Norming of IQ tests on a ratio scale

In this article, we present a solution to one of the central problems of psychometrics over the past 100 years: a method for norming cognitive tests by producing scores on a ratio scale. This new approach is accompanied by many other complementary solutions, including the ability to accurately determine consistent values for the test ceilings, even when the theoretical rarity level at the top is much larger than the sample size. For example, in a sample of 3,000 subjects from a non-selective population, we can accurately determine the ceiling at the rarity level of 1 in 3 million by grouping the lower scores to compose a metric that allows us to estimate the higher scores while preserving the scale’s internal consistency. The higher the ceiling and the more difficult it is to norm using traditional methods, the greater the benefits of this method. In a non-selective sample of 50,000 people, we can determine the ceiling down to the level of 1 in 1 billion. Alternatively, with a sample of only a few hundred people with significantly above-average IQs, heavily biased by self-selection, we were able to determine the ceiling down to the level of 1 in a few billion even without knowing the parameters of this sample’s distribution. In samples severely contaminated by self-selection, we were able to neutralize this effect naturally, without the need for epicycle. We corrected for distortions in the dense tails and obtained a series of other advantages compared to traditional methods based on IRT and TCT [10], in addition to combining all the typical conceptual advantages inherent in ratio scales. We also opened the possibility of measuring animal and artificial intelligence on the same scale as human intelligence, among other possibilities yet to be discovered. We call this new procedure the “HM Method”.