About The Sigma Test

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Criação e padronização de testes de alto nível para empresas. Testes individuais e coletivos para avaliação da capacidade de produção de executivos em diversas áreas, testes de criatividade, de inteligência, de personalidade e de habilidades específicas.

Psycometrical Properties:
Norma do Sigma Test (setembro de 2003)
Nova norma do Sigma Test (outubro de 2004)
Nova norma do Sigma Test (novembro de 2005)
Análise Fatorial Hierárquica do Sigma Test (junho de 2005)

More on the Sigma Test:
Opiniões de proeminentes intelectuais
Sigma Test (English version)
Sigma Test (versão portuguesa)
Sigma Test (other languages)
Opiniões de proeminentes intelectuais sobre a nova norma
Resumo histórico sobre testes de inteligência
Artigo envolvendo nossa metodologia em conjunto com TRI
Novo modelo de certificado (Sigma Test)
Novo modelo de certificado (Membro)

About Potential IQ gauged, Potential IQ and other scores, you need read these articles (writed in Portuguese):

Norma do Sigma Test (setembro de 2003)
Nova norma do Sigma Test (outubro de 2004)
Nova norma do Sigma Test (novembro de 2005)

You can find good on-line translator softwares in http://www.babelfish.org/.

I will try to do a summarized explanation on the difference:

Non-gauged Potential IQ is the best score to determine the antlog of ratio of mental potential. For instance: 10 people, each of them with potential IQ 100, works in synergy, have potential of intellectual production similar to 1 person with potential IQ about 126. That not have any relationship with rarity IQ, that is based on normalized scores, i.e. if 84% of people obtained raw score 5 or lower, then score 5 is equivalent to rarity IQ 116 (average + 1 standard-deviation, i.e. 100+16). If 98% of people obtained raw score 13 or lower, then score 13 is equivalent to rarity IQ 132 (average + 2 standard-deviation, i.e. 100+32). If 99.9% of people obtained raw score 21 or lower, then score 21 is equivalent to rarity IQ 148 (average + 3 standard-deviation, i.e. 100+48). Etc.

The uncertainty in scores is asymmetrical, for that an gauged IQ 160 can have 70% of probability to stay between 150 and 161 or can have 70% of probability to stay between 159 and 170. To minimize the distortion, the gauged IQ subtract 1 standard deviation and add 1 standard deviation. In this example, the first case would be about 155 and second case about 165. This problem occurs when anybody make few points in easy questions and a lot of points in difficult questions.

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Frequency distribution of rarity IQ

Frequency distribution of potential IQ

Some psychometrical properties of the Sigma Test, based on 152 testees:

The people are accustomed to the norm system based in rarity and they ask me a lot of times: "Is rarity 1/32,000 equal to 4 standard-deviation above average?" And the only answer is: "No. Rarity 1/32,000 cannot be calculated with safety, because in this level, the function that represents the distribution of IQs is completely deteriorate and doesn't make sense to speak in rarity. But if it was possible speak in rarity, maybe it would be equivalent the approximately 5 standard-deviation above average, for any test correctly gauged." To understand better, see the example of Chess games, with base in 2,600,000 games from Mega Database 2004: the average is 38 moves per game with standard-deviation 16. Is the rarity 1/1,000,000 equal the how many standard-deviation above average? Theoretically it would be +4.75sd, but in the true is more than +9.5sd (more than 190 moves), and the function doesn't behave as a gaussian out of the interval -2sd and +2sd. For that the correct way to measure the intelligence cannot be by rarity. The correct way has to be by ratio of potential. Besides, a proportion scale provides much more useful information than an approximately interval scale, with distortions and with arbitrary zero. The rarity scale is satisfactory exclusively for interval between -2sd and +2sd. The Sigma Test certificate also informs rarity IQ because practically all of high QI societies use criteria based on this score, but this is an information without meaning.

Scale type: ratio (antilog of potential IQ). This is the pioneer test in the world to use a coherent ratio scale. See more details in the texts on the norms sep. 2003 and oct. 2004.

Raw Score:
m=20.11, s=4.40

Fractional Score:
m=21.49, s=4.61

Potential IQ Gauged:
m=161.3, s=17.1

Rarity IQ Gauged:
m=150.6, s=13.8

Peason’s Linear Correlation between Oct. 2004 norm and Third norm (before Sep. 2003):
0.954

Cronbach’s a in Fractional Score:
0.874

Split-Half with Spearman-Brown adjustment among pairs and unpairs items, with base in balanced scores linearized (logarithms of the balanced scores):
0.865

Guttnan-Flanagan and Rulon among zigzag items, with base in balanced scores linearized (logarithms of the balanced scores):
0.867

More detailed properties:

Sigma Society VI 99.9999999th percentile (+6s)
Unicorn High IQ Society 99.99997th percentile
Sigma Society V 99.99997th percentile (+5s)
Pars Society 99.99997th percentile
OLYMPIQ Society 99.99997th percentile
Sigma Society IV 99.997th percentile  (+4s)
Platinum Society 99.9971th percentile (+4.0202s)
Ludomind Society 99.9th - 99.99th percentile 
Veritas Society  99.99th percentile 
ISI-S 99.916th percentile (+ps)
Glia Society 99.9th percentile
Sigma Society III 99.87th percentile (+3s)
Poetic Genius Society  99.5th percentile 
Sigma Society V subscriber 99.4th percentile (+2.5s)
Pars Society subscriber 99.4th percentile
High Potentials Society 98th percentile
Smart Society 98th percentile
Sigma Society 97.7th percentile (+2s)
High IQ Society for Humanity
Sigma Society III subscriber 93.3th percentile (+1.5s)
World Association for Highly Intelligent People