The number of people who voted in the 2020 presidential election is not statistically possible

I am posting this information again in a different format to make it simpler for people to understand. I will start with the conclusion based on statistics and then explain how the conclusion was derived.

Conclusion:

The number of people who voted in the 2020 presidential election is not statistically possible based on the results of 21 previous elections.

• One-tailed test: The p-value is extremely small (close to 0), indicating that if the null hypothesis (that the new average is not significantly different from 0.7) were true, observing an average of .8611 or higher would be very unlikely.
• Two-tailed test: The p-value is also very close to 0, suggesting that observing an average as extreme as .8611 (either higher or lower than 0.7) is highly improbable under the null hypothesis.

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Here is the statistical analysis for the above conclusion.

Interpretation (from Grok):

A p-value of approximately 0 indicates that it is extremely unlikely (almost impossible, for practical purposes) to see an average of 0.8611 if the true population mean is 0.7 with a standard deviation of 0.0358. This suggests that such an occurrence would be considered highly significant or anomalous.

Remember, in practical terms, a p-value close to zero (like this) often indicates that either:

• The sample is from a different population with a different mean than expected.
• There’s an error in the data or assumptions (like the standard deviation or normality of distribution).

Given the context provided, if you’re working with real data, this extreme result might suggest reviewing your data collection method, assumptions about the population, or considering if there’s an external factor affecting this particular result.

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I started with a hypothesis based on average percentage populations voting in from 1900 through 2000. I did not include information after 2000 since I was skeptical of the results based on voter fraud.

I asked Grok “What was the average percentage population voting in presidential elections from 1900 thought 2000”?

Calculating the average voter turnout for U.S. Presidential Elections from 1900 through 2000 involves looking at the percentage of the voting-age population that voted in each election:

• 1900: 65.2%
• 1904: 65.4%
• 1908: 65.8%
• 1912: 58.8%
• 1916: 61.6%
• 1920: 49.2% (This low turnout is often attributed to the first election where women could vote, which might have affected the percentage due to organizational unpreparedness.)
• 1924: 48.9%
• 1928: 56.9%
• 1932: 56.9%
• 1936: 61.0%
• 1940: 62.5%
• 1944: 55.9% (Lower due to World War II)
• 1948: 51.1%
• 1952: 63.3%
• 1956: 60.6%
• 1960: 63.8%
• 1964: 61.8%
• 1968: 60.9%
• 1972: 55.2%
• 1976: 53.6%
• 1980: 52.6%
• 1984: 53.1%
• 1988: 50.1%
• 1992: 55.9%
• 1996: 49.0%
• 2000: 51.2%

To find the average turnout over this period:

1. Sum all the percentages: 65.2 + 65.4 + 65.8 + 58.8 + 61.6 + 49.2 + 48.9 + 56.9 + 56.9 + 61.0 + 62.5 + 55.9 + 51.1 + 63.3 + 60.6 + 63.8 + 61.8 + 60.9 + 55.2 + 53.6 + 52.6 + 53.1 + 50.1 + 55.9 + 49.0 + 51.2 = 1,585.3
2. Divide by the number of elections (26):
   1,585.3 / 26 ≈ 60.97%

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I did not do a correlation between lowering of the voting age to 18 in 1971.

From Grok:

If you’re interested in the percentage of registered voters who turned out to vote in those elections, those figures would be higher since they only account for people who could legally vote by being registered. However, exact figures for registered voter turnout for each year might not be as readily available or standardized historically due to changes in voter registration laws and practices over time.

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From Grok:

For a rough projection: If we consider that about 70% of eligible voters are registered and take into account the historical turnouts’ lower bound within that group, you might see around 40-50% of the total eligible population voting. This number implies a turnout of 57-71% of registered voters, assuming the 70% registration rate holds.

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Since I had already received information that 70% of the population is eligible to vote and “assumed” a worst case scenario of 70% of eligible voters actually vote, I applied this to the population and number of votes cast in the 2020 presidential election. I then asked for a p value (see note 1 below) based on 21 previous elections ending in 2020 with a standard deviation 0.0358 compared to the 86.11% value of eligible voters voting in 2020.

From Grok:

Question

If you have 21 data sets of data with a standard deviation of .0358 for an average of 0.7, what is the p value that a different set will be an average of .8611?

Answer

To determine the p-value for whether a different dataset will have an average of .8611 when the existing data sets have an average of 0.7 and a standard deviation of .0358, we can follow these steps:

1. Calculate the z-score: The z-score measures how many standard deviations an element is from the mean. Here, we want to find the z-score for an average of .8611:
   z=X−μσ/n
   • X is the new sample mean, .8611.
   • μ is the population mean, 0.7.
   • σ is the standard deviation, .0358.
   • n is the number of observations in a new sample. Since you mentioned “a different set,” we’ll assume one observation for simplicity, but if you have a specific sample size in mind, you would use that.
   
   For one observation:
   z=0.8611−0.70.0358≈4.50
2. Find the p-value: The z-score tells us how far away from the mean the new average is in terms of standard deviations. A z-score of 4.50 is quite extreme.
   • If we’re doing a one-tailed test (where we’re only interested in whether the new average is significantly higher), the p-value would be the area to the right of z = 4.50.
   • For a two-tailed test (looking for any significant difference, whether higher or lower), the p-value would be twice the area to the right of z = 4.50.
   
   For a one-tailed test:
   • Using a standard normal distribution table or statistical software, the area to the right of z = 4.50 is very close to 0. This might not be precisely calculable from most tables, but it’s essentially negligible for practical purposes.
   
   For a two-tailed test:
   • The p-value would be approximately 0 * 2 = 0, again indicating it’s extremely unlikely under the null hypothesis that this difference occurred by chance.

Conclusion:

• One-tailed test: The p-value is extremely small (close to 0), indicating that if the null hypothesis (that the new average is not significantly different from 0.7) were true, observing an average of .8611 or higher would be very unlikely.
• Two-tailed test: The p-value is also very close to 0, suggesting that observing an average as extreme as .8611 (either higher or lower than 0.7) is highly improbable under the null hypothesis.

Please note:

• The actual p-value might be calculated more precisely with software or more detailed tables, but for practical purposes, it’s clear that such an extreme value as .8611 is very unlikely given the parameters provided.
• If you intended “a different set” to mean a sample of any specific size different from one, you would need to use that sample size in the calculation, which could alter the z-score and subsequently the p-value.

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Note 1 (from Grok)

In statistics, the p-value (probability value) is a measure that helps you determine the significance of your results in hypothesis testing. Here’s a detailed definition:

• Statistical Significance: The p-value is the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is true.
• Interpretation:
  • A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.
  • A large p-value (> 0.05) suggests weak evidence against the null hypothesis, so you fail to reject the null hypothesis.
• Calculation: The p-value is calculated from the test statistic of your hypothesis test, based on the sampling distribution of that statistic under the null hypothesis.
• Misconceptions:
  • It is not the probability that the null hypothesis is true.
  • It does not measure the size of an effect or the importance of a result.
• Usage: In practice, if the p-value is less than or equal to a predefined significance level (commonly set at 0.05), researchers often conclude that there is a statistically significant difference or effect. However, this threshold is somewhat arbitrary, and the choice of significance level should be justified based on the context of the study.
• Criticism: The reliance on p-values for making decisions in research has been criticized. Issues include:
  • P-hacking: Manipulating data or experimental design to achieve a low p-value.
  • Misinterpretation: Believing that a p-value can tell us the probability that the results were due to chance or that the null hypothesis is true.
• Understanding p-values is crucial for interpreting scientific research, but they should be used in conjunction with other statistical tools and considerations like effect size, confidence intervals, and the practical significance of the findings.

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