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Chi-squared tests

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Kindly , I don’t understand these points on that page

  • How we know that the calculated chi-squared value is greater than all the values in the distribution ?
  • The highest value in the chi-squared sampling distribution was about 12 . This means that our chi-squared value is higher than 100% of all the values in the sampling distribution, so we get a p-value of 0
    Kindly explain it to me


The previous page shows a distribution of chi-sq values generated from 1000 experiments of randomly spliting people into male/female. Look at the x-axis the largest number you see is 14. This is much less than 3728.95. This proves 3728.95 is more than all values in the distribution. If you don’t trust the picture, you can print the list of exact values and find max.

Try to understand p-values in general. p-values have nothing to do with chi-sq. They are part of a methodology of drawing conclusions from experiments. Different experiments may use different distributions, and each distribution may support different tests. Which distribution and test is used is chosen by the experimenter based on what he believes to best represent reality and what he is measuring.
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