Logic: "some of the scores were too low to have occurred by chance"?

In this test, the doctor was excluding tests below a certain threshold. He believed some people were purposely trying to mess with the results, like losing ball game or throwing a fight.
With most tests, you can predict the outcome. A teacher can write a test that a high percentage of students are going to fail, or an easy test that everyone will pass.
This doctor believed he had developed an experiment that would test people with ESP and he believed he could weed out the cheaters too, those that were purposefully choosing the wrong answer . Ironically, proving that either they were psychic or dreadfully unlucky. Or that instead of trying, they were attempting to guess, in order to appear more cosmic than they were, thus getting the answers wrong and then humiliating him.
In other words, the reason the article is called, The Science of Things that Aren't so..
Is because the idea, the premise and the science behind it were bunk.

Cool.
Thank you Ceili.

I won't try to improve on Ceili's answer (I couldn't!) but it seems to me that from the original question, whether too high or too low, it's the same logic.

I agreed, After reading Ceili's answer, I got the same impression.