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Ergotron_2000 t1_it2z1jh wrote

I have little idea what is being shown here. all info way to small to easily read, labeling not clear.

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terrykrohe OP t1_it5se17 wrote

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the top left plot is the incarceration rate of the fifty US states ... the states are not identified because it is not important ... what is important is the states' Electoral College vote in the 2020 election

2
the top right plot is the 'rural-urban' value of each of the fifty states (see the "top comment" for the definition of 'rural-urban')

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the bottom plot is a plot of the ('rural-urban, incarceration) coordinates of the fifty states

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the important point to see is that the best-fit line slopes of the Rep states and the Dem states are oppositely directed and that the Dem states correlation value is "less noisy" than the Rep states correlation value

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terrykrohe OP t1_it2x3gb wrote

sources
– incarceration: https://www.sentencingproject.org/the-facts/#map
– rural-urban: population density https://www.states101.com/populations
– agriculture income: https://data.ers.usda.gov/reports.aspx?ID=17839#P9dd070795569412d9525def18d45bde2_4_185iT0R0x0
– state GDP: https://apps.bea.gov/regional/downloadzip.cfm
method for "rural-urban" metric
– population density and agriculture income data values were converted to "standard scores", aka "z-scores":
z-score = (data value – mean)/SD
– the z-scores were added and divided by 2; result = the rural/urban metric z-score
– note1: 'urban' means "increasing population density"
'rural' means "increasing agriculture income as % of state GDP"
for the 'rural' metric to denote a "rural to urban" value,
the z-scores for agriculture income were 'reversed' by multiplying by "–1"
before adding to the population density z-scores
– note2: "NCE" is "normal curve equivalent" (see Wikipedia, "Normal curve equivalent")
tool: Mathematica

***************
– the ellipses are centered on the Rep/Dem means;
the standard deviations are represented by the ellipses' axes
– the 50 plot points represent the (rural-urban, incarceration) coordinates for each state;
and are colored according to their 2020 Electoral College vote
– "r" is the Pearson correlation value

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Omega_Zulu t1_it5z8tm wrote

For incarceration data to be used by state you need to exclude federal prisons and their populations since prisoners can be assigned to states other than the one they committed their crime in, which is likely what you are looking for. Or create a seperate analysis for them.

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terrykrohe OP t1_it2xyfe wrote

best-fit lines, correlations: incarcerationvs 'rural-urban'

  1. Purpose
    In order to 'understand' the non-random, top/bottom, Rep/Dem differentiation of metric values, eight "response" metrics are correlated with three "predictor" metrics. This post presents the 'response' variable incarceration vs the 'rural-urban' predictor metric.
    ... the eight "response" metrics: GDP, state taxes; suicide rate, opioids; life expectancy, infant mortality; incarceration, state+local ed spending
    ... the three "predictor" metrics: 'rural-urban', evangelical, diversity*

  2. the "big picture"
    i) There is a non-random, top/bottom, Dem/Rep pattern. Patterns have reasons/causes and are mathematical.
    ii) Rep states are always on the negative side (less GDP, more suicides, lower life expectancy, etc).
    iii) How did 150 million voters, acting individually, separate the fifty states into two such disparate groups?iv) is there a "predictive" metric or combination of metrics which can be used to explain the characteristic Rep/Dem differences seen in the data?

  3. general comments
    i) the Rep states r-value is about half of the Dem states r-value; the r-value of Rep states indicates Rep data is "noisy"
    ii) however, the best-fit lines show Rep/Dem difference: as Rep states become more "urban", there is increasing incarceration; as Dem states become more "urban", there is decreasing incarceration

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