One thing that we were trying to do in time for Hurricanes29 was estimates of the statistical significance of our results. By significance, I mean – could we state, with – say – 95% certainty that the regression coefficients we calculate differ from our null hypothesis?
In this case, the simplest null hypothesis is that the real slopes are zero, and the signals we see are from some other processes, and would disappear if we could somehow have infinite data.
In order to mask out the regions where the mean regression coefficients are not statistically significant, I do two things:
1) Firstly, I mask out all the individual regression coefficients that are not significantly different to zero (determined by whether or not the 95% interval crosses zero for each slope).
2) Then I take a mean of these slopes for each regression point to get the mean regression coefficient. The 95% interval of the mean is then calculated (1.95*std – I have assumed that the regression coefficients are normally distributed – I need to check this) and again, those intervals which include zero are masked out.
If you care, you can compare these with the plots in my poster – the signals are generally the same – and the parts that I was most interested in appear to be significant, while the parts that were hardest to understand appear to be insignificant – possibly they are related to some signal that is mostly incoherent with the MJO, but that has such a huge amplitude that the small projection on to the MJO that is seen in the finite data set looks as large as the contributions that are coherent with the MJO