Using Statistics to Test for Normality of Pi

In summary, the conversation discusses a method for testing the normality of ##\pi##. The suggested method involves randomly sampling strings of size 20 and using the Chi-squared test to analyze the frequencies. It is noted that this method can be used to test if the digits are from a uniform distribution. The question of whether normality is dependent on the base is also brought up, with the mention of a method that showed normality up to 22.5 trillion base 10 decimal places and hexidecimal ones.
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WWGD
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Is there a " reasonable" way to test for the normality of ##\pi## , i .e., that every digit occurs with the same frequency? Someone suggested randomly sampling strings of size 20 and outputting the frequency. Then I guess we could average the frequencies among samples , use a chi-squared test. Assuming random sampling can be done, is this a sound way of testing?
 
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  • #2
Yes. The Chi-squared goodness of fit test can be used to test if the digits are from a uniform distribution.
 
  • #3
Is normality dependent upon the base - is it possible for there to be a pattern in one base that then appears random in another?

anyway, here is one method that showed normality out to 22.5 trillion base 10 decimal places and an equivalent number of hexideximal ones

https://arxiv.org/pdf/1612.00489.pdf
 
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FAQ: Using Statistics to Test for Normality of Pi

What is the purpose of testing for normality of pi using statistics?

The purpose of testing for normality of pi using statistics is to determine if the distribution of pi values follows a normal or bell-shaped curve. This information can be useful in understanding the nature of pi and its potential applications in various fields of study.

How is normality of pi tested using statistics?

There are several statistical tests that can be used to test for normality of pi, including the Shapiro-Wilk test, Kolmogorov-Smirnov test, and the Anderson-Darling test. These tests compare the distribution of pi values to a normal distribution and provide a p-value which indicates the likelihood of the data being normally distributed.

What does it mean if pi is normally distributed?

If pi is normally distributed, it means that the majority of its values fall within a specific range and follow a predictable pattern. This can be useful in making predictions and analyzing data related to pi.

What are the implications if pi is not normally distributed?

If pi is not normally distributed, it may indicate that there are underlying factors or variables that are influencing its distribution. This can make it more difficult to make accurate predictions and draw conclusions from data related to pi.

Can normality of pi change over time?

Yes, normality of pi can change over time. Factors such as changes in measurement techniques or new discoveries about pi can impact its distribution and potentially change its normality. It is important to regularly test for normality to ensure accurate analysis and understanding of pi.

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