Odd and even days

Hello....

What does the underlined part, "on odd and even days" mean?
Does it mean any random days?

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Psychologists have frequently tested the notion that people's personalities cause them to exhibit consistently the same behavioral patterns in a variety of situations. In one study, for example, counselors working at a summer camp for teenage boys were asked to secretly note down the degree to which the boys displayed various forms of extroverted behavior, such as talking during mealtimes, seeking the limelight, and initiating conversations. The researchers then carefully analyzed the data by comparing the boys' level of extroversion on odd and even days.

The 'personality causes behavior' theory predicts there would be a high level of consistency in the boys' actions, with the extroverted teenagers constantly chatting away and the introverted ones repeatedly hiding away in the corner. In fact, the results failed to show any evidence of such consistency. On one day, one of the boys would be full of beans and very chatty, while on the next day the very same boy was quiet and withdrawn.