Sigma Test

See also the comments about the new norm:

"Obrigado por enviar-me as novas normas do ST. Pelo que vejo, nao tem limite a sua criatividade e originalidade. Poderia enviar o seu metodo para algum jornal de psicologia especializada em QI elevado! Ou ao Journal of Right Tail Psychometrics."

(Comment sent by Petri Widsten)

Your article and work is fantastically interessant!! It can be something *great* for a *good* psychometric journal.

(Comment sent by Albert Fank)

(This is the full e-mail received from our friend Kristian Heide):

Dear Melao,

I would very much like to receive a certificate based on the new norm of The Sigma Test. I will send the fee to your address in Sao Paulo. I have moved since you sent me the last certificate. My new address is:

Kristian Heide (This part, with his address, was excluded)

I understand that you must have put a tremendous amount of work into the process of making the new norm. I hope other test-makers will adopt your method. Your methodology with different weighting factors seems much better and superior to a system where all problems are assigned to the same weighting factor. You have put common sense into good practical use based on a sound theoretical framework.

Another strength that follows your tests (ST and STVI) is that you allow fractional points to be given. If we look at how Ronald H. is scoring the Titan test we see a whole different approach. He is only interested in the answers, not in the reasoning and logic behind. It is easy to see the weakness in Ronald’s approach. Not only is he using the same weighting factor for each problem; he is also not rewarding any points whatsoever for a close to perfect (but not correct) solution.

By allowing fractional points you need to design problems to fit with your ideology. Especially on the more difficult problems, where the fractional points are more important, I think it is very fruitful to design problems that, in themselves, are both diverse and complex. Even if a person is not able to solve the whole problem perfectly he is nevertheless motivated to start on it and give it his best shot because he knows points will be rewarded for a partial solution also. I think a test that is actually able to motivate the ones that decide to take the tests to do their absolute best, is a successful test. And when the scoring system in addition is fair, just and correct, I think the test is as complete as it can be. And that is what I believe you have succeeded in doing with your tests. You motivate, and you have a superior scoring system.

Some months ago I sent an e-mail to the designers of Thinkfast (they have now an online version that is very similar to the Thinkfast software). I have done some analysis of their scoring system, and found many weaknesses in it, which I told them about. First they did what you did with TST: they did their best the first time they designed the program by putting up the scoring rules. You did the same on TST by “guessing” each problem’s weighting factor. This is sound. But when more information comes forth, one must be ready to refine the rules. The Thinkfast designers have failed to do this. Their scoring system is roughly as follows: There are 6 games. G1 is the simplest (more primitive brain functions), and G6 the most complex. And they, correctly, use higher weighting factors for the more complex games. But they fail to give extra credit when you are able to perform, on any game, extremely well regarding to percentile. If we use G1, simple reaction time to a simple stimulus, as an example. If your reaction time is 160 ms, this is pretty fast and rewarded accordingly. If your reaction time gets as low as 140 ms, this is only rewarded according to a mathematical formulae that is purely theoretical and not empirical. There is nothing in the formulae (for later versions of the software) that tests for percentile (even though the data is available), so the extra points given are not enough. And, even worse, should your reaction time be 120 ms the scoring system does not give you the very high extra credit you deserve. Since no one has ever before performed with a reaction time at 120, this performance is so extreme that it should be reflected in the scoring. When fewer people are able to perform at a certain level, the weighting factors should be adjusted accordingly: Exactly as you did with TST. And as the TF designers should have done. They wrote me back, and they agreed. But I doubt they will do the work necessary to change their method.

I was hoping to write something for WAHIP about this and some other specifics regarding Thinkfast, but never seem to find the time for it. In addition I have been involved in some local Mensa activities, which takes some resources. Also, I want to finish with STVI, but I never feel really finished. There are always some more things to investigate and discuss. But I find pleasure in working with this test, and that is perhaps the most important thing.

I hope the next year will leave me with some spare time for interesting projects. Exciting projects are easy to find, but finding the time to follow up on them...well, that’s the key factor.

Best wishes for the new year to you from


"Quando abri a mensagem, pensei em ler depois, devido ao tamanho do artigo. Quando comecei a entender, no entanto, não pude evitar a leitura até o final, ainda que tenha lido rapidamente, sem me deter nos detalhes.

Muito embora não conheça o assunto suficientemente bem para dar uma opinião segura, nunca vi método que pudesse ser tão coerente, porque, finalmente, encontrou-se uma definição realmente clara do que é QI e de como ele pode ser medido. Gostaria de lhe dar os parabéns."

(Comment sent by José Antonio Francisco, from Brazil, member of Platinum and Sigma IV)

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