I am SO excited, a statistical anomaly causing an incorrect assumption just happened in my house!
Let me explain, if you have an insufficient sample size, then it is possible to have a very odd sample (ex: only 5 M&Ms and they are all blue), which could lead you to a wrong assumption (ex: all M&Ms are blue). This is why large sample sizes or repeat samples are better science. Or to illustrate, this is the normal distribution of X in the population, you could have bad luck and samples from the tails (highlighted areas). If you do that, your conclusion will be wrong:
So here is what happened, my son attended home daycare at my house, he's now in junior Kindergarten. Out of the six children who attended daycare, there was only one girl. She was a statistical anomaly, literally off the charts for height (so she would be in that highlighted tail) and the tallest child in care. The smallest child in the daycare was a boy.
I was talking my son, he's is still mastering pronouns (he uses "he" for everyone). He was talking about his friend "he" and I corrected him, that friend is a "she". He protested loudly, "But she's so small!"
My child has known 6 children and 1 girl and from that he has concluded that girls are the tallest.
My own child used a statistically anomalous sample to draw an incorrect conclusion that was literally the opposite of the population norm. I wish I was teaching a statistics course right now so I could brag about it!
