MHB Is a T-Test Suitable to Compare Paper and Online Registry Participation Rates?

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The discussion centers on comparing participation rates between a paper-based and an online registry in a small intervention study, with 185 participants for the paper registry over 36 months and 301 for the online registry over 13 months. The user seeks to determine if the difference in participation rates is statistically significant using a t-test, despite lacking standard deviation data. Suggestions include considering the Poisson distribution for analysis and emphasizing the importance of understanding the distribution of the data. Clarification is needed on the specific hypothesis being tested, as well as the potential to estimate standard deviations from available data. Accurate statistical analysis requires a clear understanding of the data collection methods and the nature of the variables involved.
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I have a small intervention study comparing a paper based registry versus an online based registry. In the 36 months of the paper based registry I had 185 participants in the 13 months of the online registry I had 301 participants.

The average participants per month in paper was 5.1 and online was 23.
I need to prove that this is "statistically significant".

I believe these are independent groups and should be compared with a t-test.
But I don't have any data on standard deviation. I have only the total number of enrolled participants and the length of time of enrollment.

Can someone help?

many thanks
 
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how come you have the means but not the standard deviations ?

you could try using the Poisson distribution
 
Keep in mind that a mean may not be a good method of summarizing your data, especially data with multiple peaks or long tails (or other deviations from an approximately normal distribution).

Are you certain you have no method at all to collect this data? Depending on how you executed both registries, I would expect a skewed distribution on the amount of registries collected per unit of time. If for instance you advertized your research after a lecture, you would expect to see a bump just after that.

Anyway, I'm not quite sure yet what you are trying to measure: you seem to be saying that you need to show with a certain level of certainty that both studies are independent on the variable 'date collected' ? (You do not prove differences in statistics, you reject the null hypothesis of no difference with a certain degree of certainty (for you probably a confidence interval).) What exactly do you want to do? Just explain it in normal language, e.g., I want to know if the groups had a different I.Q.)

PS. If this is what you want to measure, and you do have information on the dates these 'registers' where obtained: it is trivial to calculate standard deviations. It might also be possible to estimate the standard deviation, or at the very least attempt to construct a very conservative estimate.
 
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