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Simple Interactive Statistical Analysis


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Logit

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Explanation.

The function is intended to be of some help in interpreting the log-odds-ratio, which are the parameters that you get in a logistic regression or log linear analysis. Most people seem to know what a percentage is, however, the author of this text knows from the experience of reviewing papers for journals that not everyone knows what an odds-ratio is, many confuse it with the relative-risk-ratio or the rate-ratio. The odds-ratio is the chance of doing, having, intending, relative to chance of not doing, not having or not intending. Thus, if in place A 80% are purple and 20% pink then the odds of purple over pink equals four, there are four (4.0) times as many purples than pinks. If in place B there are 60% purples against 40% pinks then in place B the odds equals 1.5, one-and-a-halve more purples against pinks. The odds-ratio of A over B equals 2.67 (4.0/1.5), there is a 2.67 higher number of purples over pinks in A compared with B. Notice the difference with the risk ratio, which would conclude that there are 1.33 times (80%/60%) as many purples in A compared with B. The risk-ratio has the advantage of being easier to interpret, the odds-ratio has the advantage of being symmetric in a number of ways: the odds-ratio of purples in B over A equals 0.38 (1/2.67), the odds-ratio of pinks in A over B equals 0.38, the odds ratio of pinks in B over A equals 2.67 (1/0.38). Try to do that with the risk-ratio, it doesn't work. It is this symmetry which is exploited in log-linear analysis by taking the natural log of the Odds-ratio. This program changes the regression coefficients of a logistic analysis (the logits or log-odds-ratioos) back into odds-ratio's and percentages.

A more extensive discussion of the NNT and the calculation of confidence intervals for the NNT etc. can be found on the t-test page.

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