Measuring Usability: Ask a Statistics Question

June 2, 2008 | asked by Frank :

Question : I am charged with sampling expense report submissions for accuracy. We get 8000 T&E claims, and want to sample a subset making inferences about the population. I can probably get a good estimate of the populations' SD, how would i calculate required sample size? I think i would be measuring the delta between actual and claimed - the majority be 0. Is this a one sided issue? Thanks in advance - FT Also, would i need the acceptable level first? ie. we would accept an average difference of $5? How can i work backwards if the first sample size yields an average of $1? (if that made sense)

Answer :

If you are assessing claimed versus actual the only reason it would be a one-sided hypothesis test would be if you only adjust down. That is, the amount paid can never be greater than the amount claimed? If it can go both ways, then it is a two-sided issue.

If I understand the situation, you have a reasonable estimate of the standard deviation of the population, which would be the SD of the difference in actual expenses and claimed expenses.

If the 1st sample you took has an average difference of $1 and you have the standard deviation of that sample, I would construct a confidence interval around that mean to give you an idea of the likely range of the true spread. The next question will help answer you sample size question: What is it you are trying to detect, if the mean difference of the entire T&E claims are less than $5? If so, then one-sample 1-sided t-test testing against the mean of $5 would be the next approach. If you have the mean and standard deviation of the sample I can calculate that for you or you can send me the data. Your data is also probably slightly skewed, as there will likely be some differences that are very large and there is a lower-limit (0) to other claims. For that reason, you could also paste your data in the Task-Time calculator which will generate the 95% CI interval after transforming the data.

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Question Tags

Tag Name	#	Vote
1-sample t-test	2
Confidence Intervals	2
Sample Size	2

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User Provided Answers & Comments :

June 19, 2008 | frank wrote:

I would be happy to send the data if it will help Jeff - thanks

June 19, 2008 | Frank wrote:

Thanks for the input. I am struggling between treating it as attribute or continuous. For example, if an expense is inaccurate, i can treat that as 1 defect. However, most of the defects are small $'s. I took a sample and have close to 1000 records of actual vs. submitted. My question is this: how many reports (out of 10,000) do i need to review to be able to draw inferences about the overall accuracy of the population?

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