Keej,
You said you’re justified in removing the 10,000 with red socks. I’m not so sure. What if coincidentally, there was a concentration of either Neuro-typical or Autistic children in that group. That would make a very big difference on the resulting ratio.
The reason studies like this require large samples is to minimize the likelihood of coincidences such as the one you described. A major part of analyzing the results of any statistical study is calculating the probability that the results are in fact meaningful.
This is Statistical Analysis 101.