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The inpatients infection rates will be tracked from the entire inpatient population on all three adult units allowing it to be compared to the rates prior and post hand hygiene training.

My hypothesis is that "by providing hand hygiene training to the DCS, there will be an inverse relationship to inpatient infection rates."

If I use t test to determine the difference between post and pre hand hygiene training, how can I measure inverse relationship? Is it possible to measure inverse relationship? Do I have to do correlation analysis in this case?

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    $\begingroup$ Can you clarify what you mean by "inverse relationship" in this context? I'm not sure I follow you. Do you simply mean that you think the inpatient infection rate will go down? $\endgroup$ – gung - Reinstate Monica Jul 19 '13 at 16:19
  • $\begingroup$ What is the "DCS"? How many observations of rates will you have - just one before and one after, or a longer time series? And is the training being given to all three units? $\endgroup$ – Peter Ellis Jul 19 '13 at 23:21
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If I understand the heart of the question correctly: a two-sided test will work whether the post measurements are greater or less than the pre measurements. For a two-sided t-test, the null hypothesis can be thought of as, there is zero difference in the means of the two samples. If the difference is significantly positive or significantly negative, the result in either case is significantly different from zero.

As this is an older post, we are not likely to get clarification as to whether there will be a single rate measured in each time period or a larger set of data.

The case of comparing two rates of infection would probably best be addressed by techniques used in epidemiology. I'm not very familiar with these techniques, but one test that may be applicable is a test to compare two Poisson rates. Implementations of this test or similar tests are described by Medicalc and the epitools package in R.

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