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Though Formulas Exist To Give One Very Precise Estimates Of The Statistical ...

Though formulas exist to give one very precise estimates of the statistical predictive validity of test items, there are two very reliable rules of thumb that generally apply:
A sample of 30 cases is often a threshold level for acceptability. That is, if one has less than this, most reviewers would indicate more is needed and more than this, most would accept the general predictions as valid, at least within a psychographically similar population.
A sample size of over 300 is very seldom needed. Exceptions to this might be in cases such as medical research when a one-in-1000 (or 2500, 5000, etc.) unique reaction might be important to know.  
Given these rules of thumb, the actual basis for determination of sample size predictably becomes a matter of the extent to which one wishes to be confident of the probability estimate, the extent to which individual cases or measurements display a large variance, the degree to which error is tolerated and the estimated proportion of individuals displaying the desired trait or behavior. This formula is expressed mathematically as (Bowerman & O'Connell 2003, p. 279):
n = p (1 p) * ((za/2)/B)2
Thus, as each survey item has a different variance, the ideal sample size also varies yet an acceptable estimate can be arrived at by using the average variance among all items, or 0.59. Given this and an assumption of an acceptable 15% margin of error, that is, that the real and true response, if indicated to be 3.00, could actually be somewhere between 2.55 and 3.45, and given a 95% confidence that this projection will be correct, the estimated minimum sample size to achieve this is 60. If one were wish to reduce the error tolerance or increase the confidence interval (or if responses were more varying than they are), increasing the sample size would be prudent. Thus, the included sample size of 118 individuals is adequate and the fact the items are uniformly scaled and grouped by cluster according to the particular hypotheses being addressed give the study an even greater potential level of confidence due to previously studies and focus groups which indicate a comparatively high degree of inter-cluster covariance and correlation. To illustrate this, consider the difference between asking a respondent one question designed to illicit if a certain belief or behavior is present compared to asking a group of 4-7 questions that ask about the same thing albeit from different perspectives. The first ‘test' is something of an all or none proposition whereas the second most likely has a much greater chance at capturing indicators of the belief or behavior, if it exists and affirming this with additional data items.
With this in mind, the items were tested cluster-wise as previous research and focus studies addressed the appropriability of clustering them by citing their high covariance/correlation.

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