Trend Analysis of Rainfall and Runoff

Question

I am doing a trend analysis of rainfall and runoff using parametric test.
My question is, if I do a regression analysis and find a slope of increase or decrease with a certain value, like 2mm/year, but the trend is non-significant with 90% probability, can it still be called a trend?
If yes, then what is the exact meaning of statistical significance and non-significance?

Bill Goodwin · Accepted Answer

Hello Sultan,  if the variation in the data has occurred purely by chance (random variation), then the trend you see is non-significant - that is, your regressed model (say a straight line of y=mx+b) does not adequately describe a trend (at your stated confidence of 90% probability).  It may be that the model does become significant if you lessen your probability constrains a bit and you choose say, 80%.   That would mean that 'with 80% probability' a trend is statistically likely.   The 'traditional' probability levels of 99%, 98%, 95% and 90% have no strict connection to anything.  They are simply conventional choices that get reinforced by academic efforts over time - that's it.   
So think of your project and analysis in these terms:  If your project relates to something with a huge investment and perhaps big downside consequences if your decisions are wrong - then you probably want to use fairly tight confidence levels when making recommendations.  If not, then perhaps it is OK to choose a much looser confidence level.
Another point - if you have, say, 10 data points, the chance of determining the distinction between purely random variation versus the trend is pretty small - you do not have enough 'information' available to discern between the two.  But if you have (for example) 1000 data points, there should be plenty of 'information' to make a 'more confident' analysis of the variation - separating the purely random variation from the trending variation using your statistical tools.  
Finally, consider that you are trying to describe reality - by using a 'model'.  Your model will (almost always) be an imperfect description of the reality.  So think carefully about all the potentially important parameters that are needed to describe the reality.  Are you missing something in your model?  Do you have excess or superfluous parameters in your model?  If you are not familiar with ANOVA (Analysis of Variance) - please do study this.  This tool will help you build better models, especially when there are many potentially important factors that may contribute to your description of the 'reality'.
I hope this was helpful.  All the best, Bill

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