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I have a study where I did a sample size calculation using N=2800, CI=95%, margin or error = 3.5% to yield n=613.

In the study (auditing of charts), I wanted to look at the error rate in my sample. I came up with 41 errors so p=41/613=0.067

I want to know if this proportion is significantly higher than what I should expect so I thought I could use the test of single proportion, however, to calculate this, I need both my sample proportion (p) and my population proportion (pi).

My question is --> how do I know my population proportion? Is it the same as the margin of error? Maybe I'm using the wrong formula even?

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  • $\begingroup$ The crucial element missing from this post is the value of "what I should expect." What is it? (We can't tell you, nor can we calculate it: it depends on the study and its objectives.) $\endgroup$ – whuber May 28 '15 at 22:15
  • $\begingroup$ Yes, you're right. I don't know what I should expect, so this is probably not the right calculation for this study. Thanks for confirming. $\endgroup$ – kristayyc May 28 '15 at 22:17
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Without knowing the exact context of your study, it's difficult to give a concrete advice. In general though, you could:

  • Use the information from previous studies in your field (if available, of course) to get an idea of the "normal" prevalence of the event of interest and compare your proportion to that value. For example, in medical research, the population prevalence of a known disease would typically be available.
  • If no such information is available from previous studies, use your expert opinion and hypothesize a value that might be critical for a given application. Again, using the medical analogy, one could say that if the prevalence of a certain disease reaches a level that is significantly larger than X% then there is an outbreak situation and the respective mitigation measures must be undertaken. The actual data would then be compared with that threshold value of X%.
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