Self reported IQ by Gender

I used the Data from ssc2018public.xlsx (as available at: http://slatestarcodex.com/2018/01/03/ssc-survey-results-2018/). The data is not clean and before further analysis can be conducted text responses and obvously false data was removed.

some statistical key characteristics of the data:

Statistical key characteristics of self reported IQ by Gender.
Gender Mean Max Min Median SD n
F (cisgender) 137.3588 177 105 135.0 11.812918 170
F (transgender m -> f) 136.9677 172 108 135.0 13.202232 31
M (cisgender) 138.2355 190 90 138.0 12.654659 1762
M (transgender f -> m) 143.2500 150 136 143.5 6.396614 4
No Answer 130.5714 141 120 130.0 8.638232 7
Other 139.2245 180 114 140.0 12.191639 49

A density plot visualizes the distribution for each gender:

In adddition a combined plot of density and histograms was produced seperate for each gender to vizualize how the data is distributed in more detail:

An additional histogram plot shows the number of subject in each bin instead of the density:

A combined Scale for self reported IQ and SAT data

In order to increase the number of datapoints the IQ equivalent of the Sat scores was calculated using the following formulas: \[\begin{align}IQ_{sat1600}& =26.8+0.085\cdot S_{sat1600}\\ IQ_{sat2400}& =28.142 + 0.05327\cdot S_{sat2400}\\ IQ_{combined}& =mean(IQ_{selfReported}, IQ_{sat1600}, IQ_{sat2400})\\ \end{align}\\ \text{The mean function is configured to omit NA values (e.g. empty responses).}\]

Statistical key characteristics of combined Scale for self reported IQ and IQ derived from SAT data by Gender.
Gender Mean Max Min Median SD n
F (cisgender) 146.1823 177.000 105.00000 148.4911 10.468892 422
F (transgender m -> f) 143.9140 165.275 120.00000 144.8250 10.797465 58
M (cisgender) 145.5830 180.025 87.42332 147.0000 11.144422 3928
M (transgender f -> m) 147.9019 161.950 136.00000 147.4111 7.939274 12
No Answer 137.2735 162.800 118.60000 136.1625 13.918666 12
Other 144.9718 167.575 114.00000 146.0125 10.857336 78

IQ from SAT scores without self reported values

The SAT score might be more reliable than the self reported IQ therefore the same analyses as above were conducted on IQ scores derived from SAT scores without self reported IQ.

Statistical key characteristics of IQ scores derived from SAT scores.
Gender Mean Max Min Median SD n
F (cisgender) 149.8776 162.80 111.8000 151.7284 8.084869 346
F (transgender m -> f) 148.5903 161.95 131.2025 148.2659 8.367304 44
M (cisgender) 149.6573 162.80 94.7295 150.9000 8.689050 3083
M (transgender f -> m) 149.5260 161.95 140.0090 150.6630 8.196164 9
No Answer 143.2394 162.80 118.6000 143.6750 13.724685 8
Other 151.1167 162.80 129.3550 152.7938 7.283427 51