Init

library(kirkegaard)

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load_packages(
  googlesheets4,
  ggrepel
)

theme_set(theme_bw())

Calculations

#68th centile in IQ scale
qnorm(.68, 100, 15)

## [1] 107.0155

#0.78 standard deviations in IQ scale
15*.78

## [1] 11.7

#99th centile on IQ scale
qnorm(.99, 100, 15)

## [1] 134.8952

#99th centile on SAT scale, with SD 200
qnorm(.99, 1010, 200)

## [1] 1475.27

#99th centile on SAT scale, with SD 195
qnorm(.99, 1010, 200)

## [1] 1475.27

#99th centile to z score
qnorm(.99)

## [1] 2.326348

#99th centile to z score, to IQ z score
qnorm(.99) * 0.8

## [1] 1.861078

#99th centile to z score, to IQ score
(qnorm(.99) * 0.8) * 15 + 100

## [1] 127.9162

#perfect SAT 1600 to centile
pnorm(1600, 1010, 200)

## [1] 0.9984111

#perfect SAT 1600 to z score
pnorm(1600, 1010, 200) %>% qnorm()

## [1] 2.95

#perfect SAT 1600 to z score to IQ z score
(pnorm(1600, 1010, 200) %>% qnorm()) * .8

## [1] 2.36

#perfect SAT 1600 to z score to IQ scale score
((pnorm(1600, 1010, 200) %>% qnorm()) * .8)*15+100

## [1] 135.4

A look-up table

map_df(seq(200, 1600, 10), function(SAT) {
  tibble(
    SAT = SAT,
    SAT_centile = pnorm(SAT, 1010, 200),
    SAT_z = qnorm(SAT_centile),
    IQ_z = SAT_z*0.8,
    IQ = IQ_z*15+100
  )
}) -> SAT_IQ_table

SAT_IQ_table

SAT to IQs by major

#read data
gs4_deauth()
sats = read_sheet(
  "https://docs.google.com/spreadsheets/d/13gaFgtCMnvdgZdxaR3zwwpPf_WrGru_AxzTKnaMwRpY/edit?usp=sharing",
  sheet = 2)

## ✓ Reading from "SAT to IQ table".

## ✓ Range ''SAT means by major''.

#add IQs
sats %<>% mutate(
    SAT_centile = pnorm(`Mean total`, 1010, 200),
    SAT_verbal_tilt = (`Mean verbal`-`Mean math`) %>% standardize(),
    SAT_z = qnorm(SAT_centile),
    IQ_z = SAT_z*0.8,
    IQ = IQ_z*15+100
)

#plot it
sats %>% 
  ggplot(aes(IQ, SAT_verbal_tilt)) +
  geom_point() +
  geom_text_repel(aes(label = Major), size = 3, max.overlaps = 99) +
  scale_x_continuous("Average IQ of probable undergraduates (from SAT)", breaks = seq(90, 130, 5), limits = c(95, 116)) +
  scale_y_continuous("Verbal tilt (verbal - math score, in z scale)")

GG_save("figs/SAT_major_IQ_tilt.png")

#simpler plot
sats %>% 
  mutate(
    Major = fct_reorder(Major, IQ),
  ) %>% 
  ggplot(aes(IQ, Major, color = SAT_verbal_tilt)) +
  # geom_bar(stat = "identity")
  geom_point() +
  scale_x_continuous("Average IQ of probable undergraduates (from SAT)", breaks = seq(90, 130, 5), limits = c(95, 116)) +
  scale_color_gradient2("Verbal tilt", mid = "grey")

GG_save("figs/SAT_major_IQ_tilt2.png")

Meta

write_sessioninfo()

## R version 4.1.3 (2022-03-10)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Linux Mint 20.2
## 
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## 
## attached base packages:
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SAT to IQ calculations

15 April, 2022

Init

Calculations

A look-up table

SAT to IQs by major

Meta