Chi-squared and p-values for California pick 3Prev TopicNext Topic

• oate

  

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  October 22, 2018
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  Nov 5, 2018, 12:43 am

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  Since the California lottery website conveniently lets you download all their raw draw data as a CSV file, it's super easy to run analysis on it if you like that sort of thing.  So for fun, I ran the numbers on the past 2000 pick 3 drawings (1000 evening and 1000 midday).  Here are some chi-squared tests I computed along with their p-values.

  Evening Draws (1000)
  First digit: chi-square = 11.04, p-value = 0.2730
  Second digit: chi-square = 7.16, p-value = 0.6205
  Third digit: chi-square = 6.80, p-value = 0.6579
  Digits in all positions: chi-square = 14.11, p-value = 0.1184

  Midday Draws (1000)
  First digit: chi-square = 14.40, p-value = 0.1088
  Second digit: chi-square = 2.94, p-value = 0.9666
  Third digit: chi-square = 8.32, p-value = 0.5022
  Digits in all positions: chi-square = 6.6267, p-value = 0.6759

  Combined Evening and Midday (2000)
  First digit: chi-square = 11.48, p-value = 0.2442
  Second digit: chi-square = 6.32, p-value = 0.7075
  Third digit: chi-square = 11.75, p-value = 0.2278
  Digits in all positions: chi-square = 14.81, p-value = 0.0962

   

  In many disciplines, like psychology and biology, a chi-square test value is considered statistically significant if the associated p-value is less than 0.05.  It's an arbitrary threshold, but a common standard nonetheless.  When the p-value is low, it means that the deviation from the expected distribution less likely to be due to chance, and more likely to be due to bias or an incorrect assumption about the data's distribution (the "null hypothesis"). If it's all Greek to you, the wikipedia article has a good rundown.

  As you can see from the numbers above, none of the p-values are less than 0.05. The lowest is 0.0962.  It suggests to me that the California pick 3 lottery is probably not biased and that their random number generator is spitting out all the digits fairly. At least as far as the past 2000 draws go.

  Just something I thought I would share. You can interpret it how you wish.  This post will soon be buried by a hundred other posts about magical pairs to watch out for, LOL.  Best of luck to you if you play CA pick 3.

  Only my hairdresser knows for sure.