In time-series ecological study, do we take positive results (but statistically non-significant) serious enough to be generalized in the real population?
I agree with David Eugene Booth. After all, the purpose of statistical tests is to find out whether the observed and measured results provide sufficient evidence for a hypothesis (more precisely, the rejection of the null hypothesis) or can be just as random.
Perhaps you can tell us a little more about the results and the statistical tests used?
You could do that in the very rare case that your sample is identical to the population. However, there a lively debate whether using frequentist methods (vs. Bayesian ones) is a fruitful approach in that particular case.
1.. that was an ecological study so whole population was included.
2.. We used GLM approach with Poisson to evaluate the data.
Most of the results were statistically insignificant. For example, increased levels of PM10 is a risk factor for heart disease in elderly people above 65 years of age. The result is insignificant. So could we trust this association? and recommend to device the policies accordingly at national level based on this result ?
You say that the "whole population" was included. If the model is correct (have you done any model misspecification tests?) then the population coefficients are those estimated and t-statistics are not appropriate. I would be very doubtful if your results can be extended to a wider population unless you can justify an assumption that your restricted "whole population" can be regarded as an appropriately designed probability sample of the wider population.
John C Frain if i modify my question as:
an ecological time series study from whole population of one city, but the results are mostly insignificant. Can those results be trusted to formulate policies for that specific city?
Probability theory is basic in regression model, so that statistical significance test basic test the regression model, is important result that have to be analysed. I suspect a model mis-specification has occurred. You may check the model specifications that are appropriate for it.
Perhaps I have misread your question. You have a variable, y, say the number of some kind of organisms, and a number of explanatory variables, each measured as time series. You have done a time series regression and find that several of the explanatory variables are not significant. Let us assume that your underlying theory model is sound, you have no endogeneity problems and that your variables are stationary. Then you may apply your model to the city from which the data was derived.
Insignificant coefficients are often due to insufficient data. If some of the insignificant coefficients are of the correct sign and of expected size then I might be reluctant to delete them. If you can not extend the data set for this city can you get data from other cities and perhaps use a SURE or panel or similar estimate (as appropriate)
I have worked in statistics and econometrics but never in ecological studies. I was under the impression (my faullt entirely) hat you had measurements for each member of the population rather than each variable being aggregate for the entire population of the city.
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