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Just a note

The first graph of this set is also known as a 'quantile' scatterplot. However, because these are the entire population of results, the relative rank is simply the sequential rank divided by the highest rank - in this case 120.

The second graph of this set is a scatterplot of the relative rank of sets of results that have identical outcomes. The height of each bar is the total probability of that event.

 

To make this distribution look more symmetrical we have plotted the X-axis using a logarithmic scale - because the statistic of interest is a ratio, we would expect its distribution to be skewed.

    For example:
  • If the treatment is ineffective we would expect T = P so T / P = 1.
  • But, if the pour on was 100% effective P = 0 and T / P is infinite.
  • If however the tags were 100% effective T = 0 so T / P = 0.

However, as you can see from these graphs, none of these 3 results are actually possible under this model.