Correlation of planet sizes with star sizes? I did my own amateur Kepler data analysis in May of this year of data from Kepler.nasa.gov/Mission/ discoveries. I found a strong correlation between star size and planet size (percentages). 37 of the 44 planets confirmed (84.1%) orbiting M dwarfs were less than 2.0 R(Earth) with only one hot Jupiter. 129 of 241 (53.6%) orbiting K dwarfs were less than 2.0 R(Earth) with 9 hot Jupiters (3.7%). 196 of 517 (37.9%) orbiting G dwarfs were less than 2.0 R(Earth) with 49 hot Jupiters (9.5%). 92 of 213 (43.2%) orbiting F dwarfs were less than 2.0 R(Earth) with 23 hot Jupiters (10.8%). I would like to know how much of this correlation is probably real and how much is biased by the limits of the study? Biases I am aware of are the fact that the Kepler study is primarily of systems with "close in" planets, (only 90 of 1015 confirmed as of 4/1/15 are over 0.3 AU) and that only 4.3% of the "Kepler stars" are M dwarfs. I also see biases that might arise from the methods of confirming the planets (Kepler stars from 110 to 405 had planets confirmed by the "multiple candidate" method). It also appears that there may be a greater difference between K and G star systems than between G and F. Where can I find a more professional analysis of this type?
I think there are a number of studies that look at these statistics; I'll try to dig some out. In the meantime I can give you some further things to ponder.

First, let's assume a null hypothesis that the statistics and mass distribution of planets were independent of stellar mass - what would we observe?

Well one selection bias you don't mention is that the likelihood of transit detection depends on the ratio of planet to star size. This means you are less likely to see small planets around F-stars than M-stars. Or to put it another way, you expect the fraction of large planets to increase with stellar mass - as you have found.

It is quite likely that the material available to form planets is correlated with the stellar mass - in other words there is a correlation between stellar mass and protoplanetary disc mass. In which case it could be quite difficult for smaller stars to have the requisite protoplanetary disc density to form giant planets before the disc disperses.