Jeffrey Epstein emailed Steven Bannon the day before Trump nominated Bill Barr to be AG with a subject line:
Do you know bill barr. CIA.
Jeffrey Epstein emailed Steven Bannon the day before Trump nominated Bill Barr to be AG with a subject line:
Do you know bill barr. CIA.
I don't think we should assume that these are Americans doing this.
I don't think we should assume that these are Americans doing this.
"Please do a statistical analysis of the data in columns b and c. Each row is a data point. Tell me about a correlation between these two data sets."
That's just math, bro.
"Please do a statistical analysis of the data in columns b and c. Each row is a data point. Tell me about a correlation between these two data sets."
That's just math, bro.
58-24
45-02
58-01
45-12
66-37
58-27
66-41
58-03
58-20
58-35
55% Trump, 48% Turnout
58-38
58-25
63-06
66-32
26-16
66-15
58-08
58-02
58-05
58-19
54% Trump, 51% Turnout
26-22
45-06
58-33
66-05
63-11
26-10
66-12
66-08
45-07
63-12
58-24
45-02
58-01
45-12
66-37
58-27
66-41
58-03
58-20
58-35
55% Trump, 48% Turnout
58-38
58-25
63-06
66-32
26-16
66-15
58-08
58-02
58-05
58-19
54% Trump, 51% Turnout
26-22
45-06
58-33
66-05
63-11
26-10
66-12
66-08
45-07
63-12
They went from Trump 37%, and 35% of the registered voters turned out.
45-18
45-09
63-07
45-10
45-14
45-19
45-17
45-13
58-44
58-18
These went 42% with 50% Turnout.
45-08
45-11
58-40
45-21
58-15
58-36
58-31
63-22
45-16
63-25
They went from Trump 37%, and 35% of the registered voters turned out.
45-18
45-09
63-07
45-10
45-14
45-19
45-17
45-13
58-44
58-18
These went 42% with 50% Turnout.
45-08
45-11
58-40
45-21
58-15
58-36
58-31
63-22
45-16
63-25
"Your observed correlation is far outside the realm of chance.
It lies: More than 10 standard deviations away from the null mean. Far beyond the maximum correlation seen in 20,000 random trials. Literally off the chart compared to random permutations"
"Your observed correlation is far outside the realm of chance.
It lies: More than 10 standard deviations away from the null mean. Far beyond the maximum correlation seen in 20,000 random trials. Literally off the chart compared to random permutations"
This creates a null distribution where B and C have no relationship.
Then we compared your actual correlation to this null world.
This creates a null distribution where B and C have no relationship.
Then we compared your actual correlation to this null world.
In those 163 precincts, why would the relationship between turnout and Trump's vote share behave like a function?
To be naturally occurring. The voters would have had to coordinate it in advance.
In those 163 precincts, why would the relationship between turnout and Trump's vote share behave like a function?
To be naturally occurring. The voters would have had to coordinate it in advance.
f(b)≈18.775b3−31.144b2+17.617b−2.796
You can plug any b in [min(b), max(b)] into either of those to get an estimated c.
f(b)≈18.775b3−31.144b2+17.617b−2.796
You can plug any b in [min(b), max(b)] into either of those to get an estimated c.
⭐ The smoothness, predictability, and binning behavior are all signatures of a generated or model-driven relationship.
⭐ The smoothness, predictability, and binning behavior are all signatures of a generated or model-driven relationship.
✔ There is an underlying function
✔ But the noise around the function grows as B grows
This again fits a modeled or formula-based relationship.
✔ There is an underlying function
✔ But the noise around the function grows as B grows
This again fits a modeled or formula-based relationship.
C is a smooth mathematical function of B (slightly curved, monotonic) plus random scatter.
C is a smooth mathematical function of B (slightly curved, monotonic) plus random scatter.
When you group the data into bins, the noise cancels out—and the underlying curve becomes almost perfectly monotonic and smooth
This is not typical for behavioral or social data
It is typical for data generated from a mathematical function plus noise
When you group the data into bins, the noise cancels out—and the underlying curve becomes almost perfectly monotonic and smooth
This is not typical for behavioral or social data
It is typical for data generated from a mathematical function plus noise
We tested whether the relationship between columns B and C is:
Linear
Quadratic (curved)
Cubic (more flexible curvature)
Based on model fits and R² values, the relationship is not perfectly linear, but also not strongly nonlinear — it shows only a mild upward curvature.
We tested whether the relationship between columns B and C is:
Linear
Quadratic (curved)
Cubic (more flexible curvature)
Based on model fits and R² values, the relationship is not perfectly linear, but also not strongly nonlinear — it shows only a mild upward curvature.
The relationship between columns B and C is strong, smooth, and very unlikely to be due to random variation, whether you look at raw points or average them into groups.
The relationship between columns B and C is strong, smooth, and very unlikely to be due to random variation, whether you look at raw points or average them into groups.
Null distributions look roughly bell-shaped, centered near 0.
Your observed r ≈ 0.94 and 0.91 sit far beyond anything the null generates.
Null distributions look roughly bell-shaped, centered near 0.
Your observed r ≈ 0.94 and 0.91 sit far beyond anything the null generates.
p_bin10 ≈ 0.0000
20-bin correlation:
p_bin20 ≈ 0.0000
p_bin10 ≈ 0.0000
20-bin correlation:
p_bin20 ≈ 0.0000
Kept column B fixed.
Randomly shuffled C (breaking any structure) 10,000 times.
For each shuffle, I recomputed:
Raw correlation
5-bin correlation
10-bin correlation
20-bin correlation
This gives four null distributions—what each statistic looks like if B and C are unrelated.
Kept column B fixed.
Randomly shuffled C (breaking any structure) 10,000 times.
For each shuffle, I recomputed:
Raw correlation
5-bin correlation
10-bin correlation
20-bin correlation
This gives four null distributions—what each statistic looks like if B and C are unrelated.
This analysis supports the high Pearson and Spearman correlations you already observed.
This analysis supports the high Pearson and Spearman correlations you already observed.
These show how many points fall in each bin:
Observations:
The densest bins are in the middle (consistent with a unimodal distribution for B).
The highest bin contains only 1 point, so that final point should be interpreted cautiously (but it still fits the trend).
These show how many points fall in each bin:
Observations:
The densest bins are in the middle (consistent with a unimodal distribution for B).
The highest bin contains only 1 point, so that final point should be interpreted cautiously (but it still fits the trend).