# Sample Size

Sample Size

Sample size calculation is one of the crucial steps in statistical analyses.  The extraction of the sample size is generally a tedious process in the preparation of a particular statistical study.

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The statistical studies that consist of various kinds of surveys, experiments, observational studies, etc. always give valid conclusions only if they are appropriately and significantly planned by keeping certain things in mind.  These things include the reliability of the instruments to be used for measuring, the appropriate understanding of the problem, and the determination of an adequate sample size.

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Because type II errors are generally committed by the researcher due to inadequate sample size, some clinical trial sample size calculation programs have been developed.  This has been specifically designed in order to avoid Type II errors which are a serious kind of error, especially in the field of medicine.

According to Peers (1996), sample size is one of the four unified features of a study design that can manipulate the detection of the significant differences, relationships or interactions.  Suppose a researcher has conducted a simple survey on a product.  If that survey reveals numerous errors, then it is advisable to check the researcher’s approach in making an appropriate sample size selection.

Most researchers can always benefit from a real life manuscript that describes the common procedure of sample size determination for simple random and systematic random samples.  This real life manuscript consists of sample size issues that have been determined in order to solve certain problems.

Krejcie and Morgan’s (1970) developed the formulas for determining the sample size for categorical types of data.  These formulas for determining the sample size provide identical sample sizes in cases where the researcher adjusts the tabulated value based on the size of the population, which should be less than or equal to 120.

However, the researcher should always be cautious while using Krejcie and Morgan’s (1970) formulas for the sample size selection. This is because in these formulas, the value of alpha is assumed to be 0.05 and the degree of accuracy is 0.05.  Other formulas for sample size selection are also available, but these two formulas for sample size selection are more popular.

Cochran (1977) has given a technique for sample size determination. Cochran (1977) stated that in order to determine the sample size, one has to identify the limits of the errors in the items that have been considered as the most essential items in the survey.

According to Cochran (1977), an estimation of the required sample size is initially made separately for each of the essential items in the survey.  After this, the researcher will have a range of sample sizes that include smaller sample sizes for scaled and continuous variables, and larger sample sizes for dichotomous categorical variables.  The researcher should make sampling decisions based on the data.

If the range of the sample size is relatively close to the variable of interest, then the researcher can confidently use the largest sample size that would provide him/her the desired result.  A serious component for sample size determination is the estimation of the variance in the significant variables of interest under the study.  This is called a serious component because the researcher does not have direct control over the variance and therefore must include the variance estimates.

Cochran (1977) has stated four steps needed to estimate the population variances for sample size determination.

In the first step of estimating the population variances, the researcher obtains the sample in two steps and uses the results of the first step in order to determine the desired number of additional responses to achieve an appropriate sample size based on the variance observed in the data in the first step. In the second step of estimating the population variances for sample size determination, the researcher uses the results of the pilot study. In the third step of estimating the population variances for sample size determination, the data from previous studies of similar populations are used by the researcher. And in the last step of estimating the population variances for sample size determination, the researcher estimates the formation of the population with the help of some logical mathematical results.

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