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What is the best test to evaluate a vote's significance and why?

This article evaluates the US Supreme Court voting system and the voting system of the congress and says both fail significance tests https://medium.com/@akashkamble8488/the-usa-supreme-court-and-congress-fail-basic-statistical-significance-tests-b49f74f1ba41

The methods used in the article are the A/B, Welch's test and binary test.

Details: To measure a vote's significance, as to how likely that the vote is not by chance, there are many tests that can be used to give good approximations to a Null test without all its complications. For example: A Random vote R has p of R = 1/2 and q of R = 1/2 and u = 0. A regular vote V has p and q, and then Welch's test was used to measure the distance between the means of R and V divided by the combined standard deviation of R and V. If the results are 2 or greater (z >= 2 for 95% Confidence Level), then the article shows when the vote V (for a US Supreme Standard or Congress) passes the significance test or fails.

Example: The standard of the US Supreme Court of accepting a 5 to 4 for a vote is shown to fail the significance test, the standard for accepting a vote needs to be 8-1 or 9-0 depending on needed Confidence Level of 95% or 99.7%

The article notes that when doing the computation of a vote's mean and SD, a "yes" vote has a value 1 and a "no" vote has a value of -1 (not 0), and in this case, SD=sqrt(4pq) NOT sqrt(pq).

I hope that this clarifies the question more.

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    $\begingroup$ The linked article strikes me as ridiculous and making a fundamental error. Votes in the House, Senate, and SCOTUS (and similar bodies in other countries) are not random samples of any population: You have the whole population. There is no inference to be done. Also "voting systems" do not pass or fail significance tests. And, finally, I think the article confuses two meanings of "fail" a test in English. $\endgroup$
    – Peter Flom
    Commented Oct 26 at 9:58
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    $\begingroup$ Agree with @PeterFlom. Many members of these bodies vote along party lines, and if there are slim majorities, results will be around 50/50, which at the same time means they will not be statistically significant (in the sense of the cited article), and also obviously nonrandom (which means that the 50% randomness null hypothesis that is tested there doesn't make sense). Also, the Supreme Court has nine members, a very small number making it hard to see anything that rejects the 50% randomness null hypothesis (which is nonsensical here anyway). $\endgroup$
    – Christian Hennig
    Commented Oct 26 at 10:17
  • $\begingroup$ Could you elaborate on what you mean by the "significance" of a vote? $\endgroup$
    – whuber ♦
    Commented Oct 26 at 13:17
  • $\begingroup$ What is the null hypothesis? $\endgroup$
    – Dave
    Commented Oct 26 at 13:32
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    $\begingroup$ Not to put too fine a point on it, but the thesis of the referenced post, "statistical significance helps determine whether a voting result is meaningful or could have arisen by chance," reflects a thoroughgoing ignorance of both statistics and voting. Please do not pay any attention to that post. Consider researching the concepts of statistical testing with a good textbook or even by exploring our site. We have many threads about voting. cc @Graham $\endgroup$
    – whuber ♦
    Commented Oct 28 at 13:10

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