This is the most current version.
A Multi-Instrument Analysis of the PAS - Preliminary Analysis
Earl Rodd - August 2017
Version 1.3 Revised September 9, 2017 Addied biographical data logic and results. Corrected some values for an error found in processing computer programs.
This preliminary analysis has not completed formal review. It is made available for the purpose of inviting review and comment.

Abstract

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:

The WAIS was used to determine PAS profiles. Analysis was performed to examine whether the extent to which various factors in the different personality related instruments overlapped. Specific analysis was used to determine the extent to which the PAS can predict 16PF or MBTI factors. Preliminary analysis shows that the instruments do not strongly overlap. Results with one instrument do not generally predict results on a different instrument, although there are some isolated cases otherwise. Limited analysis was done on the relationship of 16PF and MBTI factors.

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.

Reminder

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.

Introduction

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.

Basic Demographics and Summary of Data

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.

Summary of 16PF Data

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

Summary of MBTI Data

        Extraversion 156         Introversion  46
             Sensing 172            Intuition  30
            Thinking 172              Feeling  30
             Judging 161           Perceptive  41

Summary of PAS Data

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%) 

Discussion

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.

Method

Two kinds of calculations were performed:

  1. Correlations of factors in different instruments.
  2. Correlations of scores in different instruments.
  3. Ability of a factor in one instrument to predict a factor in a different instrument.

Coding of Factors

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.

Coding of Scores

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.

Correlation

Correlations were computed using the standard definition of statistical correlation using either:

Predictive Ability

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

Example of standard score calculation.

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

Confirmation

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 for which both correlations and predictive standard scores were computed

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:

Cases for which just correlations were computed.

Every combination of any two of the following:

  1. An MBTI score (4 of them)
  2. A 16PF score (16 of them)
  3. A PAS subtest deviation from NL (13 of them). They include Color Naming, Time Estimation and Vocabulary.

Results

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.

Correlations of raw scores

"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.

Standard Scores

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.

Correlations

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.

Intra-instrument Correlations

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:

Biographical Data

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:

Results

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.

This Study PAS Profiles vs. WAIS Standardization Sample

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.

Intra Intrument Correlations

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".

Differences in Proportions

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".

Discussion

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:

  1. The instruments truly measure independent factors of personality.
  2. The factors defined by the instruments are actually made up of parts of different factors in another instrument.

I believe that the second hypothesis is the most likely.