A Multi-Intrument Analysis of the PAS
Over the years, in the PAS research community, there has been speculation of how the PAS related to other theories and instruments. In this paper, a data set containing multiple instruments was analyzed.
A data set was analyzed which contained multiple instruments for the same subjects including the:
Analysis was limited to two kinds:
No ANOVA analysis was done to try to determine to what extent a factor in one instrument contributes to the value of a factor in another instrument.
This article discusses the concept of using one personality assessment instrument to predict results of another. But the reader is reminded that this is an academic exercise for the purpose of understanding the instruments. The purpose of each of the instruments is to predict human behavior and contrast that behavior to people with different results.
A set of 202 cases was used for the analysis. For each case a 16PF, MBTI, and WAIS were available. Also included in the data set were biographical information and the MMPI instrument. The biographical information was used only for the demographic summary although further analysis is planned. The MMPI data has not yet been included in analysis. The subject data is not representative of the population in general. All subjects are in the same profession and as shown below, the various factors in all instruments are not typical of known population distributions.
PAS profiles were computed using the NL2001 method. Profiles were computed automatically without reference to other subject case information.
Male: 187 Female: 15
Average age: 28.6 with 85% of all subjects between 21 and 35 years of age.
16 subjects did not finish high school, 122 had a high school education, and the remainder had some higher degree ranging from Associates to MS.
Totals for each factor Cool 135 Warm 67 Concrete 79 Abstract 123 Affected-by-feelings 39 Emotionally-stable 163 Submissive 70 Dominant 132 Sober 49 Enthusiastic 153 Expedient 66 Conscientious 136 Shy 39 Bold 163 Tough-minded 147 Tender-minded 55 Trusting 126 Suspicious 76 Practical 145 Imaginative 57 Forthright 60 Shrewd 142 Self-assured 175 Apprehensive 27 Conservative 150 Experimenting 52 Group-orented 106 Self-sufficnet 96 Undiscipined-self-co 27 Following-self-image 175 Relaxed 173 Tense 29 1 2 3 Extroversion 12 91 77 Anxiety 103 72 5 Tough-Poise 7 88 85 Independence 18 130 32
Extraversion 156 Introversion 46 Sensing 172 Intuition 30 Thinking 172 Feeling 30 Judging 161 Perceptive 41
Externalizer 30 Internalizer 172 Regulated/Literal 136 Flexible/Sensitive 66 Role Adaptive 127 Role Uniform 75 Eu 2 ( 0.99%) Ec 28 ( 13.86%) Iu 61 ( 30.20%) Ic 111 ( 54.95%) Ru 60 ( 29.70%) Rc 76 ( 37.62%) Fu 34 ( 16.83%) Fc 32 ( 15.84%) Au 52 ( 25.74%) Ac 75 ( 37.13%) Uu 20 ( 9.90%) Uc 55 ( 27.23%) ERA 10 ( 4.95%) ERU 9 ( 4.46%) EFA 9 ( 4.46%) EFU 2 ( 0.99%) IRA 73 ( 36.14%) IRU 44 ( 21.78%) IFA 35 ( 17.33%) IFU 20 ( 9.90%)
It is clear from the above numbers that this population is not typical of the population as a whole or the standardization samples for the instruments. This was expected because the entire set of subjects are in the same profession.
Two kinds of calculations were performed:
For processing factors, each factor was converted to a 1 or a 0. For MBTI and 16PF instruments, a 1 meant that the given case matched the factor under analysis. For PAS, a 1 meant that the case matched the specific profile or profile factor under analysis.
For processing scores, for MBTI and 16PF, the actual score from the instrument is used. For PAS, the deviation from Normal Level for each subtest was used.
Correlations were computed using the standard definition of statistical correlation using either:
For factors, the ability of a factor in one instrument was used to predict a factor in another instrument. Prediction was considered only for the ability of PAS factors or profiles to predict factors in the MBTI or 16PF. This was done using the following method to obtain a standard score (which can be readily converted to a p-Value):
To predict whether factor A in instrument 1 predicts factor B in instrument 2: Define: A = times factor A occurs in population of cases B = times factor B occurs in population of cases Tm = total matches - times a case has both factor A and factor B Pop = population size (202) 1. Determine the global likelihood of factor B in the population. ProbA = A/Pop 2. Estimate what the standard deviation would be of ProbA in a total population (i.e. if there were an unlimited number of sets of 202 cases and we take the number of times Factor A occurs in each of those samples). sd = SQRT(ProbA*(1-ProbA) / B) 3. Compute a standard score for how likely it is to have the number of times that factor B predicts factor A that occured in our sample. To do this, compute the portion of all incidents of factor B which are also factor A. Compare this to the expected proportion of ALL cases which are factor A. StdScore = (Tm / B - ProbA) / sd
For the case of computing the predictive value of a PAS contact "f" (Ruu, Fuu, Fcu, Rcu) profile predicting an MBTI S factor.
Of 202 cases: 172 are MBTI S 65 are PAS contact f 59 are both MBTI S and PAS contact f ProbA = 172/202 = .8515 Sd = sqrt(ProbA*(1-ProbA)/65) = .0441 Standard Score = (59/65 - ProbA) /sd = 1.27
The method was compared to running a discrete simulation model in which a large number of samples of size 202 are randomly selected with a mean number of cases of each factor equal to a test case (e.g. 172 out of 202 in the above example). Within each batch of 202 cases, each case had the probability of being the factor as that of the actual subject cases. The actual statistics, in particular, the standard deviation of the fraction of cases that are the first factor, on the resulting values match the ones using the method above. Ultimately, the number of times the sets of 202 samples showed at least the number of cases of the PAS factor predicting the other factor compared to the computed p-Value based on the standard score.
Cases were run for all combinations of a factor from an MBTI or 16PF factor combined with a PAS factor. These factors are defined as:
Every combination of any two of the following:
There were no instances of correlations so high as to point to any two factors compared as certainly measuring the same thing. Given the number of factors compared, one would expect some fairly strong correlations simply due to randomness.
A one line result could reasonably say that the MBTI, 16PF, and PAS measure independent aspects of personality. However, there are some modest correlations (in the .25 range) and high standard scores for the ability of a PAS factor(s) to predict MBTI or 16PF factors. Qualitative reading of the descriptive definitions of the factors with the strongest correlations "make sense", but of course this does not constitute much evidence beyond what a knowledgeable reader would predict from reading.
"Raw" scores as defined earlier were compared for all three combinations:
16PF and MBTI
The strongest correlation was between MBTI E and 16PF "H" (Shy). But this was only .2788. Qualitatively, this would seem to be a random effect. Only two other correlations exceeded .2:
PAS and MBTI
The strongest correlation found was .1619 for MBTI E and PAS Time Estimation.
PAS and 16PF
The strongest correlation found was -.2633 for 16PF "B" (Concrete thinking/Abstract thinking) and PAS high Similarities. This is a qualitatively expected correlation in that high similarities in the PAS relates to basic level ability to see relationships and subtleties. In PAS terms, this is the opposite of "concrete thinking", although PAS does not call this opposite "abstract thinking", but sensitivity, ability to see relationships, and ability to feel other's emotions.
There are instances of very high standard scores, indicating a very low probability of a result due to randomness, for the value of a PAS factor or profile to predict an MBTI or 16PF factor(s). However, if we examine one high standard score as an example, it is statistically true that the portion of PAS profiles which are in turn a certain 16PF factor(s) is unlikely due to randomness; however, when we examine the actual numbers, we see that practical use for prediction is useless due to the small number of cases. For example, PAS basic era predicts 16PF combination of Q1 and Q3 with a standard score of 3.45 (p-Value of .001. However, the numbers are these:
Cases out of 202 with Q1(Conservative) and not-Q3(Self-sufficient): 13 Cases out of 202 with pas basic era: 26 Cases out of 202 with both Q1/not-Q3 and era: 6 Thus: portion of cases with Q1/not-Q3: .064 portion of PAS era that are Q1/not-Q3: .230 So if PAS era, the probability is far higher of Q1/not-Q3 than in the population, but still only 23% so not useful for actual prediction.
Strong predictive values are shown in the table below. Only cases meeting these criteria are shown:
Using PAS profiles (primitive, basic or contact) to predict 16PF (1) StdScr 16PF PAS (2) Correlation 91.7 of 12 1.2869 Or+ IuRcAc 75.7 0.0933 91.7 of 12 1.3179 hO+ IuRcAc 75.2 0.0956 92.3 of 13 1.3934 f+ IcRuAc 75.7 0.1013 92.3 of 13 1.6444 M+ IcRuAc 71.8 0.1196 92.3 of 13 1.7060 fO+ IcRuAc 70.8 0.1240 92.3 of 13 1.7981 ch+ IcRcUc 69.3 0.1307 100.0 of 12 1.9340 rS+ IuRcAc 76.2 0.1403 100.0 of 10 2.0069 cr+ IcRuUc 71.3 0.1448 100.0 of 10 2.0312 hr+ IcRuUc 70.8 0.1465 92.3 of 13 2.0428 e+ IcRuAc 65.3 0.1485 100.0 of 10 2.1044 ch+ IcRuUc 69.3 0.1518 100.0 of 12 2.1189 hS+ IuRcAc 72.8 0.1537 91.7 of 12 2.1847 b+ IcRcAu 60.9 0.1584 100.0 of 12 2.2251 hr+ IuRcAc 70.8 0.1614 92.3 of 13 2.2588 MO+ IcRuAc 61.9 0.1643 92.3 of 13 2.4793 eO+ IcRuAc 58.4 0.1803 Using PAS "lookalikes" to predict 16PF. 92.9 of 14 1.7521 M+ iru 71.8 0.1277 Using PAS profiles to predict MBTI. 91.4 of 35 1.7247 J IFA 79.7 0.1334 100.0 of 13 1.9579 E IcRuAc 77.2 0.1424 Using PAS "lookalikes" to predict MBTI 92.9 of 14 1.2237 J iru 79.7 0.0892 (1) This is percent of the PAS cases which are also the 16PF factor. (2) This is the percent of the population that are the 16PF factor. 1. PF16 factors: lower case is the opposite. For example, A iw Cool, and a is warm. If two factors are shown, it means both were true. 2. PAS lowercase means basic factor (i.e. r = Ru or Fc) 3. PAS with an 'S' means contact. (i.e. a = Uuc, Ucu, Acc, Auu) 4. PAS with '.' separated values means all of them true. 5. PAS "lookalikes" are all profiles with the same basic factors (e.g. IcRcAc = EuFuUu = efu) or all profiles with the same contact factors (e.g. IucRccAcc = EcuFccUuu = eru.) 6. Ignore '+' signs which mean AND logic if there is more than one 16PF factor shown.
To give a feel for the low magniture of the correlations, below are the maximum correlations for the various kinds of PAS profile portions:
Only examples with at least 10 cases of corresponding PAS and MBTI/16PF factors are considered. MBTI vs PAS facs -0.1474 93 J aS MBTI vs PAS factors -0.1511 30 J IRU MBTI vs PAS lookalike 0.1244 143 E eS.fS.aS PF16 vs PAS facs 0.2725 24 Bl r PF16 vs PAS factors 0.2774 12 lN IRU PF16 vs PAS lookalike -0.2492 61 np iS.rS.aS Raw scores for 16PF vs MBTI 0.2788 F H M E Raw scores for 16PF vs PAS 0.2234 F G S OA (Object Assembly) Raw scores for MBTI vs 16PF 0.2788 M E F H Raw scores for MBTI vs PAS 0.1619 M E S TE (Time Estimation) Notes: 1. PF16 factors: lower case is the opposite. For example, A iw Cool, and a is warm. If two factors are shown, it means both were true. 2. PAS lowercase means basic factor (i.e. r = Ru or Fc) 3. PAS with an 'S' means contact. (i.e. a = Uuc, Ucu, Acc, Auu) 4. PAS with '.' separated values means all of them true.
For the MBTI, 16PF, and PAS, intra-instrument correlations were computed. For PAS, the factors compared were each primitive (EIRFAU), each basic(eirfau) and each contact(eirfau).
The higher intra-instrument correlations tend to be stronger than the inter-intrument correlations of factors.
The higher intra-intrument correlations are shown below with comments:
Sensing and Thinking: .21 Sensing and Judging: .20
Factor O: Self-Assured and Factor: Q3 Undisciplined Self-conflict: .50 Factor F: Sober and Factor: H Shy: .43 Factor H: Shy and Factor: O Self-Assured: -.40 Factor F: Sober Factor: O Self-Assured: -.35
Primitive E and contact e: -.42 (i.e. Primitive externalizers are NOT contact externalizers). Primitive E and basic e: -.41 (i.e. Primitive E do not remain uncompensated) Primitve A and basic a: -.31 (i.e. Primitive A do compensate).
Some of the biographical data available was encoded using a numeric scheme. Statistics were then run comparing this data to various instruments. For all statistics, a match was given a value of 1 and failure to match a value of 0 when doing correlations. The encoding scheme and the biographical items used included:
The strongest correlations of interest using the coding above were:
Correlation Biographical-factor Instrument-Factor .20 Male MBTI T .20 Female MBTI F .34 Not High School grad 16PF H(shy) and Q3(Undisciplined) .31 Female 16PF L(suspicious) and Q2(Group-Oriented) .28 Not High School grad 16PF E(submissive) and q1(Experimenting)
No PAS factors had even these strong of correlations (except for cases with a trivial number of instances). This is somewhat expected because the PAS primitives are believed to be non-sex linked genetic factors.
The incidence of the various PAS factors was compared to that in the WAIS standardization sample obtained from the charts in "Personality and Ability" by Krauskopf and Saunders.
Differences between the WAIS standardization sample and this sample of subjects indicate that the nature of the sample, whose primary link is being in the same profession in the same geography, is biased to certain PAS profiles.
The greatest differences in intra-intrument correlations are:
Factors Wais-std-sample Subjects-of-this-study basic r and contact r .35 -.15 Primitive A and basic a .12 -.31 Primitive R and contact r .43 -.16
Thus the subjects in this sample are more likely, when basic "r", to not remain contact "r"; when primitive "A", to not remain basic "a", and when primitive "R", not to remain contact "r".
There were instances where the percentage of the sample which is a certain PAS factor is very different for the WAIS standardization sample and this set of subjects. Significant differences are:
Factor %-of-WAIS-sample %-of-this-study E 42% 15% I 58% 85% IRA 26% 36% IRU 11% 22% Eu 14% 1% (1) Au 47% 25% (2)
(1) Even though only 15% of the total were "E", this still represents a very small portion of "Eu".
(2) The WAIS sample has slighly more primitive "A" (65%) than this study set (63%), but this is still a significant difference in the prevalence of compensation of the "A".
The 16PF and MBTI are both "self reporting" tests asking a subject their beliefs or feelings about situations, themselves, others, and how others perceive them. Self reporting tests are inherently blind to a subject's lack of insight into their own misperceptions. The PAS uses a completely different approach based on the theory as made clear in "Peronality and Ability" that and the paper "A Radical Hypothesis" that personality is a function of abilities, abilities which can be measured by the WAIS/PAS and not dependent on the subjects perceptions.
Given the lack of ability to predict results on one instrument with the results of a different instrument, there are two possible hypotheses:
I believe that the second hypothesis is the most likely.