 254/0.99 = 256.5657

Therefore the appropriate sample size will be 257.

References:

Chadwick H. (2001). Organizational Research: Determining Appropriate Sample Size, Information Technology and Performance Journal, Volume 19, Number 1, 43-50

Cochran, G. (1977). Sampling techniques, New York: Wiley and Sons