If you mean a regression model then that was a mistake. You should have done a paired comparison on the 445 individuals before and after intervention(sometimes called a pretest-posttest experiment). Then compared these scores properly by or between group.(depending on your research question(s)). This can be done several ways. If you DO NOT have before and after measurements on the individuals. I can't help you. This is why statistical consultants have the 6 Ps. PROPER PRIOR PLANNING PREVENTS POOR PERFORMANCE. DESIGN your research carefully and think about what you can do with the data BEFORE you collect it. If what I described does not correspond to what you did then ask your question more clearly. Perhaps you should see your university statistical consultant prior to continuing. Good Luck, D. Booth

Hello Ahmed,

A lot depends on whether the "final" score is more of interest to you, or the resultant category is of more interest.

If category is of interest, then here are two suggestions:

1. If you do have paired scores (and therefore, category memberships) for the cases before and after, but you're interested in changes in categories, one place to start would be McNemar's test (which looks only at the inconsistently classified cases across the pairings).

2. A second, and more descriptive method would be to count the rate of changes from each of the four baseline categories. As an example (assuming categories A-D are ordered from lowest to highest):

Baseline category: Post category status

A Lower = 0; Same = 65%; Higher = 35%

B Lower = 10%; Same = 70%; Higher = 20%

C Lower = 15%; Same = 60%; Higher = 25%

D Lower = 12%; Same = 88%; Higher = 0% (max category)

You could take the collective counts in each class to derive expected cell frequencies and run chi-square goodness-of-fit tests for individual baseline categories, to see which (if any) depart from the overall pattern.

If score is of greater interest, you could compute gain/difference scores, and compare those across the four starting categories, via a one-way anova.

This approach has several important technical problems, however.

1. Gain/change/growth/improvement/difference scores are always less reliable than either of the scores used to create them, unless both scores are perfectly reliable to begin with.

2. There is frequently a negative correlation between initial status and gain. Part of this phenomenon is due to the fact that, all things being equal, cases with lower initial scores have greater opportunity to demonstrate gain than do cases with higher initial scores. Another reason is that, if initial scores are less than perfectly reliable (almost always the case), follow-up scores will tend to manifest the phenomenon called regression to the mean. Hence, low initial scores tend to rise on follow-up; high initial scores may decline!

For these reasons, I concur with David Eugene Booth 's advice that the best time to consider analytic choices is before collecting the data! In any event, do try to connect with someone locally to help you sort out your question in the most suitable way, in light of your research aims.

Good luck with your work.

David Morse I don't understand some of your comments given what the question says, " where I applied a prediction model to get their values after an intervention for improvement. Hence, as a result I have a pair of ...." If he used a prediction model, most likely that would mean regression. If so wouldn't the predicted have an unknown prediction error unless that was specifically taken into account which is something I don't know how to do under your posited models.This would NOT be the same as in the standard pre-post design. How then would one evaluate the intervention which is what the question asks(See the title of the post).? Have I missed something entirely or are you trying to rescue any possible information that might be in the data. Please tell me what I am missing? Best wishes, David Booth

Dear professors David Eugene Booth and David Morse.

Thank you very much for your help. Yes I have the before and after measures on each location. May be I was not very clear or what I want to do is not statistically possible. I will try to better explain.

In fact these are observations for outdoor air temperature data in different 445 locations. And yes we simulated the impact on lowering temperature on these locations using a GWR model where the predictor was a vegetation index (NDVI) that was consequently increased. As result we have the paired observations for each location before and after. Further, since we can classify our locations into 4 or more classes, based on another criterion which is the ventilation score at these locations. Our hypothesis is that, regardless the initial temperature was high or low, the impact of vegetation can be more influential in lowering the temperature (the difference before and after) in some groups (those that have high ventilation score) more than others.

Thanks again for your time.

Ahmed Hazem Eldesoky Ah, I think I see now the prediction was essentially the intervention, in a simulation. I follow you now I think. but GWS is Glashow-Weinberg-Salam model? so you are trying to predict the final temperature in your simulation as a test of the electroweak theory?. Do I have it now? I see so your intervention was the prediction. I would not have thought of particle physics until i remembered what G-W-S stood for. Please in the futrue identify things like that. It would be a large help to me at least. Three Nobel laureates in this problem. Apologies to all for not understanding the experiment. Best wishes to all, David Booth PS please advise if I still am missing something. Thanks all.