## Simple Interactive Statistical Analysis

### Input.

Odds into proportion. Give an odds in the top box and push the 'odds' button
Log-odds into proportion. Give a log-odds in the top box and push the 'log' button
Odds-ratio into proportion. Give a odds-ratio in the top box __and__ a proportion in the second box. Push the 'odds' button.
Odds-ratio into Number Needed to Treat (NNT). As above.
Log-odds-ratio into proportion. Give a log-odds-ratio in the top box __and__ a proportion in the second box. Push the 'log' button.
Log-odds-ratio into NNT. As above
Percentage into odds. Give a percentage in one of the percentage boxes and push the 'odds' button
Percentage into log-odds. Give a percentage in one of the percentage boxes and push the 'log-odds' button
Two percentages into odds-ratio. Give a percentage in each of the percentage boxes and push the 'odds' button
Two percentages into NNT. As above.
Two percentages into log-odds-ratio. Give a percentage in each of the percentage boxes and push the 'log' button
### 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.

###### All software and text copyright by SISA