1. Purpose

The purpose of this document is to present the methodology and results of the analysis of the student response data for the Reasoning construct. The response data was drawn from a sample of the the world, and the Reasoning ability of the world was of research interest. Item Response Theory analysis (IRT) was undertaken and a 1 parameter logistic model (1PLM) was applied to the partial credit data.

2. Items Included in the Reasoning Instrument

Table 1 presents the 13 items included in the Reasoning instrument:

List of Items
Item abbreviation Full item description
B1 I make insightful remarks
B2 I know the answers to many questions
B3 I tend to analyze things
B4 I use my brain
B5 I learn quickly
B6 I counter others’ arguments
B7 I reflect on things before acting
B8 I weigh the pros against the cons
B9 I consider myself an average person
B10 I get confused easily
B11 I know that I am not a special person
B12 I have a poor vocabulary
B13 I skip difficult words while reading

3. Methodology

3.1 Statistical packages

Analysis was undertaken with the assistance of the \(CTT\) (version 2.3.2; Willse, 2018), \(psych\) (version 1.8.4; Revelle, 2018), \(TAM\) (version 2.10-24; Robitzsch, Kiefer, & Wu, 2018), and \(WrightMap\) (version 1.2.1; Torres Irribarra & Freund, 2018) R packages. The \(CTT\) package provided results pertaining to the frequency of response categories, point biserial (Pearson) discrimination indices, poly- and bi-serial discrimination indices, and the Cronbach’s alpha (\(\alpha\)) reliability coefficients. The \(psych\) package provided results pertaining to the full Pearson correlation matrix (between items), while the \(TAM\) package was used to carry out the 1PLM model for the partial credit data, and the \(WrightMap\) package provided for a visual illustration of the relative positions of question items and person abilities.

3.2 Assessment of reliability

Instrument reliability is theoretically conceived as the proportion of true score variance \(Var[T]\) to observed score variance \(Var[O]\),
\[Reliability = \frac{Var[T]}{Var[O]}\]
Because it is impossible to identify the proportion of variance due to true scores, we can only estimate this value. Derived from Generalisability Theory (Brennan, 2001), the following formula is often applied to estimate the reliability of a test instrument,
\[Reliability =\frac{Var[O]-Var[E]}{Var[O]}\]
where \(Var[O]\) represents the amount of observed variation in ability, and \(Var[E]\) represents the amount of variation due to error. Equivalent to the formula above, the formula for the Cronbach’s alpha coefficient (Cronbach, 1951) is expressed as follows,
\[\alpha =\frac{K\bar{c}}{(1+(K-1)\bar{c})}\]
where \(K\) is the number of items, and \(\bar{c}\) is the average of all the covariances between all items.
In accordance with DeVellis (2012), Table 2 presents some general rules-of-thumb for interpreting the meaning of the alpha \(\alpha\) coefficient for a test instrument.

Interpreting the Cronbach’s Alpha
Internal Consistency Cronbach’s alpha
Excellent 0.90 & up
Good 0.80-0.89
Acceptable 0.70-0.79
Questionable 0.60-0.69
Poor 0.50-0.59
Unacceptable under 0.50

It should be noted that the Cronbach’s \(\alpha\) coefficient assumes an equivalent contribution of each item to the total score (tau, \(\tau\), equivalence), consequently the \(\alpha\) coefficient is considered lower bound estimate of reliability. Based on the 1PLM undertaken, the expected a posteriori (EAP; Bock & Aitken, 1981) estimate (for the individual scores; see subsection 3.4) for instrument reliability is also estimated. In addition, the person-separation reliability statistic (based on Warm’s Likelihood Estimation, Warm, 1989) provides for an additional estimate of reliability based on the degree to which the test instrument sufficiently separates students.

3.3 Assessment of item discrimination

The discrimination indices (correlation coefficients) provide an estimate of the contribution of each item to the construct of interest, Reasoning. The indices for each item were estimated by ommiting each item-of-interest’s contribution to the summed totals (often termed the item-rest correlations). This was done because inclusion of the item of interest in the summed total score artificially inflates each discrimination index. Because Pearson correlations provide attenuated estimates of the relationships involving categoric variables, polyserial correlations (and biserial correlations for dichotomous items) are also included as a means to assess item discrimination (Olsson, Drasgow, & Dorans, 1982).

To assess the degree to which each discrimination index is inflated due to the inclusion of the item of interest, a full Pearson item-total correlation matrix is also generated with the assistance of the R \(psych\) package).

3.4 Item-response theory analysis

IRT analysis was undertaken with the assistance of the \(TAM\) package (\(version\hspace{.1cm}2.10{\text -}24\); Robitzsch, Kiefer, & Wu, 2018). Because the Reasoning ability of the the world was of interest, marginal maximum likelihood estimation (MML) was utilised. This form of estimation relies on the assumption that the construct of interest is distributed normally throughout the population of interest (modelling of data incorporates this assumption through the modelling of a Bayesian posterior distribution). When this form of analysis is undertaken, the specific ability levels of the sample in question is not of focus (Wu, Tam, & Jen, 2016, p. 262), however point estimates for individual students in the sample (defined as expected a posteriori, EAP, ability estimates) are be estimated in a two-step process. To do this, the item difficulties are first estimated via MML estimation. Thereafter, based on these specific item difficulties, the sample-specific EAP ability point estimates are then estimated. In the aforementioned \(TAM\) package (\(version\hspace{.1cm}2.10{\text -}24\)), the EAP point ability estimates are based on the mode of the likelihood function. Warm’s (1989) Weighted Likelihood estimation (WLE) method uses the mean of the likelihood function providing for a more precise method of estimating person point ability. For this reason, WLE-based point statistics are estimated and reported in this document.

Despite the precision with which the EAP ability estimates can be determined, their inclusion in secondary models designed to gauge differential achievement patterns within different educational ecologies is not appropriate. For such research questions, plausible values (PVs) should be used. Plausible values are random draws from students’ posterior distribution (Wu, Tam, & Jen, 2016, p. 280), and it is these values that are better suited for secondary analysts to include in statistical models designed to test distributive achievement patterns in classrooms, schools, and broader demographic ecologies (Wu, Tam, & Jen). For example, a secondary analysis may be interested in the degree to which student ability was influenced by school mean socio-economic status. To undertake this level of analysis, at least five different plausible value samples should drawn. Thereafter, five respective multilevel models (MLMs) should be run and the average result for relevant intercepts, fixed effects, and variance components should be determined (Wu, 2005; Laukaityte & Wiberg, 2017).

To interpret item outfit, the confidence interval for the item outfit distribution is also included. The 95% confidence intervals for the outfit chi-square statistics were estimated in accordance with Wu and Adams (2013, p. 344), \[95\hspace{.1cm}percent\hspace{.1cm}CI=1\pm2\sqrt{\frac{2}{N}}\] where, \(CI\) is the confidence interval, and \(N\) is the number of students in the sample. Items below the 95% confidence interval interval (i.e., under 0.80 when N is 200) could be considered over-fitting (relative to the other items analysed). Items above the 95% confidence interval could be considered relatively underfitting. Important to note is that overfitting items are generally not problematic (see Wu, Tam, & Jen, 2016, pp. 151-153) and should be retained. See Masters (1988) for exceptional circumstances when test equating across certain demographic subgroups is of primary research interest.

One way to strictly assess the performance of an underfitting (often also low discriminating) item is to assess the change in the reliability coefficient when the item is removed. If, upon removal of the item from analysis, the test reliability increases (i.e., Cronbach’s \(\alpha\) increases), there is further evidence in support of the item’s removal. Therefore, if the \(\alpha_{deleted}\) is larger than the \(\alpha_{full}\), the item should be flagged and possibly deleted.

Outfit person fit statistics are also generated for the purpose of identifying anomolous person response patterns. Respondents with higher person outfit statistics well above 1.00 could be considered underfitting the model. These respondents would likely be those with very high overall ability whom performed unusually poorly on easier items. Respondents with lower person outfit statistics well below 1.00 would be those performing in a very predictable way, perhaps those reaching the very top score for each question. Nevertheless, the identification of anomolous item-response patterns among persons can be discerned by inspecting the graph provided in Appendix A5.

Finally, with the assistance of the R \(WrightMap\) package, a Wright Map is produced which maps the Reasoning ability of the WLE ability estimates against the item steps for each of the 13 items. PVs could also be used in this instance. All results are now presented.

Finally, item expected score curves, item category characteristic curves, and Thurstonian thresholds are produced. Classical item analysis (itenal) is also produced.

4. Results

4.1 Observed scores

A total 3453 participated in the Reasoning exam. The mean overall total score was 35.14 and the standard deviation of the total score was 6.76. The frequency of categories for the partial credit items is given in Table 3.

Frequency of Categories for Each Item
category B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 B12 B13
0 90 87 22 14 35 93 128 56 321 166 301 74 171
1 292 506 129 47 204 474 524 287 1257 791 819 247 478
2 825 869 294 209 475 873 704 630 511 640 669 410 369
3 1670 1435 1696 1519 1703 1500 1551 1661 947 1390 1031 1364 1249
4 562 550 1306 1657 1029 495 534 809 411 459 625 1351 1179

4.2 Point biserial discrimination indices

The 13 point biserial and polyserial discrimination indices are included Table 4.

Point Biserial, and Bi- and Poly-serial Discrimination Indices
Item Abbreviation Point Biserial or Pearson Bi- or Poly-serial
B1 0.45 0.50
B2 0.46 0.49
B3 0.42 0.48
B4 0.53 0.61
B5 0.50 0.55
B6 0.31 0.34
B7 0.30 0.33
B8 0.33 0.37
B9 0.37 0.38
B10 0.43 0.46
B11 0.28 0.30
B12 0.50 0.55
B13 0.35 0.39

4.3 Item fit for the Reasoning items

The item fit (un-weighted and weighted mean square) fit indices for the 13 Reasoning items are provided in Table 5. Item infit and outfit t statistics and p values are also included.

Item Fit Statistics
Item Abbreviation Outfit Outfit t Outfit p Infit Intfit t Intfit p
B1 0.99 -0.48 0.63 0.95 -2.07 0.04
B2 0.96 -1.72 0.09 0.95 -2.25 0.02
B3 0.94 -1.98 0.05 0.95 -1.82 0.07
B4 0.82 -6.19 0.00 0.85 -4.74 0.00
B5 0.89 -4.11 0.00 0.89 -4.01 0.00
B6 1.10 4.23 0.00 1.08 3.42 0.00
B7 1.15 6.15 0.00 1.11 4.67 0.00
B8 1.07 2.76 0.01 1.05 1.76 0.08
B9 1.10 4.55 0.00 1.08 3.95 0.00
B10 1.03 1.52 0.13 1.00 0.22 0.82
B11 1.25 10.64 0.00 1.20 9.13 0.00
B12 0.90 -3.49 0.00 0.91 -3.34 0.00
B13 1.17 5.87 0.00 1.10 4.14 0.00

The item outfit statistics are also graphed in Figure 1. The graph includes the upper- and lower-bound 95% confidence intervals for item outfit distribution (the horizontal red lines).

Figure 1. Unweighted Fit Statistics

The alpha if item deleted (\(\alpha_{deleted}\)) values are provided in Figure 2. To note, the alpha value for the full set of 13 items is 0.7668. If the \(\alpha_{deleted}\) values are more than the full alpha value, that is evidence that the item does not contribute to the test and should be removed. For a final level of analysis of item functioning, the full item correlation matrix could be inspected for incidences of negative correlations between problematic item(s) and other items in the test instrument (Appendix A1). Incidences of negative correlations could be seen as evidence of poor item functioning and could be further investigated. An inspection of the CTT Item Analysis (Appendix A4) may also be undertaken.

Figure 2. The Alpha Full Minus the Alpha Deleted Values

4.4 Results for IRT student ability and item difficulty estimates

Based on the MML analysis, the mean ability (logit) of the population of interest was 0 (the mean ability is fixed to zero by default). The Reasoning logits ranged from -1.85 to 1.72 and the standard deviation was 0.6.

The item difficulties (deltas) had a mean of -0.74 and a standard deviation of 0.44. The difficulty logits for each respective item are provided in Table 6 (the full set of item difficulties for each item’s di- or poly-chotomous category is provided in Appendix A2).

Item Difficulties
Item Abbreviation Item Difficulties
B1 -0.64
B2 -0.60
B3 -1.35
B4 -1.58
B5 -1.12
B6 -0.56
B7 -0.50
B8 -0.89
B9 -0.06
B10 -0.34
B11 -0.25
B12 -1.00
B13 -0.69

The Cronbach’s alpha was 0.77 and the population-related MML reliability estimate was 0.78 (Wu, Tam, and Jen, 2016). In addition, the person separation reliability estimate was 0.79.

4.5 Wright map

The Wright Map is presented in Figure 3. It should be noted that although WLE ability point estimates are used for student ability, a set of plausible values could also be used.

Figure 3. Wright Map for Reasoning Construct

4.6 Item expected score curves

Following are a set of graphs illustrating all item expected score curves.

4.7 Polytomous item category characteristic curves

Following are a set of graphs illustrating all item category characteristic curves. The full set of item parameters and standard errors for each item category can be found in Appendix A2.

4.8 Thurstonian thresholds

The Thurstonian Thresholds are presented in Table 7.

Thurstonian Thresholds
Cat1 Cat2 Cat3 Cat4
B1 -2.18 -1.33 -0.49 1.43
B2 -2.48 -1.06 -0.25 1.38
B3 -2.76 -1.76 -1.30 0.44
B4 -2.64 -2.10 -1.65 0.05
B5 -2.68 -1.57 -0.97 0.76
B6 -2.38 -1.09 -0.27 1.51
B7 -2.15 -0.94 -0.33 1.44
B8 -2.51 -1.38 -0.69 1.03
B9 -1.82 -0.11 0.25 1.44
B10 -2.16 -0.63 -0.13 1.54
B11 -1.65 -0.46 0.02 1.09
B12 -2.18 -1.30 -0.86 0.33
B13 -1.83 -0.84 -0.55 0.47

5. References

Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika 46,443–59.

Brennan, R. L. (2001). Generalizability Theory. New York: Springer-Verlag.

Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297-334. doi:10.1007/BF02310555

Laukaityte, I. & Marie Wiberg, M. (2017) Using plausible values in secondary analysis in large-scale assessments. Communications in Statistics - Theory and Methods, 46(22), 11341-11357. doi.10.1080/03610926.2016.1267764

Masters, G. N. (1988). Item Discrimination: When More is Worse. Journal of Educational Measurement, 25(1),, 15-29.

Olsson, U., Drasgow, F., & Dorans, N. J. (1982). The polyserial correlation coefficient. Biometrika, 47, 337–347.

Revelle, W. (2018). psych: Procedures for Personality and Psychological Research, Version = 1.8.4. Northwestern University, Evanston, Illinois, USA. Retreived from https://CRAN.R-project.org/package=psych

Robitzsch, A., Kiefer, T., & Wu, M. (2018). TAM: Test analysis modules. R package version 2.10-24. Retreived from https://CRAN.R-project.org/package=TAM

Torres Irribarra, D. & Freund, R. (2014). Wright Map: IRT item-person map, Version = 1.2.1. Retreived from http://github.com/david-ti/wrightmap

Warm, T. A. (1989). Weighted likelihood estimation of ability in item response theory. Psychometrika, 54, 427-450.

Willse, J. T. (2018). CTT: Classical Test Theory Functions. R package version 2.3.2. Retreived from https://CRAN.R-project.org/package=CTT

Wu, M. (2005). The role of plausible values in large-scale surveys. Studies in Educational Evaluation, 31(2-3), 114-128. doi:10.1016/j.stueduc.2005.05.005

Wu, M. & Adams, R. J. (2013). Properties of Rasch residual fit statistics. Journal of Applied Measurement, 14(4), 339-355.

Wu, M., Tam, H. P., & Jen, T-H. (2016). Educational Measurement for Applied Researchers: Theory into Practice. Singapore: Springer Nature.

6. Appendices

A1. Pearson Correlation Matrix

Point Biserial or Pearson Correlation Matrix: Item-Totals
B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 B12 B13 Row_Totals
B1 1.00 0.33 0.27 0.29 0.24 0.29 0.18 0.20 0.22 0.19 0.18 0.28 0.18 0.56
B2 0.33 1.00 0.24 0.33 0.38 0.28 0.10 0.15 0.25 0.21 0.14 0.32 0.21 0.57
B3 0.27 0.24 1.00 0.38 0.27 0.23 0.29 0.30 0.17 0.17 0.10 0.19 0.14 0.52
B4 0.29 0.33 0.38 1.00 0.41 0.19 0.27 0.27 0.18 0.34 0.16 0.32 0.24 0.60
B5 0.24 0.38 0.27 0.41 1.00 0.20 0.18 0.19 0.20 0.39 0.16 0.32 0.24 0.59
B6 0.29 0.28 0.23 0.19 0.20 1.00 0.03 0.14 0.20 0.12 0.05 0.18 0.13 0.44
B7 0.18 0.10 0.29 0.27 0.18 0.03 1.00 0.34 0.09 0.19 0.10 0.15 0.12 0.44
B8 0.20 0.15 0.30 0.27 0.19 0.14 0.34 1.00 0.07 0.17 0.10 0.17 0.14 0.45
B9 0.22 0.25 0.17 0.18 0.20 0.20 0.09 0.07 1.00 0.18 0.39 0.22 0.14 0.52
B10 0.19 0.21 0.17 0.34 0.39 0.12 0.19 0.17 0.18 1.00 0.20 0.30 0.26 0.56
B11 0.18 0.14 0.10 0.16 0.16 0.05 0.10 0.10 0.39 0.20 1.00 0.15 0.04 0.45
B12 0.28 0.32 0.19 0.32 0.32 0.18 0.15 0.17 0.22 0.30 0.15 1.00 0.47 0.60
B13 0.18 0.21 0.14 0.24 0.24 0.13 0.12 0.14 0.14 0.26 0.04 0.47 1.00 0.50
Row_Totals 0.56 0.57 0.52 0.60 0.59 0.44 0.44 0.45 0.52 0.56 0.45 0.60 0.50 1.00

A2. Point Biserial or Pearson Correlation Matrix: Item-Rest

Point Biserial or Pearson Correlation Matrix: Item-Rest
B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 B12 B13
disc 0.45 0.46 0.42 0.53 0.5 0.31 0.3 0.33 0.37 0.43 0.28 0.5 0.35

A3. The Item Category Parameters and Standard Errors

Note. Note that xsi values pertain to item category difficulty levels; se.xsi values pertain to standard errors.

Item Category Parameters and Standard Errors
xsi se.xsi
B1_Cat1 -1.73 0.11
B1_Cat2 -1.36 0.06
B1_Cat3 -0.77 0.04
B1_Cat4 1.32 0.05
B2_Cat1 -2.28 0.11
B2_Cat2 -0.83 0.05
B2_Cat3 -0.53 0.04
B2_Cat4 1.23 0.05
B3_Cat1 -2.47 0.22
B3_Cat2 -1.29 0.09
B3_Cat3 -1.96 0.05
B3_Cat4 0.34 0.04
B4_Cat1 -1.98 0.27
B4_Cat2 -2.01 0.13
B4_Cat3 -2.25 0.07
B4_Cat4 -0.06 0.04
B5_Cat1 -2.41 0.17
B5_Cat2 -1.26 0.07
B5_Cat3 -1.44 0.04
B5_Cat4 0.64 0.04
B6_Cat1 -2.15 0.11
B6_Cat2 -0.90 0.05
B6_Cat3 -0.57 0.04
B6_Cat4 1.38 0.05
B7_Cat1 -1.92 0.09
B7_Cat2 -0.58 0.05
B7_Cat3 -0.82 0.04
B7_Cat4 1.33 0.05
B8_Cat1 -2.23 0.14
B8_Cat2 -1.15 0.06
B8_Cat3 -1.08 0.04
B8_Cat4 0.90 0.04
B9_Cat1 -1.73 0.06
B9_Cat2 0.77 0.04
B9_Cat3 -0.50 0.04
B9_Cat4 1.24 0.06
B10_Cat1 -2.02 0.08
B10_Cat2 -0.02 0.04
B10_Cat3 -0.76 0.04
B10_Cat4 1.42 0.05
B11_Cat1 -1.42 0.06
B11_Cat2 0.00 0.04
B11_Cat3 -0.39 0.04
B11_Cat4 0.82 0.05
B12_Cat1 -1.83 0.12
B12_Cat2 -0.91 0.06
B12_Cat3 -1.37 0.05
B12_Cat4 0.12 0.04
B13_Cat1 -1.57 0.08
B13_Cat2 -0.07 0.05
B13_Cat3 -1.32 0.04
B13_Cat4 0.22 0.04

A4. CTT Item Analysis

CTT Item Analysis
Item Total Category Count Percent Pbs MeanAbility
B1 3439 0 90 0.03 -0.11 -0.37
B1 3439 1 292 0.08 -0.26 -0.46
B1 3439 2 825 0.24 -0.33 -0.31
B1 3439 3 1670 0.49 0.11 0.06
B1 3439 4 562 0.16 0.48 0.57
B2 3447 0 87 0.03 -0.19 -0.63
B2 3447 1 506 0.15 -0.31 -0.40
B2 3447 2 869 0.25 -0.22 -0.20
B2 3447 3 1435 0.42 0.15 0.09
B2 3447 4 550 0.16 0.45 0.55
B3 3447 0 22 0.01 -0.12 -0.79
B3 3447 1 129 0.04 -0.21 -0.57
B3 3447 2 294 0.09 -0.23 -0.41
B3 3447 3 1696 0.49 -0.23 -0.13
B3 3447 4 1306 0.38 0.47 0.32
B4 3446 0 14 0.00 -0.12 -0.96
B4 3446 1 47 0.01 -0.17 -0.77
B4 3446 2 209 0.06 -0.29 -0.61
B4 3446 3 1519 0.44 -0.36 -0.22
B4 3446 4 1657 0.48 0.55 0.30
B5 3446 0 35 0.01 -0.15 -0.78
B5 3446 1 204 0.06 -0.28 -0.58
B5 3446 2 475 0.14 -0.29 -0.39
B5 3446 3 1703 0.49 -0.11 -0.06
B5 3446 4 1029 0.30 0.51 0.41
B6 3435 0 93 0.03 -0.12 -0.37
B6 3435 1 474 0.14 -0.24 -0.31
B6 3435 2 873 0.25 -0.23 -0.21
B6 3435 3 1500 0.44 0.16 0.10
B6 3435 4 495 0.14 0.34 0.44
B7 3441 0 128 0.04 -0.16 -0.42
B7 3441 1 524 0.15 -0.23 -0.29
B7 3441 2 704 0.20 -0.16 -0.16
B7 3441 3 1551 0.45 0.09 0.05
B7 3441 4 534 0.16 0.37 0.46
B8 3443 0 56 0.02 -0.10 -0.42
B8 3443 1 287 0.08 -0.22 -0.38
B8 3443 2 630 0.18 -0.25 -0.28
B8 3443 3 1661 0.48 0.00 0.00
B8 3443 4 809 0.23 0.40 0.39
B9 3447 0 321 0.09 -0.17 -0.29
B9 3447 1 1257 0.36 -0.35 -0.25
B9 3447 2 511 0.15 -0.08 -0.11
B9 3447 3 947 0.27 0.26 0.22
B9 3447 4 411 0.12 0.41 0.59
B10 3446 0 166 0.05 -0.21 -0.49
B10 3446 1 791 0.23 -0.33 -0.32
B10 3446 2 640 0.19 -0.15 -0.17
B10 3446 3 1390 0.40 0.18 0.12
B10 3446 4 459 0.13 0.44 0.60
B11 3445 0 301 0.09 -0.19 -0.33
B11 3445 1 819 0.24 -0.26 -0.24
B11 3445 2 669 0.19 -0.09 -0.10
B11 3445 3 1031 0.30 0.12 0.10
B11 3445 4 625 0.18 0.37 0.42
B12 3446 0 74 0.02 -0.19 -0.67
B12 3446 1 247 0.07 -0.30 -0.58
B12 3446 2 410 0.12 -0.27 -0.38
B12 3446 3 1364 0.40 -0.13 -0.09
B12 3446 4 1351 0.39 0.53 0.35
B13 3446 0 171 0.05 -0.20 -0.46
B13 3446 1 478 0.14 -0.28 -0.37
B13 3446 2 369 0.11 -0.16 -0.24
B13 3446 3 1249 0.36 -0.05 -0.04
B13 3446 4 1179 0.34 0.45 0.33

A5. Personfit Statistics

Figure 4. Personfit Statistics: Ordered Descendingly [see outputed csv file to identify persons of interest]