A Common Measurement Scale for Self-Report Instruments in Mental Health Care

Abstract

The diversity of measures in clinical psychology hampers a straightforward interpretation of test results, complicates communication with the patient, and constitutes a challenge to the implementation of measurement-based care. In educational research and assessment, it is common practice to convert test scores to a common metric, such as T scores. We recommend applying this also in clinical psychology and propose and test a procedure to arrive at T scores approximating a normal distribution that can be applied to individual test scores. We established formulas to estimate normalized T scores from raw scale scores by regressing IRT-based θ scores on raw scores. With data from a large population and clinical samples, we established crosswalk formulas. Their validity was investigated by comparing calculated T scores with IRT-based T scores. IRT and formulas yielded very similar T scores, supporting the validity of the latter approach. Theoretical and practical advantages and disadvantages of both approaches to convert scores to common metrics and alternative approaches are discussed. Provided that scale characteristics allow for their computation, T scores will help to better understand measurement results, which makes it easier for patients and practitioners to use test results in joint decision-making about the course of treatment.

Full text

European Journal of Psychological Assessment
A Common Measurement Scale for Self-Report Instruments in Mental
Health Care: T Scores With a Normal Distribution
Edwin de Beurs, Suzan Oudejans, and Berend Terluin
Online First Publication, December 16, 2022. https://dx.doi.org/10.1027/1015-5759/a000740
CITATION
de Beurs, E., Oudejans, S., & Terluin, B. (2022, December 16). A Common Measurement Scale for Self-Report Instruments
in Mental Health Care: T Scores With a Normal Distribution. European Journal of Psychological Assessment. Advance online
publication. https://dx.doi.org/10.1027/1015-5759/a000740

Original Article
A Common Measurement Scale
for Self-Report Instruments in
Mental Health Care
TScores With a Normal Distribution
Edwin de Beurs
1,2
, Suzan Oudejans
3
, and Berend Terluin
4
1
Department of Clinical Psychology, Faculty of Social Sciences, Leiden University, The Netherlands
2
Arkin Mental Health Institute, Amsterdam, The Netherlands
3
Mark Bench, Amsterdam, The Netherlands
4
EMGO Institute, VU Medical Center, Amsterdam, The Netherlands
Abstract: The diversity of measures in clinical psychology hampers a straightforward interpretation of test results, complicates
communication with the patient, and constitutes a challenge to the implementation of measurement-based care. In educational research
and assessment, it is common practice to convert test scores to a common metric, such as Tscores. We recommend applying this also in
clinical psychology and propose and test a procedure to arrive at Tscores approximating a normal distribution that can be applied to individual
test scores. We established formulas to estimate normalized Tscores from raw scale scores by regressing IRT-based θscores on raw scores.
With data from a large population and clinical samples, we established crosswalk formulas. Their validity was investigated by comparing
calculated Tscores with IRT-based Tscores. IRT and formulas yielded very similar Tscores, supporting the validity of the latter approach.
Theoretical and practical advantages and disadvantages of both approaches to convert scores to common metrics and alternative approaches
are discussed. Provided that scale characteristics allow for their computation, Tscores will help to better understand measurement results,
which makes it easier for patients and practitioners to use test results in joint decision-making about the course of treatment.
Keywords: IRT, Tscores, percentile ranks, common metric, norms, clinical
The importance of measurement for clinical management
and quality improvement of Mental Health Care (MHC)
is widely acknowledged (Kilbourne et al., 2018;Lambert
&Harmon,2018). Inspired by the recovery movement
(Slade et al., 2008) and developments such as shared deci-
sion-making (Patel et al., 2008), feedback informed treat-
ment (Miller et al., 2015), and measurement-based care
(Harding et al., 2011; Kilbourne et al., 2018), patients’needs
and preferences are granted a more prominent role in
MHC. Increased patient involvement requires being well-
informed about the severity of one’s condition at the onset
of treatment and about the progress made in the journey
toward recovery. Therefore, a good understanding of mea-
surement results is needed when findings of Routine Out-
come Monitoring (ROM; de Beurs et al., 2011)areshared.
However, the huge diversity of measurement instruments
in clinical practice, each with its measurement scale, com-
plicates straightforward communication among profession-
als and between professionals and patients about their
measurement results. This might hamper further imple-
mentation of measurement-based care. Using common,
measure-independent metrics for the results of clinical tests
may solve this problem (de Beurs, Fried, et al., 2022).
Two metrics have been proposed and researched in
recent years: Tscores and percentile rank. Tscores, first
proposed by McCall (1922), are standardized scores
(Z-scores) multiplied by 10 and 50 added, resulting in a
metric with M=50 (SD =10). The Tscore denotes the
commonness of a test result by its distance from the mean
of a reference group in standard units. Tscores require the
assumption that test results are measured on an interval
scale. Zscores (and Tscores) based on data from a refer-
ence population may have a highly skewed frequency distri-
bution. It is advisable first to transform the raw scores to
have a normal frequency distribution before converting
them to Tscores, which results in normalized T scores.
When the normalized Tscore metric is calibrated on the
Ó2022 Hogrefe Publishing European Journal of Psychological Assessment (2022)
https://doi.org/10.1027/1015-5759/a000740
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

general population, most psychiatric patients will score
before treatment around 65–70 on measures of psy-
chopathology, and when treated successfully, their score
will decrease to 55–60 over time. Percentile rank scores
have been proposed as an alternative way to express how
common or exceptional a test result is (Crawford & Garth-
waite, 2009;Ley,1972). They quantify the rarity of a tested
person’s score in a percentage. However, percentile scores
are not on an interval scale but ordinal and are, especially at
the extremes, easily misunderstood (Bowman, 2002).
There is quite some literature on converting measure-
ment instruments to a common metric (Dorans et al.,
2007; Holland et al., 2006) and the subject is closely linked
to norming instruments (Mellenbergh, 2011). Most fre-
quently used are distribution-based approaches, such as
percentile conversion (Kolen & Brennan, 2014), and meth-
ods based on Item Response Theory (IRT; Embretson &
Reise, 2013). Following the latter approach, several
researchers have published reports on linking measures
for the same constructs and have proposed population-
based Tscores as a common metric for the severity of
depression (Choi et al., 2014; Fischer et al., 2011; Schalet
et al., 2015;Wahletal.,2014), anxiety (Schalet et al.,
2014), pain (Cook et al., 2015), physical functioning (Schalet
et al., 2015), fatigue (Friedrich et al., 2019), psychological
distress (Batterham et al., 2018), and quality of life mea-
sures (ten Klooster et al., 2013). Usually, general population
samples are used to easy interpretability of the resulting
metric (Wahl et al., 2014). If appropriately sampled, such
samples reflect the general population. In contrast, clinical
samples vary in composition and severity or complexity of
the disorder, and as such, they are less useful as a reference
group for general psychopathology measures. Various clin-
ical measurement instruments are administered to the
same group of respondents, and an IRT estimate, usually
the expected a posteriori (EAP) method (Lord & Wingersky,
1984) is used to estimate θin order to express scores in
the common metric. This endeavor is also known as the
PROsetta Stone project (Schalet et al., 2015).
A potential drawback of the IRT approach is that it
requires a comprehensive dataset and dedicated software
to calculate θ-scores. In clinical practice, this is not always
feasible: a clinician may only have a raw scale score from
an individual patient, and he/she does not have access to
the algorithm to obtain an IRT-based θ-score. To help
out, several authors provide crosswalk tables to translate
the raw test score into a Tscore (Batterham et al., 2018;
Choi et al., 2014; Schalet et al., 2014). However, reading
from crosswalk tables is cumbersome and prone to error.
The relation between raw scores and Tscores can also be
modeledandexpressedinafunction.Suchafunctionto
calculate Tscores can easily be used or implemented in
ROM software and provides an alternative method to
obtain scores on the common metric for individual patients.
In line with international developments, Tscores may be
basedonIRTmodelsandstemfromdatafromgeneral
population samples (de Beurs, Fried, et al., 2022). However,
for everyday clinical practice, we propose an approach in
which Tscores are calculated with a conversion function.
This will be feasible, even if only a test score from a single
individual is available.
Figure 1presents an overview of various approaches
obtaining Tscores. The first approach (on the left) entails
standardizing the sum score of items of a scale into Zscores
and converting these to Tscores with T=10 Z+50
(standard Tscores). The second approach is based on per-
centile rank scores, which are converted to normalized
Zscores and subsequently to normalized Tscores and take
the frequency distribution of scores into account (per-
centile-based T-scores). The third approach is advocated
in the present paper, with crosswalk formulas derived from
the regression of Tscores based on the factor scores result-
ing from an IRT model on sum scores (calculated Tscores).
The fourth approach is the IRT-based approach itself, prac-
ticed by –among others –the PROMIS group (θ-based
Tscores).
In this article we present crosswalk formulas for three
frequently used clinical measurement instruments: the
Brief Symptom Inventory (BSI; Derogatis, 1975), the Four-
Dimensional Symptom Questionnaire (4DSQ; Terluin
et al., 2006), and the Outcome Questionnaire (OQ-45;
Lambert et al., 2004). A necessary step is to investigate
the validity of calculated Tscores by comparing them with
θ-based Tscores. If there is a high agreement, the transfor-
mation of raw scale scores with the conversion function is a
valid approach for obtaining a proxy for θ-based Tscores.
For each measure, data were used from two samples: the
general population and patients. IRT-based Tscores were
founded on both samples, with the general population as
the reference population. The patient samples allowed us
to investigate whether the Tscores were normally dis-
tributed in clinical samples. Measures for ROM, where
patients are repeatedly assessed to determine change over
time, preferably have an interval scale of measurement
Figure 1. Overview of approaches to establish T-scores.
European Journal of Psychological Assessment (2022) Ó2022 Hogrefe Publishing
2 E. de Beurs et al., A Common Metric: Normalized TScores
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

with a normal distribution. Finally, percentile ranks are pro-
vided based on the population and clinical samples.
Methods
Datasets
BSI and 4DSQ data from the general population were col-
lected on separate occasions in a large sample of the Dutch
population, called the LISS panel (Long-term Internet Stud-
ies for the Social Sciences). The LISS panel is maintained by
CentERdata, a research institute located on the Tilburg
University campus, and includes about 5,300 household
respondents who were approached with the help of the
municipal population register (van der Laan, 2009). The
sample is representative of the Dutch population (Scherpen-
zeel, 2018; Scherpenzeel & Bethlehem, 2011). In 2007/
2008, one-third of all households were approached, of
which one person each completed the BSI (n=1,662). This
sample was stratified by age (four strata: 18–29,30–49,
50–64,65+ years), gender, and ethnic origin. In 2013,
normativedataonthe4DSQ were collected from the entire
LISS panel (n=5,273). The sample and the procedure for
collecting 4DSQ data were described by Terluin and
colleagues (2016).
For the OQ-45,datawereusedfromn=1,810 respon-
dents, which have been described by Timman and col-
leagues (2017): 1,000 respondents came from a panel of
the TNS-NIPO research agency and were stratified by gen-
der, age, socioeconomic status, and education level; 810
came from an earlier validation study (de Jong et al.,
2007), 448 came from a sample drawn from the telephone
directory, and 362 were invited via internal mail from 14
companies or non-commercial organizations (Timman
et al., 2017).
Patient data for the BSI came from a dataset of patients
referred for treatment of depression, anxiety disorders, or
somatoform disorders at RijnVeste, the outpatient clinic
of GGZ Rivierduinen in the city of Leiden. Data from n=
4,853 patients collected between 2002 and 2013 were used.
The procedure of data collection has been described by de
Beurs and colleagues (2011). For the 4DSQ, patient data
were used from 199 patients from primary care physicians.
All patients were on sick leave, reported elevated levels of
stress, and participated in a trial evaluating an intervention
for stress-related mental disorders (Bakker et al., 2007).
The patient data for the OQ-45 came from 12,436 patients
describedbyTimmanandcolleagues(2017). This com-
prised a mixed sample: patients in daycare (n=481)or
inpatient care (n=484) from various MHC institutes;
patients in outpatient care (basic and specialized MHC,
n=1,581 and n=9,433 respectively), and patients treated
by private practitioners (n=457). According to Dutch law,
anonymized questionnaire data collected to support treat-
ment may be used for scientific research and such use is
exempt from an informed consent procedure.
Measures
The Brief Symptom Inventory (BSI; Derogatis, 1975;Dutch
version: de Beurs & Zitman, 2006) consists of 53 items
describing symptoms. Respondents can indicate to what
extent they were bothered by each symptom on a Likert-
type scale from 0(= notatall)to4(= very much)inthepast
week. In this study, we limited ourselves to investigating
the three most important scales of the BSI: depression
(BSI-DEP), anxiety (BSI-ANX), and somatic complaints
(BSI-SOM). Scale scores are calculated as the mean score
of the comprising items and range from 0to 4. In addition,
the global score for the severity of psychopathology was
analyzed: the mean score on all 53 items (Global Severity
Index or BSI-GSI, range: 0–4).
The Four-Dimensional Symptom Questionnaire (4DSQ;
Terluin et al., 2006) consists of 50 items, each describing
one symptom. Respondents can indicate how often they
experienced the symptom in the past week on a scale from
0(= no)to4(= very often or constantly). The 4DSQ com-
prises four scales: general distress (4DSQ-DIS, 16 items,
range: 0–32), depression (4DSQ-DEP, 6items, range:
0–12), anxiety (4DSQ-ANX, 12 items, range 0–24), and
somatic complaints (4DSQ-SOM, 16 items, range 0–32).
All scores are sum scores (after recoding the two response
options for high frequency: 4=2and 3=2), as recom-
mended in the scoring instruction of this instrument
(Terluin et al., 2006).
The Outcome Questionnaire (OQ-45; Lambert et al.,
2004; Dutch version: de Beurs et al., 2005;deJongetal.,
2007) comprises 45 items describing symptoms or prob-
lems. The respondent is asked to indicate how often these
emerged during the past week on a scale from 0(= never)
to 4(= almost always). A total score can be calculated
(OQ-TOTAL, 45 items, range: 0–180)andfoursubscale
scores: Symptom Distress (OQ-SD, 25 items, range:
0–100), Interpersonal Relations (OQ-IR, 11 items, range:
0–4), Social Role, (OQ-SR, 9items, range: 0–36), and Anxi-
ety and Social Distress (OQ-ASD, 13 items, range: 0–52). All
scores are sum scores.
Statistical Analysis
Calculations According to Item Response Theory
The “Graded Response Model for polytomous items”and
itsExpectedAPosteriori(EAP)scorewasusedastheesti-
mator for the θ-score with the multidimensional IRT (mirt)
package (Chalmers, 2012) version in R. There are other
Ó2022 Hogrefe Publishing European Journal of Psychological Assessment (2022)
E. de Beurs et al., A Common Metric: Normalized TScores 3
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

estimates available for the latent variable scores in IRT,
such as Maximum Likelihood (ML) and Weighted Likeli-
hood Estimates (WLE). We performed a sensitivity analysis,
comparing EAP with these alternatives, and found suffi-
ciently similar results regarding the mean θ’s, with their
95% confidence intervals (CI95) mostly overlapping and
highly correlated (results are provided in Table C in the
supplementary materials; de Beurs, Oudejans, et al.,
2022). Item parameters were established in the combined
general population and clinical samples. Thus, θscores
were estimated with the multigroup mirt option (Smits,
2016). We fixed the item parameters to be equal across
groups. The latent trait (θ) was standardized to a scale with
a mean of 0and a standard deviation of 1for the general
population. The unidimensionality of scales, a requirement
for IRT, was investigated with confirmatory factor analysis
using the R package lavaan (version 06.5; Rosseel, 2012).
We used the DWLS estimator based on the polychoric
correlation matrix for ordinal items and inspected (scaled)
fit statistics and set as requirements for unidimensionality:
Table 1.Raw scores, θ-based, and calculated T-scores of the population sample and patients on BSI, 4DSQ, and OQ-45
Raw scores θ-based Tscores Calculated Tscores
M Mdn SD Skew. Kurt. M Mdn SD Skew. Kurt. M Mdn SD Skew. Kurt.
BSI
Population
GSI 0.38 0.28 0.34 2.00 5.97 49.81 49.95 9.17 0.16 0.07 50.37 50.38 9.26 0.24 0.06
DEP 0.39 0.17 0.48 2.20 6.75 49.94 49.35 8.48 0.65 0.05 51.09 48.05 8.74 0.76 0.32
ANX 0.34 0.17 0.43 2.02 5.23 49.97 48.50 8.17 0.66 0.34 52.04 50.02 7.94 0.58 0.41
SOM 0.33 0.14 0.42 2.30 7.50 49.98 48.03 7.96 0.75 0.19 51.67 49.17 8.22 0.77 0.33
Patients
GSI 1.21 1.09 0.73 0.67 0.02 66.71 66.62 11.36 0.02 0.25 66.57 66.36 11.49 0.02 0.26
DEP 1.57 1.50 1.03 0.37 0.80 67.94 67.95 12.10 0.01 0.41 67.54 68.33 12.42 0.11 0.41
ANX 1.35 1.17 0.96 0.63 0.41 66.14 66.18 9.94 0.11 0.41 65.46 65.77 10.55 0.11 0.24
SOM 0.95 0.71 0.83 1.06 0.67 62.17 61.83 11.06 0.32 0.23 61.60 60.98 11.41 0.28 0.24
4DSQ
Population
DIST 5.52 3 6.40 1.72 2.87 50.00 49.63 9.20 0.50 0.11 50.03 49.07 9.20 0.53 0.01
DEP 0.70 0 1.92 3.69 14.71 50.00 46.57 7.05 1.88 2.44 50.17 46.77 6.97 1.87 2.38
ANX 1.05 0 2.53 4.14 21.64 50.00 45.48 7.46 1.56 1.77 50.13 45.58 7.42 1.52 1.69
SOM 4.92 4 4.91 1.58 3.07 50.00 49.68 8.87 0.42 0.10 50.11 50.79 8.87 0.42 0.05
Patients
DIST 19.02 20 8.32 0.24 0.93 66.90 66.77 8.32 0.12 0.38 66.19 66.43 8.55 0.16 0.32
DEP 3.45 2 3.66 1.06 0.05 62.77 61.97 6.45 0.65 0.24 60.39 61.66 9.52 0.16 0.92
ANX 5.21 4 5.14 1.06 0.43 63.38 63.16 7.28 0.37 0.58 61.28 63.12 9.59 0.16 0.67
SOM 12.77 11 7.00 0.46 0.51 63.82 62.90 8.20 0.35 0.04 62.36 60.96 8.95 0.14 0.12
OQ-45
Population
OQ-TOT 40.83 39 17.80 0.82 1.15 49.62 49.49 9.03 0.26 0.75 50.43 50.25 9.41 0.32 0.42
SDIS 23.76 22 11.43 0.83 1.09 49.76 49.58 8.98 0.30 0.78 50.84 50.13 9.50 0.39 0.37
IR 8.96 8 4.97 0.81 0.93 49.83 49.69 8.68 0.31 0.02 51.78 50.69 8.69 0.38 0.03
SR 8.12 8 3.88 0.64 0.71 49.81 50.44 7.94 0.10 0.22 50.46 50.39 8.39 0.49 0.42
ASD 14.37 14 6.82 0.59 0.45 49.84 49.73 8.60 0.11 0.38 51.67 51.81 9.52 0.26 0.21
Patients
OQ-TOT 78.23 79 24.00 0.00 0.24 68.52 68.89 10.96 0.10 0.17 68.34 68.95 10.85 0.17 0.07
SDIS 48.24 49 15.51 0.06 0.28 69.63 69.88 11.35 0.07 0.14 69.45 70.09 11.33 0.13 0.14
IR 16.54 16.5 6.79 0.11 0.35 64.31 64.93 10.46 0.12 0.15 63.95 64.62 10.35 0.22 0.19
SR 13.35 13 5.42 0.20 0.27 61.58 62.13 11.77 0.05 0.27 61.42 61.05 11.12 0.04 0.40
ASD 25.62 26 8.86 0.02 0.29 66.81 66.91 11.37 0.01 0.17 66.43 67.00 11.40 0.03 0.09
Note. Brief Symptom Inventory (BSI): GSI = Global Severity Index; DEP = Depression; ANX = Anxiety; SOM = Somatic complaints; Four-Dimensional Symptom
Questionnaire (4DSQ): DIST = Distress; DEP = Depression; ANX = Anxiety; OM = Somatization; Outcome Questionnaire (OQ): TOT = OQ45 Total score; SDIS =
Symptomatic Distress; IR = Interpersonal Relationships; SR = Social Role; ASD = Anxiety and Social Distress; M= Mean; Mdn = Median; SD = Standard
deviation; Skew. = Skewness; Kurt. = Kurtosis.
European Journal of Psychological Assessment (2022) Ó2022 Hogrefe Publishing
4 E. de Beurs et al., A Common Metric: Normalized TScores
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

CFI > .95,TLI0.95,RMSEA<.06,andSRMR<.08.If
insufficient fit of a unidimensional model is found, IRT
based scores are potentially flawed, and alternatives (e.g.,
percentile conversion or regression-based norming) can
be utilized.
We used non-linear least squares modeling of R (nls) to
establish the best fitting function (which had the lowest
AIC value and/or the most parsimonious number of coeffi-
cients) for the relation between raw scores and θ-based
T-scores. Linear, polynomial, exponential, logarithmic,
power, division, rational, sigmoid, and hyperbolic equations
were evaluated. We cross-validated each equation by
randomly splitting each dataset in two and using the first
dataset to establish the best-fitting function and using the
second dataset as a validation sample (Camstra &
Boomsma, 1992). Applying the conversion formula to the
raw scale score results in a calculated Tscore. The distribu-
tions of the resulting scores (mean, median, standard devi-
ation, skewness, and kurtosis) were investigated for the
population and the patient samples and visually inspected
on normality with histograms/density plots and QQ-plots.
ICC estimates for absolute agreement and consistency of
θ-based and calculated Tscores and their CI95 were deter-
mined using R and based on a two-way mixed-effects
model. We established “bias”(mean difference between
both Tscores (van Stralen et al., 2012), as well as the “per-
centage error”(the width of the CI95 interval proportional
to the population mean; Van Hoeck et al., 2000). If the
CI95 interval was within 5Tscore points, we would con-
clude that both approaches yielded sufficiently similar
results since 5Tscore points are the proposed limit for sta-
tistically reliable change in score over time (de Beurs et al.,
2019). We also inspected the agreement between θ-based
Tscores and calculated Tscores with Bland-Altman plots
for the full range of severity (Bland & Altman, 1986).
We did this for the entire sample and for the population
and clinical samples separately. Finally, to establish the
effect of normalization, we also compared standard
(A)
Figure 2. Frequency distribution (histograms with density and normal curves) and QQ-plots of scores for raw scores above, θ-based Tscores, and
calculated Tscores of the BSI General Severity Index (BSI-GSI; A), 4DSQ-Distress (4DSQ-DIS; B), and OQ-Symptomatic Distress (OQ-SD; C) of the
general population (above) and patient samples (below).
Ó2022 Hogrefe Publishing European Journal of Psychological Assessment (2022)
E. de Beurs et al., A Common Metric: Normalized TScores 5
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

Tscores (based on the standard conversion formula “stan-
dard T=10 Z+50”)withθ-based Tscores and calcu-
lated Tscores.
Results
Unidimensionality of Scales
Most scales met criteria for unidimensionality, using CFI 
0.95,TLI0.95,RMSEA<0.06 to 0.08;SRMR.08
(Schreiber et al., 2006). Table A in the supplementary
materials provides CFA results for all scales (de Beurs,
Oudejans, et al., 2022). The CFI, TLI, and SRMR require-
ments were met by all scales of the BSI and the 4DSQ,
except for the BSI-GSI and the DIS-SOM. The OQ scales
did not meet CFI and TLI requirements. RMSEA was larger
than 0.06 for most scales but not substantially larger,
except for the BSI-ANX and –again –the OQ-SR (RMSEA
>0.12). As a consequence, the precision of the θ’s for the
OQ scales, in particular, may be compromised, as these
scales appear to lack sufficient unidimensionality (Cris
ßan
et al., 2017).
Distribution of Raw Scores and TScores
Table 1presents an overview of raw scores, θ-based T
scores, and calculated Tscores and characteristics of the
frequency distribution for scales of the BSI, 4DSQ, and
OQ-45.Figure2shows the main score on each instrument,
the frequency distribution of the raw score, θ-based Tscore,
and calculated Tscore in the general population sample
(upper half) and the clinical sample (lower half), and
QQ-plots. The Similarity of the frequency distribution, the
density curve, and the normal curve and accordance with
the dots in the QQ-plot and the straight diagonal line, indi-
cate how close the distributions approximate normality.
(Figure A1–A3in the supplementary materials presents plots
for all scales; de Beurs, Oudejans, et al., 2022). The average
BSI-GSI score in the population sample was M=0.38 (SD =
0.34). For the BSI-GSI, score skewness was 2.00; kurtosis
was 5.97, showing substantial deviation from the normality
(B)
Figure 2. Continued.
European Journal of Psychological Assessment (2022) Ó2022 Hogrefe Publishing
6 E. de Beurs et al., A Common Metric: Normalized TScores
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

of the scores with a tail to the right. Many respondents had
a low score, but this is to be expected when a symptom list
is completed by a population sample. The raw scores on
the 4DSQ scales in the population were also skewed. For
the depression and anxiety scale, values for skewness
and kurtosis were extreme, as 78.7%and67.6%ofthe
respondents had the lowest possible score. In contrast,
raw scores of the general population on the OQ-45 had
an almost normal distribution; only the total score and
the OQ-SD score showed marginal kurtosis in the popula-
tion sample (some surplus of scores below the average
score). Most Tscores based on θ’sandcalculatedTscores
had a normal distribution.
Conversion functions for the BSI, 4DSQ, and OQ-45
are shown in Table 2. For BSI scores rational functions
provided the best fit; indices of skewness and kurtosis
decreased considerably compared to the raw scores. Raw
scale scores in the patient sample had a normal distribution,
and this was preserved in the calculated Tscores.
For 4DSQ scales, also rational functions best fit the rela-
tion between raw scores and θ-based Tscores. Again, raw
scores were skewed and peaked, whereas θ-based and
calculated Tscores approximated the normal distribution
better, although the depression score and the anxiety score
of the population sample were still skewed and showed
kurtosis due to a large proportion of respondents with the
lowest possible score on these scales. Thus, transformation
to a normal distribution was successful for only two of the
four subscales of the 4DSQ. Patient scores had a normal
distribution. Finally, for the OQ-45, two rational functions,
a cubic, a quadratic, and a hyperbolic function, provided the
best fit.
In the supplementary materials, Figure A1–A3(de Beurs,
Oudejans, et al., 2022) presents histograms with density lines
and QQ-plots for all scales. These graphs reveal a sufficiently
normal distribution for most scales, except for the 4DSQ
depression and anxiety scales, but also reveal some surplus
of extreme high and extreme low scores for all scales.
Comparison of θ-Based and Calculated
TScores
We cross-validated the equations shown in Table 2by
applying a random split of each dataset into a calibration
(C)
Figure 2. Continued.
Ó2022 Hogrefe Publishing European Journal of Psychological Assessment (2022)
E. de Beurs et al., A Common Metric: Normalized TScores 7
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

sample and a cross-validation sample. Table 2provides the
Root Mean Squared Error (RMSE), the coefficient of deter-
mination (R
2
), and the Mean Absolute Error (MAE) for the
correspondence of predicted scores (calculated Tscores
with formulas based on the calibration sample) with
observed Tscores (θ-based Tscores in the cross-validation
sample). Overall, correspondence was high; the lowest
R
2
=.869 for the OQ-SR scale.
Furthermore, we calculated ICCs for absolute agreement
between θ-based and calculated Tscores and consistency
(similar ranking of subjects according to both scores; van
Stralen et al., 2012). Table 3presents the ICCs and
Table 2.Formulas to calculate T-scores and indicators of correspondence from cross-validation
Scale Formula y=... RMSE R
2
MAE
BSI-GSI 31.1 + (138.641x+ 22.4779x
2
)/(1 + 4.089x0.3392x
2
) 1.456 0.988 1.116
BSI-DEP 41.6 + (47.593x+ 0.7650x
2
)/(1 + 1.444x0.1909x
2
) 1.627 0.986 1.304
BSI-ANX 43.4 + (50.294x1.9425x
2
)/(1 + 1.564x0.2368x
2
) 2.658 0.950 2.189
BSI-SOM 42.9 + (56.622x+ 9.3246x
2
)/(1 + 2.233x0.1947x
2
) 1.725 0.978 1.396
4DSQ-DIST 38.0 + (6.460x0.0284x
2
)/(1 + 0.258x0.0050x
2
) 1.087 0.988 0.788
4DSQ-DEP 46.8 + (27.876x0.8495x
2
)/(1 + 1.411x0.0766x
2
) 1.497 0.961 0.854
4DSQ-ANX 45.6 + (15.735x+ 0.0349x
2
)/(1 + 0.718x0.0155x
2
) 1.875 0.946 1.222
4DSQ-SOM 37.4 + (5.746x+ 0.0336x
2
)/(1 + 0.203x0.0031x
2
) 1.208 0.984 0.845
OQ-TOT 20.9 + (1.157x+ 0.0017x
2
)/(1 + 0.018x0.0001x
2
) 2.434 0.963 1.895
OQ-SD 25.8 + (1.487x0.0051x
2
)/(1 + 0.014x0.0001x
2
) 2.287 0.970 1.796
OQ-IR 33.5 + 2.46x0.0447x
2
+ 0.00058x
3
3.370 0.914 2.649
OQ-SR 32.1 + 2.39x0.0121x
2
3.879 0.896 3.016
OQ-ASD 68.2 + 1.094 (x27.0) + sinh((x27.0)/8.533) 2.350 0.965 1.840
Note. Brief Symptom Inventory (BSI): GSI = Global Severity Index; DEP = Depression; ANX = Anxiety; SOM = Somatic Complaints; Four-Dimensional Symptom
Questionnaire (4DSQ): DIST = Distress; DEP = Depression; ANX = Anxiety; SOM = Somatization; Outcome Questionnaire (OQ): TOT = Total score; SD =
Symptomatic Distress; IR = Interpersonal Relationships; SR = Social Role; ASD = Anxiety and Social Distress; y= calculated T-score; x= raw scale score;
RMSE = Root Mean Squared Error; R
2
= coefficient of determination; MAE = Mean Absolute Error.
Table 3.Indicators of correspondence between θ-based and calculated T-scores
> 5 Difference
5 and 5
<5
Scale ICC-A CI95 ICC-C CI95 Bias Perc. Err. CI95+ CI95%%%
BSI-GSI .99 .99–.99 .99 .99–.99 0.02 12.3 3.87 3.83 2.37 97.60 0.03
BSI-DEP .99 .99–.99 .99 .99–.99 0.01 11.4 3.61 3.62 0.82 99.04 0.14
BSI-ANX .97 .97–.97 .97 .97–.97 0.02 17.8 5.56 5.51 3.45 93.54 3.01
BSI-SOM .99 .98–.99 .99 .98–.99 0.01 13.1 3.88 3.86 1.36 98.63 0.02
4DSQ-DIST .99 .99–.99 .99 .99–.99 0.02 11.3 2.88 2.91 0.00 99.98 0.02
4DSQ-DEP .98 .98–.98 .98 .98–.98 0.03 11.8 3.03 2.98 0.00 98.36 1.64
4DSQ-ANX .99 .99–.99 .99 .99–.99 0.00 9.9 2.52 2.52 0.41 98.56 1.03
4DSQ-SOM .99 .99–.99 .99 .99–.99 0.02 9.9 2.54 2.50 0.00 99.82 0.18
OQ-TOT .98 .98–.98 .98 .98–.98 0.02 14.7 4.79 4.83 1.77 95.44 2.79
OQ-SD .98 .98–.99 .98 .98–.99 0.02 13.5 4.52 4.49 1.32 96.89 1.79
OQ-IR .96 .95–.96 .96 .95–.96 0.01 21.3 6.61 6.60 6.89 86.44 6.67
OQ-SR .95 .95–.95 .95 .95–.95 0.03 25.1 7.47 7.52 10.14 81.33 8.53
OQ-ASD .98 .98–.98 .98 .98–.98 0.02 14.7 4.68 4.72 1.92 96.03 2.05
Note. Brief Symptom Inventory (BSI): GSI = Global Severity Index; DEP = Depression; ANX = Anxiety; SOM = Somatic complaints; Four-Dimensional Symptom
Questionnaire (4DSQ): DIST = Distress; DEP = Depression; ANX = Anxiety; OM = Somatization; Outcome Questionnaire (OQ): TOT = OQ45 Total score; SD =
Symptomatic Distress; IR = Interpersonal Relationships; SR = Social Role; ASD = Anxiety and Social Distress; ICC-A = Absolute agreement; ICC-C =
consistency; Bias = difference between both T-scores (positive bias values indicates that θ-based T-scores are higher than calculated T-scores); Perc. Err. =
Percentage error, the width of the limits of agreement interval divided by the mean T-score of the population [(CI95+ CI95+)/M]; “Difference 5 and 5 %”=
The percentage of subjects for whom both T-scores differ less than 5 points; “Difference < 5 and > 5 %”= The percentage of subjects for whom the
difference between both methods is greater than 5 points.
European Journal of Psychological Assessment (2022) Ó2022 Hogrefe Publishing
8 E. de Beurs et al., A Common Metric: Normalized TScores
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

additional information on the association between both
scores. All ICCs were high, suggesting excellent agreement
and consistency. Bias and percentage error were also low,
with the exception of a higher percentage error for BSI-
ANX, OQ-IR, and OQ-SR, and for these scales, the CI95
extended beyond 5Tscore points. Figure 3presents
Bland-Altman plots for selected scales. Figures B1–B3in
the supplementary materials present plots for all scales
(de Beurs, Oudejans, et al., 2022).
For the BSI, θ-based Tcorresponded well to calculated
Tscores (mean difference M=0.01–0.02,thesolidgray
line in the BA plot); only for the BSI-ANX, less than 95%
Figure 3. A Bland-Altman plot displays the difference between two methods for the full range of scores; the x-axis displays the range based on
the average of both methods; the y-axis displays for each subject the difference in score between both methods. BSI-GSI = Global Severity Index;
DSQ-DIST = 4DSQ Distress; OQ-SD = Symptomatic Distress.
Ó2022 Hogrefe Publishing European Journal of Psychological Assessment (2022)
E. de Beurs et al., A Common Metric: Normalized TScores 9
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

of the cases fell within the 5to 5interval for acceptable
difference. For the 4DSQ θ-based Tscores and calculated
Tscores corresponded well (mean difference M=0.02),
99% of the cases fell within the 5to 5interval. For the
OQ-SD also, excellent correspondence was found (mean
difference M=0.02); however, on average, 91.2%ofthe
Table 4.Indicators of correspondence of standardized Tscores with θ-based and calculated Tscores for the main scale of each self-report
measure
> 5 Difference
5 and 5
<5
Scale Pair ICC-A CI95 ICC-C CI95 Bias Perc. Err. CI95+ CI95%%%
BSI-GSI ST-TT .93 .93–.93 .93 .93–.93 0.29 35.6 11.42 10.83 18.89 67.92 13.19
ST-CT .93 .93–.94 .93 .93–.94 0.26 34.3 11.01 10.49 18.90 75.59 5.51
4DSQ-DIST ST-TT .93 .93–.94 .94 .93–.94 0.78 29.7 8.40 6.85 10.22 89.16 0.62
ST-CT .94 .93–.94 .94 .94–.94 0.79 28.5 8.10 6.52 9.72 90.28 0.00
OQ-SD ST-TT .97 .96–.98 .98 .97–.98 1.00 18.3 7.12 5.12 11.27 87.13 1.60
ST-CT .99 .98–.99 .99 .99–.99 0.99 12.5 5.16 3.19 1.00 99.00 0.00
Note. BSI-GSI = Brief Symptom Inventory –Global Severity Index; 4DSQ-DIST = Four-Dimensional Symptom Questionnaire –Distress; OQ-SD = Outcome
Questionnaire –SD = Symptomatic Distress; ICC-A = Absolute agreement; ICC-C = Consistency; Bias = Difference between both T-scores (positive bias
values indicates that θ-based T-scores are higher than calculated T-scores); Perc. Err. = Percentage error, the width of the limits of agreement interval
divided by the mean T-score of the population [(CI95+ CI95+)/M]; “Difference 5 and 5 %”= The percentage of subjects for whom both T-scores differ less
than 5 points; “Difference < 5% and > 5 %”= The percentage of subjects for whom the difference between both methods is greater than 5 points; ST =
Standardized T-score; CT = Calculated T-score; TT = θ-based T-score.
Table 5.Crosswalk table for a selection of raw scores to calculated T-scores and percentile scores for the BSI global severity index, depression,
anxiety, and somatic complaints scale
Global severity index Depression Anxiety Somatic complaints
RS T-score PRn PRcl RS T-score PRn PRcl RS T-score PRn PRcl RS T-score PRn PRcl
0.00 31.1 13.2 2.1 0.00 41.6 16.1 2.6 0.00 43.4 17.1 2.9 0.00 42.9 45.9 27.4
0.17 45.5 52.9 8.3 0.17 48.2 41.5 7.5 0.17 50.1 44.0 8.9 0.17 50.1 91.8 54.8
0.33 52.0 79.3 12.5 0.33 52.5 58.4 12.2 0.33 54.4 62.0 15.3 0.33 54.4 91.8 54.8
0.50 56.4 79.3 12.5 0.50 55.9 71.5 17.7 0.50 57.7 75.5 22.0 0.50 57.7 91.8 54.8
0.67 59.8 79.3 12.5 0.67 58.7 80.6 23.7 0.67 60.3 83.4 28.8 0.67 60.4 91.8 54.8
0.83 62.5 83.3 21.7 0.83 61.0 86.7 29.4 0.83 62.3 88.2 36.1 0.83 62.5 91.8 54.9
1.00 65.0 90.2 40.2 1.00 63.1 90.6 35.1 1.00 64.2 91.7 43.4 1.00 64.6 95.6 69.3
1.17 67.4 96.0 59.8 1.17 65.0 92.9 40.9 1.17 65.8 94.1 50.1 1.17 66.5 99.3 83.6
1.33 69.5 98.9 70.2 1.33 66.6 94.5 46.4 1.33 67.2 95.8 56.2 1.33 68.2 99.3 83.7
1.50 71.7 98.9 70.2 1.50 68.3 96.1 51.6 1.50 68.6 97.2 61.6 1.50 69.9 99.3 83.9
1.67 73.9 98.9 70.2 1.67 70.0 97.2 56.6 1.67 70.0 98.1 66.6 1.67 71.7 99.3 84.0
1.83 75.9 99.4 75.5 1.83 71.5 97.9 61.7 1.83 71.2 98.6 71.2 1.83 73.3 99.3 84.0
2.00 78.1 100.0 84.9 2.00 73.1 98.5 66.6 2.00 72.6 99.1 75.2 2.00 75.0 99.7 89.7
2.17 80.3 100.0 92.1 2.17 74.7 98.9 71.0 2.17 73.9 99.4 78.9 2.17 76.7 100.0 95.4
2.33 82.4 100.0 95.1 2.33 76.2 99.1 75.1 2.33 75.1 99.5 82.4 2.33 78.3 100.0 95.4
2.50 84.6 100.0 95.1 2.50 77.8 99.4 78.9 2.50 76.5 99.7 85.5 2.50 80.1 100.0 95.4
2.67 86.9 100.0 95.1 2.67 79.5 99.5 82.5 2.67 77.9 99.8 88.3 2.67 81.9 100.0 95.4
2.83 89.2 100.0 95.5 2.83 81.2 99.6 86.0 2.83 79.3 99.9 90.7 2.83 83.6 100.0 95.5
3.00 91.6 100.0 97.0 3.00 83.0 99.8 89.1 3.00 80.8 100.0 92.9 3.00 85.5 100.0 97.4
3.17 94.2 100.0 98.9 3.17 84.9 99.9 91.6 3.17 82.5 100.0 94.7 3.17 87.5 100.0 99.3
3.33 96.6 100.0 99.6 3.33 86.8 99.9 94.1 3.33 84.1 100.0 96.2 3.33 89.4 100.0 99.3
3.50 99.3 100.0 99.6 3.50 89.0 99.9 96.1 3.50 86.0 100.0 97.6 3.50 91.4 100.0 99.3
3.67 102.1 100.0 99.6 3.67 91.2 100.0 97.6 3.67 88.0 100.0 98.6 3.67 93.6 100.0 99.3
3.83 104.8 100.0 99.6 3.83 93.5 100.0 98.6 3.83 90.1 100.0 99.3 3.83 95.7 100.0 99.3
4.00 107.8 100.0 99.8 4.00 96.1 100.0 99.5 4.00 92.4 100.0 99.8 4.00 98.0 100.0 99.6
Note. Brief Symptom Inventory (BSI): GSI = Global Severity Index; DEP = Depression; ANX = Anxiety; SOM = Somatic complaints; RS = Raw Score; T=
Calculated T-score; PRn = Percentile rank in the normal population; PRcl = Percentile rank in the clinical population.
European Journal of Psychological Assessment (2022) Ó2022 Hogrefe Publishing
10 E. de Beurs et al., A Common Metric: Normalized TScores
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

cases fell within the 5to 5interval with less correspon-
dence for the OQ-IR and OQ-SR scales. Generally, in
the low scoring range (< 40) and in the high score range
(> 70), calculated Tscores were somewhat higher; in the
mid-range θ-based, Tscores were higher. We also estab-
lished ICC’s denoting correspondence between θ-based
and calculated Tscores for the population and the clinical
sample separately. Correspondence was somewhat lower
in the clinical sample, especially for the 4DSQ-DEP,
4DSQ-ANX, OQ-IR, and OQ-SR, but was still very high
(see Table B in the supplementary materials; de Beurs,
Oudejans, et al., 2022).
We also compared the θ-based and the calculated
Tscores for the BSI-GSI, 4DSQ-DIS, and OQ-SD with
standard Tscores (based on the simpler linear equation
T=10 Z+50). ICCs ranged from ICC = .81 for the
BSI-GSI to ICC = .99 for the OQ-SD (see Table 4). Corre-
spondence between standard Tscores and calculated
Tscores was still substantial, especially for the OQ-SD.
However, for the BSI-GSI, there was a large subgroup with
higher standard Tscores than θ-based or calculated
Tscores (for both comparisons Δ<5;18.9%), which is
understandable, as negative skewness (a low mean score
relative to the maximum scale score) results in more
respondents with extremely high standard Tscores. After
all, the non-linear conversion formula yielding calculated
Tscores corrects for precisely this undesirable effect.
Crosswalk From Raw Scores to TScores
and Percentiles
Table 5,6,and7present crosswalk tables for the conver-
sion of a selection of raw scores to calculated Tscores
and percentile ranks for the general population and the
clinical population. Per measurement instrument, the first
column gives raw scores (RS) and the second Tscores
are calculated according to the functions in Table 2for all
respondents. The conversion functions stretch the scales
at the extremes: a change in raw score of one scale point
in the low or high score area is larger than a change of
one scale point in the mid-range score area, and the nor-
malized Tscore reflects this appropriately. Figure 4depicts
the relationship between raw scores on the instruments and
Tscores.
Discussion
We analyzed community data of frequently used generic
outcome measures in the Netherlands to link raw scores
to two common metrics: Tscores and percentile ranks. In
line with previous research (Cook et al., 2015;Fischer&
Rose, 2016; Friedrich et al., 2019; Schalet et al., 2015;Wahl
et al., 2014),weappliedmethodsbasedonIRT,which
Table 6.Cross walk table for a selection of raw scores to calculated T-scores and percentile scores for the 4DSQ scales for distress, depression,
anxiety, and somatization
4DSQ-DIST 4DSQ-DEP 4DSQ-ANX 4DSQ-SOM
RS TPRn PRcl RS TPRn PRcl RS TPRn PRcl RS TPRn PRcl
0 38.0 10.4 0.2 0 46.8 39.5 13.3 0 45.6 42.6 16.2 0 37.4 14.6 0.3
2 46.6 37.7 1.1 1 58.3 82.8 33.8 2 58.9 89.4 41.6 2 45.8 39.5 2.5
4 51.0 54.9 4.0 2 61.7 88.7 46.7 4 63.1 94.9 55.6 4 50.8 57.8 9.2
6 54.0 67.2 8.1 3 63.5 91.9 57.5 6 65.7 96.9 66.2 6 54.4 71.5 18.7
8 56.2 75.5 11.8 4 64.8 93.9 66.5 8 67.9 98.0 75.4 8 57.3 81.2 29.9
10 58.1 81.7 17.7 5 66.0 95.4 72.5 10 69.9 98.7 82.1 10 59.8 87.9 42.7
12 59.8 86.0 22.8 6 67.1 96.6 77.8 12 71.9 99.1 88.0 12 62.1 91.9 51.7
14 61.4 89.4 29.7 7 68.3 97.4 83.1 14 74.0 99.4 92.2 14 64.3 94.5 58.9
16 63.0 92.0 36.5 8 69.6 97.8 86.1 16 76.2 99.5 94.7 16 66.5 96.6 68.2
18 64.7 93.8 42.4 9 71.1 98.3 87.7 18 78.7 99.7 96.6 18 68.7 97.8 76.5
20 66.4 95.2 50.0 10 72.8 98.7 89.8 20 81.6 99.8 98.3 20 70.9 98.6 83.0
22 68.3 96.3 59.6 11 74.9 99.2 92.4 22 84.8 99.9 99.4 22 73.3 99.2 88.5
24 70.3 97.3 68.3 12 77.5 99.7 96.7 24 75.8 99.5 93.6
26 72.6 98.2 76.3 26 78.4 99.7 96.1
28 75.1 98.8 83.6 28 81.2 99.8 97.8
30 78.0 99.5 89.0 30 84.3 99.9 99.2
32 81.3 99.9 96.8 32 87.6 100.0 99.7
Note. Four-Dimensional Symptom Questionnaire (4DSQ): DIST = Distress; DEP = Depression; ANX = Anxiety; OM = Somatization; RS = Raw Score; T=
Calculated T-score; PRn = Percentile rank in the normal population; PRcl = Percentile rank in the clinical population.
Ó2022 Hogrefe Publishing European Journal of Psychological Assessment (2022)
E. de Beurs et al., A Common Metric: Normalized TScores 11
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

resulted in θ-based Tscores with a normal frequency distri-
bution. We also determined functions to convert sum
scores into Tscores and showed that for most scales, calcu-
lated Tscores approximated θ-based Tscores very well, as
the scores were strongly related (all ICC > .95,seeTable3).
Scores were similar across the width of the entire scale and
yielded similar mean values for the groups. Correspon-
dence between calculated and θ-based Tscores supports
the validity of our approach to calculate Tscores with a
function based on curve fitting. However, at the extreme
end of the scales, the two approaches diverged somewhat.
Thus, caution with extreme scores is in order, especially
with T<40 and T>80.Furthermore,thefindingsof
two scales of the 4DSQ revealed that if raw scale scores
are too skewed or too leptokurtic, to begin with (due to
an excess of respondents with the lowest possible score),
conversion to θ-based or calculated Tscores will not yield
scores with a normal frequency distribution.
Compared to standard Tscores (T=10 Z+50), the
correspondence of the more complex conversion formulas
(correcting for a non-normal frequency distribution of raw
scores) with θ-based Tscores was better. For instance,
the ICC between standard Tscores and θ-based Tscores
for the BSI-GSI was ICC = .93 (see Table 4), whereas calcu-
lated Tscores showed almost perfect correspondence with
θ-based Tscores (ICC = .99; see Table 3). Better correspon-
dence was especially obtained in the higher score range.
For each scale, we cross-validated the formulas on subsam-
ples (splitting the samples randomly in half, and we also
compared the population and clinical samples). The results
revealed a similarity and high correlation between pre-
dicted scores from the “learning sample”with obtained
scores in the “test sample”. However, thus a substantial
number of statistical tests were done per scale in each data-
set, and the applicability of these formulas still needs fur-
ther validation with data from other samples.
Table 7.Crosswalk table for a selection of raw scores to calculated T-scores and percentile scores for the OQ total score, symptomatic distress,
interpersonal relations, social role functioning, and anxiety and social distress
OQ-TOT OQ-SD OQ-IR OQ-SR OQ-ASD
RS TPRn PRcl RS TPRn PRcl RS TPRn PRcl RS TPRn PRcl RS TPRn PRcl
0 20.9 0.0 0.0 0 25.8 0.4 0.0 0 33.5 1.0 0.2 0 32.1 1.0 0.2 0 26.9 0.3 0.0
10 30.9 2.5 0.0 5 32.6 3.2 0.2 2 38.3 5.7 1.1 2 36.8 5.4 1.0 2 31.5 1.4 0.2
20 38.7 11.0 0.8 10 38.5 11.7 0.8 4 42.7 15.8 3.1 4 41.4 15.3 3.5 4 35.7 4.3 0.6
30 45.2 30.7 2.5 15 43.7 26.4 1.9 6 46.8 29.7 6.6 6 46.0 31.3 9.7 6 39.4 10.7 1.3
40 50.8 54.6 6.0 20 48.4 43.8 3.8 8 50.7 46.0 11.6 8 50.4 52.4 18.7 8 42.9 19.7 2.4
50 55.8 73.9 12.7 25 52.6 60.0 7.0 10 54.3 61.7 18.6 10 54.7 72.3 29.7 10 46.0 29.8 4.1
60 60.6 86.2 22.5 30 56.6 72.7 12.0 12 57.7 75.2 27.4 12 59.0 85.6 42.6 12 49.0 41.0 6.6
70 65.0 93.9 35.5 35 60.3 83.1 19.3 14 60.9 85.7 37.2 14 63.1 92.4 56.3 14 51.8 51.7 10.0
80 69.4 98.2 50.2 40 63.9 90.2 29.4 16 63.9 91.8 48.0 16 67.2 95.9 69.4 16 54.5 62.3 14.5
90 73.7 98.5 67.1 45 67.4 93.7 40.8 18 66.8 95.4 59.2 18 71.1 98.1 80.5 18 57.1 71.6 20.4
100 77.9 99.1 82.8 50 70.8 96.3 53.8 20 69.6 97.6 69.8 20 75.0 99.2 88.9 20 59.6 79.4 27.3
110 82.3 99.7 92.1 55 74.2 98.2 66.7 22 72.3 98.7 79.5 22 78.7 99.8 94.4 22 62.1 86.2 35.0
120 86.7 100.0 96.7 60 77.6 98.8 77.5 24 74.9 99.3 86.9 24 82.4 100.0 97.4 24 64.6 90.6 43.3
130 91.2 100.0 99.0 65 81.2 99.1 85.5 26 77.5 99.7 91.5 26 85.9 100.0 98.9 26 67.0 93.8 51.9
140 95.9 100.0 99.9 70 84.9 99.6 90.7 28 80.1 99.9 95.0 28 89.4 100.0 99.7 28 69.4 96.5 60.6
150 100.8 100.0 100.0 75 88.8 99.9 95.1 30 82.8 100.0 97.4 30 92.8 100.0 99.9 30 71.9 98.0 68.8
160 106.0 100.0 100.0 80 93.0 100.0 98.2 32 85.5 100.0 98.8 32 96.0 100.0 100.0 32 74.3 98.7 76.4
170 111.4 100.0 100.0 85 97.6 100.0 99.4 34 88.3 100.0 99.5 34 99.2 100.0 100.0 34 76.8 99.1 83.0
180 117.2 100.0 100.0 90 102.6 100.0 99.9 36 91.2 100.0 99.9 36 102.3 100.0 100.0 36 79.3 99.4 88.1
95 108.3 100.0 100.0 38 94.3 100.0 100.0 38 81.9 99.6 92.0
100 114.7 100.0 100.0 40 97.5 100.0 100.0 40 84.6 99.7 94.7
42 100.9 100.0 100.0 42 87.4 99.8 96.7
44 104.5 100.0 100.0 44 90.4 99.8 98.1
46 93.6 99.9 99.0
48 97.0 100.0 99.5
50 100.8 100.0 99.8
52 104.9 100.0 100.0
Note. Outcome Questionnaire (OQ): TOT = OQ45 Total Score; SD = Symptomatic Distress; IR = Interpersonal Relationships; SR = Social Role; ASD = Anxiety
and Social Distress; RS = Raw Score; T= Calculated T-score; PRn = Percentile rank in the normal population; PRcl = Percentile rank in the clinical
population.
European Journal of Psychological Assessment (2022) Ó2022 Hogrefe Publishing
12 E. de Beurs et al., A Common Metric: Normalized TScores
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

The results show that some scales evoked the lowest pos-
sible score from many respondents (especially the 4DSQ;
see Figure 2). This zero inflation in the data is quite com-
mon when measures of psychopathology are administered
in the general population. With zero-inflated data, the
Graded Response Model may yield biased results of IRT
analyses, and alternative models to deal with zero inflation
have been proposed (Wall et al., 2015), such as Zero
Inflated Mixture GRM (ZIM-GRM). In a simulation study
with zero-inflated scores, GRM showed substantial bias
(Smits et al., 2020). In future studies, the effect of zero
inflation on factor score estimates should be investigated
to ascertain the added value of these models.
It should be noted that there are viable alternatives to
arrive at normative values and subsequently calculate
Tscores and percentile rank scores instead of the IRT-
based methods or the approach advocated in the present
paper. When scales are not unidimensional and/or the
IRT model does not fit, alternatives can be used, for
example, frequency-based percentile rank scores. Espe-
cially, regression-based norming (Mellenbergh, 2011)isan
interesting option, for example, with the GAMLSS model
Figure 4. Linking raw scores to the Tscore metric for subscales of the BSI, 4DSQ, and OQ (GSI = Global Severity Index; DEP = Depression; ANX =
Anxiety; SOM = Somatic complaints; 4DIST = Distress; 4DEP = Depression; 4ANX = Anxiety; 4SOM = Somatization; TOT = OQ-45 Total score; SD =
Symptomatic Distress; IR = Interpersonal Relationships; SR = Social Role; ASD = Anxiety and Social Distress).
Ó2022 Hogrefe Publishing European Journal of Psychological Assessment (2022)
E. de Beurs et al., A Common Metric: Normalized TScores 13
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

(Stasinopoulos et al., 2018), in which the shape of the fre-
quency distribution of raw scores, as well as relevant
“norm-predictors”, such as gender, age, and educational
level can be taken into account. A useful introduction to
the continuous norming approach, which corrects for all
levels of these demographic variables, is offered by Tim-
merman and colleagues (2021). However, for the present
purposes, we build upon the previous work of the PROsetta
stone initiative and the PROMIS group.
The strengths of the study are the use of large datasets
with representative samples from the general population
and patients, warranting trust in the findings. The data from
the Dutch general population were collected by research
institutes with a good reputation, and the representative-
ness of these population samples has been documented
by Scherpenzeel (2018) and Timman and colleagues
(2017). A relatively simple and straightforward approach
is outlined, which leads to calculated Tscores that approx-
imate θ-based Tscores well. A potential limitation of the
proposed method is that it relies heavily on data from
the general population, as this is the basis of the item
parameters and θ’susedtoobtainTscores. The clinical
measurement instruments were not developed for the
population at large but rather for patients suffering from psy-
chological complaints or symptoms of psychiatric disorders.
Cronbach (1984) noted that, ideally, instruments should be
validated with data from the population for which the instru-
ment was intended. Indeed, the frequency distribution of
responses of non-clinical respondents deviated much more
from normality than was the case with data obtained in
the clinical samples, as the present findings show.
The present results were based on normative data from
the Netherlands. Application of the conversion formulas
listed in Table 2or the crosswalk Tables 5–7is limited to
this context, as general population respondents from other
countries may score differently on these self-report mea-
sures. A further limitation may be the composition of the
clinical sample used to evaluate the frequency distribution
of the conversion formula in clinical data. All these patients
suffered from mild to moderate common mental disorders,
and patients with severe mental illness were not included.
Future research should investigate other clinical samples.
Conclusion
The high correlations found in this study between θ-based
and calculated Tscores for assessment with the 4DSQ, the
BSI, and the OQ-45, suggest that the proposed approach of
using conversion functions provides a good approximation
toward a common normalized metric for MHC. The use
of such a common metric will make the interpretation of
test results easier for therapists and patients (de Beurs,
Fried, et al., 2022) and will allow for better involvement
of the patient in shared decision-making regarding the
treatment (Patel et al., 2008), and will stimulate the future
uptake of measurement-based mental health care (Kil-
bourne et al., 2018).
References
Bakker, I. M., Terluin, B., Van Marwijk, H. W., van der Windt,
D. A. M., Rijmen, F., van Mechelen, W., & Stalman, W. A. (2007).
A cluster-randomised trial evaluating an intervention for
patients with stress-related mental disorders and sick leave
in primary care. PLoS Clinical Trials, 2(6), Article e26. https://
doi.org/10.1371/journal.pctr.0020026
Batterham, P. J., Sunderland, M., Slade, T., Calear, A. L., &
Carragher, N. (2018). Assessing distress in the community:
Psychometric properties and crosswalk comparison of eight
measures of psychological distress. Psychological Medicine,
48(8), 1316–1324. https://doi.org/10.1017/S0033291717002835
Bland, J. M., & Altman, D. G. (1986). Statistical methods for
assessing agreement between two methods of clinical
measurement. Lancet, 84767, 307–310. https://doi.org/
10.1016/S140-6736(86)90837-8
Bowman, M. L. (2002). The perfidy of percentiles. Archives of
Clinical Neuropsychology, 17(3), 295–303. https://doi.org/
10.1016/S0887-6177(01)00116-0
Camstra, A., & Boomsma, A. (1992). Cross-validation in regression
and covariance structure analysis: An overview. Sociological
Methods & Research, 21(1), 89–115. https://doi.org/10.1177/
0049124192021001004
Chalmers, R. P. (2012). mirt: A multidimensional item response
theory package for the R environment. Journal of Statistical
Software, 48(6), 1–29. https://doi.org/10.18637/jss.v048.i06
Choi, S. W., Schalet, B., Cook, K. F., & Cella, D. (2014). Establishing
a common metric for depressive symptoms: Linking the BDI-II,
CES-D, and PHQ-9 to PROMIS Depression. Psychological Assess-
ment, 26(2), 513–527. https://doi.org/10.1037/a0035768
Cook, K. F., Schalet, B. D., Kallen, M. A., Rutsohn, J. P., & Cella, D.
(2015). Establishing a common metric for self-reported pain:
Linking BPI Pain Interference and SF-36 Bodily Pain Subscale
scores to the PROMIS Pain Interference metric. Quality of Life
Research, 24(10), 2305–2318. https://doi.org/10.1007/s11136-
014-0790-9
Crawford, J. R., & Garthwaite, P. H. (2009). Percentiles please: The
case for expressing neuropsychological test scores and
accompanying confidence limits as percentile ranks. The
Clinical Neuropsychologist, 23(2), 193–204. https://doi.org/
10.1080/13854040801968450
Cris
ßan, D. R., Tendeiro, J. N., & Meijer, R. R. (2017). Investigating
the practical consequences of model misfit in unidimensional
IRT models. Applied Psychological Measurement, 41(6), 439–
455. https://doi.org/10.1177/0146621617695522
Cronbach, L. J. (1984). Essentials of psychological testing (4th ed.).
Harper & Row.
de Beurs, E., Carlier, I. V., & van Hemert, A. M. (2019). Approaches
to denote treatment outcome: Clinical significance and clinical
global impression compared. International Journal of Methods
in Psychiatric Research, 28(4), Article e1797. https://doi.org/
10.1002/mpr.1797
de Beurs, E., den Hollander-Gijsman, M., Buwalda, V., Trijsburg,
W., & Zitman, F. G. (2005). De Outcome Questionnaire (OQ-45):
Een meetinstrument voor meer dan alleen psychische klachten
[The Outcome Questionnaire (OQ-45): A measure for psychiatric
symptoms and more]. De Psycholoog, 40(1), 53–63.
European Journal of Psychological Assessment (2022) Ó2022 Hogrefe Publishing
14 E. de Beurs et al., A Common Metric: Normalized TScores
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

de Beurs, E., den Hollander-Gijsman, M. E., van Rood, Y. R., van
der Wee, N. J., Giltay, E. J., van Noorden, M. S., van der Lem, R.,
van Fenema, E., & Zitman, F. G. (2011). Routine outcome
monitoring in the Netherlands: Practical experiences with a
web-based strategy for the assessment of treatment outcome
in clinical practice. Clinical Psychology & Psychotherapy, 18(1),
1–12. https://doi.org/10.1002/cpp.696
de Beurs, E., Fried, E. I., & Boehnke, J. (2022). Common measures
or common metrics? A plea to harmonize measurement results.
Clinical Psychology and Psychotherapy, 29(5), 1755–1767.
https://doi.org/10.1002/cpp.2742
de Beurs, E., Oudejans, S., & Terluin, B. (2022). Acommon
measurement scale for self-report instruments in mental health
care: T scores with a normal distribution (supplementary
materials). https://www.psycharchives.org/en/item/86e598e9–
4828-4127–86ae-5f0d18e9586a
de Beurs, E., & Zitman, F. G. (2006). De Brief Symptom Inventory
(BSI): De betrouwbaarheid en validiteit van een handzaam
alternatief voor de SCL-90 [The Brief Symptom Inventory:
Reliability and validity of a handy alternative for the SCL-90].
Maandblad Geestelijke Volksgezondheid, 61, 120–141.
de Jong, K., Nugter, M. A., Polak, M. G., Wagenborg, J. E. A.,
Spinhoven, P., & Heiser, W. J. (2007). The Outcome Question-
naire (OQ-45) in a Dutch population: A cross-cultural validation.
Clinical Psychology & Psychotherapy, 14(4), 288–301. https://
doi.org/10.1002/cpp.529
Derogatis, L. R. (1975). The Brief Symptom Inventory. Clinical
Psychometric Research.
Dorans, N. J., Pommerich, M., & Holland, P. W. (Eds.). (2007).
Linking and aligning scores and scales. Springer.
Embretson, S. E., & Reise, S. P. (2013). Item response theory for
psychologists. Erlbaum.
Fischer, H. F., & Rose, M. (2016). www.common-metrics.org: A
web application to estimate scores from different patient-
reported outcome measures on a common scale. BMC Medical
Research Methodology, 16(1), Article 142. https://doi.org/
10.1186/s12874-016-0241-0
Fischer, H. F., Tritt, K., Klapp, B. F., & Fliege, H. (2011). How to
compare scores from different depression scales: Equating the
Patient Health Questionnaire (PHQ) and the ICD-10-Symptom
Rating (ISR) using item response theory. International Journal
of Methods in Psychiatric Research, 20(4), 203–214. https://doi.
org/10.1002/mpr.350
Friedrich, M., Hinz, A., Kuhnt, S., Schulte, T., Rose, M., & Fischer,
F. (2019). Measuring fatigue in cancer patients: A common
metric for six fatigue instruments. Quality of Life Research,
28(6), 1615–1626. https://doi.org/10.1007/s11136-019-02147-3
Harding,K. J.,Rush,A.J.,Arbuckle,M.,Trivedi,M. H.,&Pincus,H. A.
(2011). Measurement-based care in psychiatric practice: A policy
framework for implementation. Journal of Clinical Psychiatry,
72(8), 1136–1143. https://doi.org/10.4088/JCP.10r06282whi
Holland, P. W., Dorans, N. J., & Petersen, N. S. (2006). Equating
test scores. In C. R. Rao & S. Sinharay (Eds.), Handbook of
statistics (Vol. 26, pp. 169–203). https://doi.org/10.1016/
S0169-7161(06)26006-1
Kilbourne,A.M.,Beck,K.,Spaeth-Rublee,B.,Ramanuj,P.,O’Brien,
R.W.,Tomoyasu,N.,&Pincus,H.A.(2018).Measuringand
improving the quality of mental health care: A global perspective.
World Psychiatry, 17(1), 30–38. https://doi.org/10.1002/wps.20482
Kolen, M. J., & Brennan, R. L. (2014). Test equating, scaling, and
linking: Methods and practices (3rd ed.). Springer Science &
Business Media.
Lambert, M. J., Gregersen, A. T., & Burlingame, G. M. (2004). The
Outcome Questionnaire –45. In M. E. Maruish (Ed.), The use of
psychological testing for treatment planning and outcomes
assessment: Volume 3: Instruments for adults (3rd ed., pp.
191–234). Erlbaum. http://search.ebscohost.com/login.aspx?
direct=true&db=psyh&AN=2004-14941-006&site=ehost-live
Lambert, M. J., & Harmon, K. L. (2018). The merits of implement-
ing routine outcome monitoring in clinical practice. Clinical
Psychology: Science and Practice, 25(4), Article e12268. https://
doi.org/10.1111/cpsp.12268
Ley, P. (1972). Quantitative aspects of psychological assessment
(Vol. 1). Duckworth.
Lord, F. M., & Wingersky, M. S. (1984). Comparison of IRT true-
score and equipercentile observed-score “equatings”.Applied
Psychological Measurement, 8(4), 453–461. https://doi.org/
10.1177/014662168400800409
McCall, W. A. (1922). How to measure in education. MacMillan.
Mellenbergh, G. J. (2011). A conceptual introduction to psycho-
metrics: Development, analysis and application of psychological
and educational tests. Eleven International. https://books.
google.es/books?id=jRJJYAAACAAJ
Miller, S. D., Hubble, M. A., Chow, D., & Seidel, J. (2015). Beyond
measures and monitoring: Realizing the potential of feedback-
informed treatment. Psychotherapy, 52(4), 449–457. https://
doi.org/10.1037/pst0000031
Patel, S. R., Bakken, S., & Ruland, C. (2008). Recent advances in
shared decision making for mental health. Current Opinion in
Psychiatry, 21(6), 606–6012. https://doi.org/10.1097/
YCO.0b013e32830eb6b4
Rosseel, Y. (2012). Lavaan: An R package for structural equation
modeling and more. Version 0.5–12 (BETA). Journal of Statistical
Software, 48(2), 1–36. https://doi.org/10.18637/jss.v048.i02
Schalet, B. D., Cook, K. F., Choi, S. W., & Cella, D. (2014).
Establishing a common metric for self-reported anxiety: Link-
ing the MASQ, PANAS, and GAD-7 to PROMIS Anxiety. Journal
of Anxiety Disorders, 28(1), 88–96. https://doi.org/10.1016/
j.janxdis.2013.11.006
Schalet, B. D., Revicki, D. A., Cook, K. F., Krishnan, E., Fries, J. F., &
Cella, D. (2015). Establishing a common metric for physical
function: Linking the HAQ-DI and SF-36 PF subscale to
PROMIS
Ò
Physical Function. Journal of General Internal Medi-
cine, 30(10), 1517–1523. https://doi.org/10.1007/s11606-015-
3360-0
Scherpenzeel, A. C. (2018). “True”longitudinal and probability-
based Internet panels: Evidence from the Netherlands. In M.
Das, P. Ester, & L. Kaszmirek (Eds.), Social and behavioral
research and the Internet (pp. 77–104). Routledge. https://doi.
org/10.4324/9780203844922-4
Scherpenzeel, A. C., & Bethlehem, J. G. (2011). How representa-
tive are online panels? Problems of coverage and selection and
possible solutions. In M. Das, P. Ester, & L. Kaczmirek (Eds.),
Social and behavioral research and the Internet: Advances in
applied methods and research strategies (pp. 105–132). Taylor
& Francis.
Schreiber, J. B., Nora, A., Stage, F. K., Barlow, E. A., & King, J.
(2006). Reporting structural equation modeling and confirma-
tory factor analysis results: A review. The Journal of Educa-
tional Research, 99(6), 323–338. https://doi.org/10.3200/
JOER.99.6.323-338
Slade, M., Amering, M., & Oades, L. (2008). Recovery: An interna-
tional perspective. Epidemiology and Psychiatric Sciences,
17(2), 128–137. https://doi.org/10.1017/S1121189X00002827
Smits, N. (2016). On the effect of adding clinical samples to
validation studies of patient-reported outcome item banks: A
simulation study. Quality of Life Research, 25(7), 1635–1644.
https://doi.org/10.1007/s11136-015-1199-9
Ó2022 Hogrefe Publishing European Journal of Psychological Assessment (2022)
E. de Beurs et al., A Common Metric: Normalized TScores 15
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

Smits, N., Öğreden, O., Garnier-Villarreal, M., Terwee, C. B., &
Chalmers, R. P. (2020). A study of alternative approaches to
non-normal latent trait distributions in item response theory
models used for health outcome measurement. Statistical
Methods in Medical Research, 29(4), 1030–1048. https://doi.
org/10.1177/0962280220907625
Stasinopoulos, M. D., Rigby, R. A., & Bastiani, F. D. (2018). GAMLSS:
A distributional regression approach. Statistical Modelling,
18(3–4), 248–273. https://doi.org/10.1177/1471082X18759144
ten Klooster, P. M., Oude Voshaar, M. A. H., Gandek, B., Rose, M.,
Bjorner, J. B., Taal, E., Glas, C. A. W., van Riel, P. L. C. M., & van
de Laar, M. A. F. J. (2013). Development and evaluation of a
crosswalk between the SF-36 Physical Functioning Scale and
Health Assessment Questionnaire Disability Index in rheuma-
toid arthritis. Health and Quality of Life Outcomes, 11, 199–199.
https://doi.org/10.1186/1477-7525-11-199
Terluin, B., Smits, N., Brouwers, E. P. M., & de Vet, H. C. W. (2016).
The Four-Dimensional Symptom Questionnaire (4DSQ) in the
general population: Scale structure, reliability, measurement
invariance and normative data: A cross-sectional survey.
Health and Quality of Life Outcomes, 14(1), Article 130.
https://doi.org/10.1186/s12955-016-0533-4
Terluin, B., van Marwijk, H. W., Adèr, H. J., de Vet, H. C., Penninx,
B. W., Hermens, M. L., van Boeijen, C. A., van Balkom, A. J., van
der Klink, J. J., & Stalman, W. A. (2006). The Four-Dimensional
Symptom Questionnaire (4DSQ): A validation study of a multi-
dimensional self-report questionnaire to assess distress,
depression, anxiety and somatization. BMC Psychiatry, 6(1),
Article 1. https://doi.org/10.1186/1471-244X-6-34
Timman, R., de Jong, K., & de Neve-Enthoven, N. (2017). Cut-off
scores and clinical change indices for the Dutch Outcome
Questionnaire (OQ-45) in a large sample of normal and several
psychotherapeutic populations. Clinical Psychology & Psy-
chotherapy, 24(1), 72–81. https://doi.org/10.1002/cpp.1979
Timmerman, M. E., Voncken, L., & Albers, C. J. (2021). A tutorial on
regression-based norming of psychological tests with GAMLSS.
Psychological Methods, 26(3), 357–373. https://doi.org/
10.1037/met0000348
van der Laan, J. (2009). Representativity of the LISS panel.
Statistics Netherlands.
Van Hoeck, K. J. M., Lilien, M. R., Brinkman, D. C., & Schroeder,
C. H. (2000). Comparing a urea kinetic monitor with Daugirdas
formula and dietary records in children. Pediatric Nephrology,
14(4), 280–283. https://doi.org/10.1007/s004670050759
van Stralen, K. J., Dekker, F. W., Zoccali, C., & Jager, K. J. (2012).
Measuring agreement, more complicated than it seems.
Nephron Clinical Practice, 120(3), c162–c167. https://doi.org/
10.1159/000337798
Wahl, I., Löwe, B., Bjorner, J. B., Fischer, F., Langs, G., Voderholzer,
U., Aita, S. A., Bergemann, N., Brähler, E., & Rose, M. (2014).
Standardization of depression measurement: A common metric
was developed for 11 self-report depression measures. Journal
of Clinical Epidemiology, 67(1), 73–86. https://doi.org/10.1016/
j.jclinepi.2013.04.019
Wall, M. M., Park, J. Y., & Moustaki, I. (2015). IRT Modeling in the
presence of zero-Inflation with application to psychiatric
disorder severity. Applied Psychological Measurement, 39(8),
583–597. https://doi.org/10.1177/0146621615588184
History
Received April 19, 2021
Revision received July 6, 2022
Accepted August 3, 2022
Published online December 16, 2022
EJPA Section / Category Clinical Psychology
Acknowledgments
In this paper, we gratefully made use of BSI- and 4DSQ data of the
LISS (Longitudinal Internet Studies for the Social sciences) panel
administered by CentERdata (Tilburg University, The Netherlands)
and OQ-45 data from TNS-NIPO, The Netherlands. We would also
like to thank MHC providers in the Netherlands for providing
patient data on the BSI and the OQ-45 and the VU Medical Center
for providing patient data on the 4DSQ.
Conflict of Interest
The authors report no conflict of interest.
Publication Ethics
The data and narrative interpretations of the data/research
appearing in the manuscript have not been presented at a
conference or meeting, posted on a listserv, shared on a website,
including academic social networks like ResearchGate, and so
forth.
Open Science
We report on a reanalysis of data about which has been published
before. We report and refer to previous publications on how we
determined our sample size, all data exclusions, all data inclu-
sion/exclusion criteria, whether inclusion/exclusion criteria were
established prior to data analysis, all measures in the study, and
all analyses including all tested models. If we use inferential tests,
we report exact pvalues, effect sizes, and 95% confidence or
credible intervals.
Open Data: The information needed to reproduce all of the
reported results are not openly accessible, but can be requested
from the first author.
Open Materials: The information needed to reproduce all of the
reported methodology is made available. We provided suffi-
cient information for an independent researcher to reproduce
the reported results, including a codebook (https://www.
psycharchives.org/en/item/86e598e9-4828-4127-86ae-5f0d18e9
586a; de Beurs, Oudejans, et al., 2022). Moreover, we have
uploaded an annotated version of our R-code with two practice
datasets, which will allow other researchers to apply it to these
data (and their own data).
Preregistration of Studies and Analysis Plans: This study was not
preregistered.
Edwin de Beurs
Department of Clinical Psychology
Faculty of Social Sciences
Leiden University
Wassenaarseweg 52
2333 AK Leiden
The Netherlands
e.de.beurs@arkin.nl
European Journal of Psychological Assessment (2022) Ó2022 Hogrefe Publishing
16 E. de Beurs et al., A Common Metric: Normalized TScores
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.