In my last article I wrote:

Based on the 352 self-reported Gestalt scores, we get the following IQ distribution of Pumpkin Person readers.

We could simply calculate the mean and SD, but given the ceiling bumping (26% got a perfect score) it seems wiser to convert each IQ into a percentile and then a normalized Z score with respect to blog readers.

IQ 74 = 1.13 percentile = -2.27
IQ 90 = 4.39 percentile = -1.73
IQ 98 = 8.225 percentile = -1.4
IQ 106 = 17.6 percentile = -0.93
IQ 114 = 29.68 percentile = -0.53
IQ 121 = 47.15 percentile = -0.07
IQ 129 = 67.04 percentile = +0.47

From here we get the following line of best fit:

y = 122.61+19.546x

The Y intercept = the mean and the slope = standard deviation.

Thus I estimate that on a scale where random whites score 100 with an SD of 15 my readers have a mean IQ of 123 with a standard deviation of 19.5. Such a huge SD is a bit hard to believe but it could be because IQ blogs attract both geniuses and the mentally impaired, thus pulling the curve to both extremes.

It seemed suspicous to me that my readers would have such a huge SD, so I decided to look more closely at the Gestalt test. The Gestalt test was normed using a randomish sample of 14 white Ontarian youngish adults who obtained the following raw scores:

3.5, 3, 2.5, 2.5, 2, 2, 1.5, 1, 1, 1, 1, 1, 0.5, 0.5.

This distribution has a mean of 1.64 and a standard deviation of 0.95 so these numbers were equated to 100 and 15 respectively (the IQ scale). But if the difficulty increase between items is too large or uneven, this might not give a normal distribution, so to be safe, I assigned each raw score a percentile based on where they ranked in the sample of 14 and then equated each percentile to the appropriate IQ on the bell curve:

3.5 = 14/14 = 100 percentile

3 = 13/14 = 92.86 percentile = IQ 122

2.5 = 11.5/14 = 82.14 percentile = IQ 114

2 = 9.5/14 = 67.86 percentile = IQ 107

1.5 = 8/14 = 57.14 percentile = IQ 103

1 = 5/14 = 35.71 percentile = IQ 94

0.5 = 1.5/14 = 10.71 percentile = IQ 81

Armed with these new IQs, I once again found the percentile that each IQ equated to among my readers and the corresponding normalized Z score

IQ 94 = 4.39 percentile = -1.73
IQ 103 = 8.225 percentile = -1.4
IQ 107 = 17.6 percentile = -0.93
IQ 114 = 29.68 percentile = -0.53
IQ 122 = 47.15 percentile = -0.07

This time the line of best fit was:

y = 122.818 + 15.89x

In other words, my readers have a mean IQ of about 123 with an SD of about 16, which sounds more plausible then the absurdly high SD of 19.5 I got before I normalized the Gestalt IQs.