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Statistic Unit 3 Db

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Autor:  anton  02 May 2011
Tags:  Statistic
Words: 497   |   Pages: 2
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Unit 3 DB

The selected article is “Research: A numbers game” by Jason Ball. The theme of the article is the technique involved in determining the correct sample size. Ball appropriately begins by describing the conflict involved in this issue. A too large sample size means unaffordable costs and a too small sample size means inaccurate results.

The technique involves answering two questions. The first question is “Are you going to analyze your data by the entire sample or do you plan on a more detailed examination of subgroups within the sample?” In the context of the job satisfaction survey, this means whether we are treating the employees as a unified group or are interested in analyzing the variations in job satisfaction with respect to the qualitative variables like gender or department. The second question is “… How accurate do you want your results to be?” The greater the accuracy required the larger is the sample size needed. An example of the specification of accuracy is ± 5% at a 95% confidence interval. This means that if 100 samples are drawn in 95 cases the results would be within plus or minus 5%. This accuracy corresponds to a sample size of about 400. If the accuracy were relaxed to 10% the sample size would reduce to about 100. In the context of the job satisfaction survey the required accuracy has not been specified, however, the accuracy obtainable can be determined from the given sample size. In the absence of a specific formula we can only say that the expected accuracy will be less than 10% with a sample size of only 29.

Ball states that if comparisons are to be made across a set of sub-samples then the minimum required number of observations required to carry out z tests and t tests is 30. The number of observations in the job satisfaction survey is 29, which just falls short of 30. Hence, if we want to compare the satisfaction levels between genders or departments (or other qualitative variables) we are just short by 1 observation. However, if deeper analysis of sub-samples is required then according to Ball the minimum sample size should be 100. Hence, if we want to compare the satisfaction levels between males and females of the administration department then we are woefully short of the required number.

The greatest drawback of this article is that Ball deals with the technique of sample size determination only in a qualitative manner and does not specify the exact formula. He also does not discuss the relation of sample size to the population standard deviation. If the population has larger standard deviation then a larger sample will be required for the same accuracy and confidence level. (Anderson, Sweeney, Williams, 2001)


Anderson, D.R., Sweeney, D. J., & Williams, T.A., (2001). Statistics for Business and Economics. United States: South Western

Ball, J (2004).Simple rules shape proper sample size. Marketing News. 38,

Bluman, A.G. (2008). A brief version elementary Statistics 4th edtion. New York, N.Y.: McGraw-Hill, Inc.

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