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I am doing a Poisson regression analysis and have found that the type of programme a student is enrolled on to does not have a significant effect on the outcome. When it comes to writing out the fitted equation would I need to include the programme if it does not have an effect?

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    $\begingroup$ An interesting change occurs between the beginning and end of your question, Emily. Initially you refer to a "[not] significant effect." That means you could not estimate the effect with sufficient reliability given the data you have. At the end, though, you appear to use "effect" in the sense of the true effect, not its measurement. The two differ in an important sense: the former is your estimate, the latter is real (but unknown). If we now reread your question, understanding the last "effect" in the first sense, it may clarify the situation. $\endgroup$ – whuber Feb 8 '13 at 16:54
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When you report on your statistical analysis, yes, you should report the model you based your conclusions on, not drop components that are not statistically significant - those may still influence the effect of other regressors.

If you are really asking whether you should drop the insignificant predictor and re-fit your model (called "stepwise regression") - you should not do that if your goal is inference, but this may be defensible if your goal is prediction.

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