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Common measures or common metrics? A plea to harmonize measurement results

Abstract Objective There is a great variety of measurement instruments to assess similar constructs in clinical research and practice. This complicates the interpretation of test results and hampers the implementation of measurement‐based care. Method For reporting and discussing test results with patients, we suggest converting test results into universally applicable common metrics. Two well‐established metrics are reviewed: T scores and percentile ranks. Their calculation is explained, their merits and drawbacks are discussed, and recommendations for the most convenient reference group are provided. Results We propose to express test results as T scores with the general population as reference group. To elucidate test results to patients, T scores may be supplemented with percentile ranks, based on data from a clinical sample. The practical benefits are demonstrated using the published data of four frequently used instruments for measuring depression: the CES‐D, PHQ‐9, BDI‐II and the PROMIS depression measure. Discussion Recent initiatives have proposed to mandate a limited set of outcome measures to harmonize clinical measurement. However, the selected instruments are not without flaws and, potentially, this directive may hamper future instrument development. We recommend using common metrics as an alternative approach to harmonize test results in clinical practice, as this will facilitate the integration of measures in day‐to‐day practice.


| INTRODUCTION OF THE PROBLEM
Measurement is the most basic building block of scientific research.
Since the days of Wundt and Thurstone, measurement has played a prominent role in psychology and a separate branch is dedicated to its research: psychometrics. The past decades have seen a proliferation of measurement instruments for a broad range of psychological constructs. On the one hand, the vast number of available measurement instruments for psychological concepts reflect the importance of assessment and psychometrics in clinical psychology. Novel measures often incorporate new theoretical perspectives on the phenomenology or treatment of psychopathology (e.g., by stressing cognitive aspects), or signify a change in key features of a disorder (Böhnke & Croudace, 2015). Measures are often validated for different populations (general population vs. clinical sample) or different purposes (diagnosis vs. tracking treatment progress) (McPherson & Armstrong, 2021;Patalay & Fried, 2020), or simply reflect innovations in measurement technology itself. On the other hand, the number of available measurement instruments also poses a challenge to psychological research. There are at least 19 instruments to measure anger (Weidman et al., 2017), and over 280 instruments have been developed to measure depression, many of which are still in use (Fried, 2017;Santor et al., 2006). This is also reflected in little consistency in use of measures in therapy outcome research as noted by Ogles (2013): across 163 studies, authors used 435 unique outcome measures, of which 371 were used only once in a study. This plethora of instruments, in combination with questionable measurement practices, such as outcome switching (Weston et al., 2016) and lack of transparency on how scores are derived from these measures (Weidman et al., 2017), hampers the establishment of a consistent body of knowledge. It complicates the comparison of results from various studies, and unnecessarily slows down scientific progress (Flake & Fried, 2020).
In clinical practice, measurement instruments are increasingly used to aid the initial evaluation of patients and to assess outcomes.
Measurement-based care has been called for repeatedly in numerous editorials and reviews (Boehnke & Rutherford, 2021;Fortney et al., 2017;Harding et al., 2011;Lambert, 2007;Lewis et al., 2019;Snyder et al., 2012). Paradoxically, the abundance of measurement instruments poses barriers to their use in clinical practice (Fried, 2017;Santor et al., 2006). Firstly, the use of a wide variety of instruments, each having its own metric, complicates communication among professionals. For instance, severity of depression symptomatology expressed in a score on the Beck Depression Inventory (BDI-II; Beck et al., 1996), with scores ranging from 0 to 63, is not compatible with severity expressed in a score on the Patient Health Questionnaire (PHQ-9; Kroenke & Spitzer, 2002), with scores ranging from 0 to 27. This complicates matters when a clinician using the BDI-II refers a patient to a colleague more familiar with the PHQ-9. Secondly, communication about test results between therapists and patients is complicated by the use of various metrics (Snyder et al., 2019).
Moreover, the knowledge gap between clinicians and patients widens, when only clinicians are able to properly interpret test results. More patient engagement, involvement, and shared decision making about the course of treatment is called for (Patel et al., 2008), in part because this leads to better outcomes (Lambert & Harmon, 2018).
The knowledge gap may hinder patients in their attempts to obtain a more equal role in the therapeutic process on their journey to recovery. Clear information on the meaning of a test result and how much progress is made towards treatment goals, will help to better involve patients, will grant them a more active role, and will strengthen engagement with the information provided (Goetz, 2010).
Finally, the knowledge of measurement instruments and the specific psychometric properties required for the interpretation of test scores, may hinder implementation in daily clinical practice, and allow practitioners to maintain beliefs that standardized measures are not as accurate as their clinical judgement (de Beurs et al., 2011).
A strategy to facilitate the interpretation of test results in clinical practice has been around for many decades and is well-known: use of common metrics. With a metric we mean a system or standard of measurement. Metrics describe the units in which measurements are provided and interpreted. Examples would be the imperial and the metric system which are used across a range of measurement domains as diverse as distance, volume, and weight to describe amounts. In the medical field, common metrics are usually based on physical entities, such as the metre, kilogramme, mol and Kelvin. In psychology we mostly measure non-physical entities, abstract constructs or latent traits, such as depression, which do not permit direct observation (Flake & Fried, 2020;Kellen et al., 2021). Consequently, we cannot fall back on these physical entities and have to express scores on metrics that have no physical counterpart, for example, when expressing severity as the distance from the mean score of a reference group. In the case of psychological assessments, use of a common metric would involve the conversion of raw test scores into universally applicable common metrics, such as standardized scores and percentile ranks, based on normative samples (Kendall et al., 1999). Converting raw scores to common metrics is discussed in many textbooks on psychological testing (Anastasi, 1968;Cronbach, 1984), but it is underused in clinical research and practice. An example of how use of a common metric has worked out well is available in another area of psychological assessment: the measurement of intellectual capacity.
The IQ metric was developed more than a century ago by Binet and Simon (1907) and has found universal application; professional psychologists as well as the lay public understand the meaning of IQ-scores, no matter the specific measurement instrument that was used. Interpretation of test results in clinical practice would be much easier if their meaning was as self-evident as IQ test scores.
The remainder of the paper is structured as follows. First, we describe two candidate metrics for universal application: T scores and percentile ranks. Both are commonly used in neuropsychological and educational research and are gaining popularity in clinical assessment.
Second, we describe the T score metric and percentile ranks metric in more detail, and present their main merits and drawbacks. We also

Key Practitioner Message
• Converting raw scores from neuro-psychological assessments to common metrics will ease the interpretation of test results among professionals and will facilitate communication with patients receiving mental healthcare.
• Common metrics will clarify the severity of patients' conditions and increase their engagement with outcome data.
• Treatment progress (or lack thereof) can be more easily monitored, understood and communicated to by using common metrics. describe how they can be derived by various approaches, illustrate their use with measures for depression, and discuss the choice of a proper reference group for these metrics. Finally, we propose further steps required for widespread implementation and suggest various subjects for future research.

| CANDIDATE METRICS
Two options have been proposed: (1) Standard scores (z scores and their more convenient alternatives, such as T scores, stanines and stens) and (2) percentile rank scores Ley, 1972). Table 1 presents an overview of these metrics, their calculation, and some of their properties. Figure 1, adapted from Seashore (1955), shows the various metrics under the normal distribution and provides labels for the interpretation of scores when used as a severity indicator or screener. For example, in order to label levels of severity for depression, the PROMIS group has followed the convention of dividing the general population up in four segments (from bottom to top: 69.1%, 15.0%, 13.6% and 2.3%, respectively). Labels and corresponding T scores are: 'within normal limits' (T < 55.0), 'mild' (T = 55.0-59.9), 'moderate' (T = 60.0-69.9) and 'severe' (T ≥ 70.0) (healthmeasures, n.d.) (see https://www.healthmeasures.net/scoreand-interpret/interpreTscores/promis/promis-score-cut-points). As an illustration, Figure 1 also includes raw scores on the PHQ-9 (Kroenke & Spitzer, 2002), CES-D (Radloff, 1977) and BDI-II from the US population  to demonstrate how they would translate into these metrics. For all three instruments, the raw score units are stretched at the lower end, illustrating the negative skewness of the frequency distribution of raw scores in the general population: Low scores are much more common than high scores.

| T SCORES
T scores, so named by McCall (1922) to honour the psychometric pioneers Thorndike, Terman and Thurstone, are based on standardized or Z scores. Z scores are raw scores converted to a standard scale with M = 0 and SD = 1 and are calculated based on the mean and standard deviation of a reference group. Standardization to Z scores yields inconvenient scores (with a range of À3 to 3 implying negative scores with several decimals to denote sufficient precision) and alternatives have been put forth with a more convenient format, such as stans, stanines and T scores. Stans and stanines yield a rather crude categorization of score levels and we left them out from further consideration. T scores are Z scores multiplied by 10 with 50 points added. They have a mean of 50, a standard deviation of SD = 10, and range, in practice, from 20 to 80. Figure 1 shows that a T score of 80 is three standard deviations above the mean, a score obtained by only 0.13% of the population, according to the cumulative normal distribution. Thus, 99.7% of the population will score in the 20-80 range. scores can be fixed in most cases by transformations (Box & Cox, 1964;Liu et al., 2009). Another, more thorough approach is to first establish normalized standard scores with regression-based norming (Zachary & Gorsuch, 1985), and to convert these to T scores (Lenhard & Lenhard, 2021). Statistical software is available in R (GAMLSS; Stasinopoulos et al., 2018) and Timmerman et al. (2020) offers a detailed tutorial.
Recently, Item Response Theory (IRT)-based approaches to convert item responses to legacy instruments into T scores have gained popularity, using EAP-factor scores or alternatives . The result of the IRT-based approach applied by Choi et al. (2014) to convert scores to the PROMIS metric (a T score with the US population as reference group) is illustrated for the CES-D, PHQ-9 and BDI-II in Figure 1. These approaches again require the assumption that the trait under study is normally distributed. However, the distributions of observed test and latent trait scores do not necessarily coincide (Kellen et al., 2021;Liddell & Kruschke, 2018). Their correspondence depends on the assumptions of the underlying measurement model and therefore impacts all test score interpretations equally, for example, approaches described as 'classical test theory' deal only with test scores as an observed property (DeMars, 2018) and latent variable models separate observed test and latent trait scores (Molenaar & Dolan, 2018). For a non-normal distribution of raw scores, commonly found when clinical traits such as depression or anxiety are assessed in general population samples, alternatives have been developed (Reise et al., 2018). As IRT factor scores are often scaled as a standard score (M = 0.00, SD = 1.00), they can be easily converted into T scores with the linear formula in Table 1.
T scores are well established in clinical psychometrics. They were chosen as a metric by the PROMIS initiative, aimed at developing a new set of measures in health research (Cella et al., 2010). Considerable work has been done in this area, for instance by the Prosetta Stone initiative Schalet et al., 2015). Here, raw scores have been converted to the PROMIS T score metric for many legacy measures, assessing a wide variety of constructs, including depression Wahl et al., 2014), anxiety  and pain . Also other researchers have chosen T scores as a common metric, for example, for depression When a unidimensional latent variable model holds and distributions are appropriately smoothed (Lord & Wingersky, 1984), conversion based on percentile ranks (equipercentile linking) and IRT based approaches tend to yield very similar results, as demonstrated by Choi et al. (2014), and more recently by Schalet et al. (2021). The T scores metric has been linked to expert judgement regarding the severity of pain interference, fatigue, anxiety and depression for oncology patients . Severity levels matched almost perfectly with the T score metric: 60 differentiated mildly from moderately symptomatic and 70 differentiated moderately from severely symptomatic. Furthermore, T scores on the Brief Symptom Inventory (Derogatis, 1975) Achenbach, 1991). The Prosetta Stone Initiative (https://www.prosettastone.org) provides crosswalk tables for many measures to the PROMIS T score, which is based on the general US population. T scores can also be derived using a webapp (Fischer & Rose, 2016). Further, a crosswalk formula allows for the arithmetic conversion of raw scores to T scores or percentile ranks.
These formulas can be established from cross-walk tables with statistical software, such as curve fitting in the regression module of SPSS or the nls and nlstools packages for Non-linear Least Squares modelling in R (Baty et al., 2015). An example of conversion by formula is provided by Roelofs et al. (2013)

| PERCENTILE RANK SCORES
Contrasting standard scores, the percentile rank of a score ranges from 0 to 100, indicating the percentage of cases that are less than that score. In other words, percentile ranks denote with a score of 0 to 100 the relative position of the tested person among their peers from a reference group in 101 intervals (Kurtz & Mayo, 1979). In clinical contexts, this may translate into a message to the patient, such as, 'At least 75% of our patients have a lower score at the onset of treatment'. As such, percentile ranks are an easily understood representation of a test result, which helps to convey its meaning to colleagues and patients. This may explain why percentile ranks are widely used in educational assessment. Percentile ranks are also depicted in Figure 1.
Percentile ranks are calculated with the formula in the last column of Table 1

| T SCORES AND PERCENTILE RANKS COMPARED
A minimum requirement for a universally applicable metric is that it should be easy to interpret and express in a straightforward manner how common or exceptional a test result is (Snyder et al., 2012). The COSMIN checklist defines interpretability as 'the degree to which one can assign a qualitative meaning' to a score (Prinsen et al., 2018). This would solve many of the issues of idiosyncratic scoring methods men-  perception of percentile ranks was demonstrated in a study by Bowman (2002) with third-year undergraduate students, who appeared inclined to overestimate percentile ranks above 80 or below 20 as quite extreme test result (whereas under the normal curve PR = 80 corresponds to T = 58.4, that is, less than 1 SD removed from the mean, see Figure 1). Furthermore, given the prevailing view around admissible transformations and their link with arithmetical and statistical operations with percentile ranks, simple operations are not permissible, such as calculating an average over a set of scores, or calculating a difference score between repeated assessments. For some discussion of the topic, see Meijer and Oosterloo (2008). Interestingly, this drawback interferes with the advantage of percentile scores that they are generally more intuitive to interpret.
We conclude that for the interpretation of test results and further processing of scores, T scores are the best choice, but for communication with colleagues and patients, we recommend supplementing these with percentile ranks. This is because T scores are more versatile given their psychometric properties, but percentile ranks are more intuitive to interpret. We further note that, as extreme percentile scores are susceptible to misinterpretation, caution in communication is required.

| CHOOSING APPROPRIATE REFERENCE GROUPS
The two common metrics we propose, T scores and percentile ranks, have a lower score), but below average compared to other patients attending the clinic (only 33% have a lower score). The information offered will depend on the context, but we caution against overloading the lay user with too much information, as this may be confusing and runs counter to the principle of simplicity and minimalism of 'less is more' (Peters et al., 2007).
F I G U R E 3 Selected raw scores on the BDI-II with T scores (x axis) and percentile rank scores relative to the clinical population (y axis); horizontal and vertical grid lines are based on raw scores

| ILLUSTRATION
To demonstrate the utility of common metrics, we provide as an example, the crosswalk tables in Table 2. Data for Table 2 stem from tab. A1-A3 of Choi et al. (2014). They provide crosswalk tables to convert raw scores on three commonly used depression measures, the Centre for Epidemiologic Studies Depression scale CES-D, the PHQ-9 and the BDI-II to the PROMIS depression scale T score. For a selection of raw scores correspondence with the T score metric is shown, based on the US general population sample of PROMIS. According to interpretation guidelines for the CES-D (Radloff, 1977), a summed item raw score of 0-15 indicates absent to mild depression, T A B L E 2 Raw scores, PROMIS T scores, on the CESD, PHQ-9 and BDI-II (from Choi et al., 2014)   16-23 moderate and 24-60 or more indicates severe depression. The cut-off for caseness is ≥16; this corresponds to a T score of 56.2. For the PHQ-9, scores from 0 to 4 indicate minimal depression, 5-9 mild, 10-14 moderate, 15-19 moderately severe and 20-27 severe depression (Kroenke & Spitzer, 2002). The proposed cut-off for caseness is ≥10, corresponding with 59.9 on the T score metric. Interpretation guidelines from the manual of the BDI-II denote a total score of 0-13 as within the minimal range, 14-19 as mild, 20-28 as moderate and 29-63 as severe. A recent meta-analysis suggested ≥18.2 as optimal cut-off for clinical caseness (Von Glischinski et al., 2019). For these three measures, caseness starts at T = 56 to 60, and the cut-off values between mild and moderate depression generally coincide with T = 60, which was also proposed for the T score metric by the PROMIS group (www.promis.org). When linking multiple depression measures to one common construct and metric, Wahl et al. (2014) suggested T = 54.0, T = 66.2 and T = 72.9 as thresholds for mild, moderate and severe depression in the BDI-II.
These cut-off values are similar, but not equal which may be due to differences in operationalization of the construct or differences between the normative samples.
For the BDI-II, we also added percentile ranks to Table 2

| DISCUSSION
The current practice of using a wide diversity of instruments for similar constructs in psychological research contributes to weakly defined measurement, as opposed to the strongly defined measurement of the physical sciences (Finkelstein, 2003 where 'Delta T' has become a commonly used metric to denote patients' progress from pretest to posttest. Yet, we see two crucial areas of further development, each with several suggestions. The first area is practical: Common metrics should be used universally, and several steps ought to be taken to make common metrics a reality. These include a better understanding of the need for common metrics, and a demonstration of the utility of such metrics. We hope our manuscript contributes in this regard. Another crucial step for practical implementation is that crosswalk tables and figures become more easily available to demonstrate the conversion of raw scores to  Thissen et al., 2015) are justified by a greater accuracy of the resulting T scores. Second, existing normative data are limited to specific countries. The PROMIS T score metric, for instance, is based on normative data of the US population. To test whether we can apply this metric internationally requires collecting data in other countries and comparing scores (Terwee et al., 2021).
This will ease the international comparison of treatment outcome research and make such data more relevant for practice contexts as well. Third, the possible influence of translation of measures and their adaptations to other languages and cultures needs to be investigated (Sousa & Rojjanasrirat, 2011;Van Widenfelt et al., 2005). We also need to study whether measures are invariant for gender, age, education level, and/or socio-economic status, as influence of these factors would imply that different norms (and T scores and percentile ranks) may be used for subgroups of respondents (Teresi et al., 2009). To accommodate this, additional conversion formulas should be provided that include coefficients for gender and age, which may result from regression-based norming (Timmerman et al., 2020). Furthermore, other external variables may need to be taken into account, such as the cultural background of clients or aspects of their psychopathology (Böhnke & Croudace, 2015). Finally, conversion to T scores should correct for non-normality of raw test scores, in order to end up with T scores with genuine equal intervals. To do so, conversion tables and formulas could be based on IRT approaches, the frequency distribution of summed item scores (rank order-based normalization), or on other normalization approaches. The approach that yields the best T score metric warrants further study (Kolen & Brennan, 2014).
The area of harmonizing mental health assessment is a key methodological issue and finding solutions has recently been put on the policy agenda far beyond practical solutions for clinical reporting and discussion, as is presented here. For instance, mandating a limited set of instruments has been suggested as a solution (Wolpert, 2020 (Patalay & Fried, 2020). The selected instruments are not without flaws or drawbacks. For instance, the PHQ-9 and GAD-7 were developed to screen for depression and anxiety in the general population, and not to track progress during treatment.
Both are quite brief, which limits their scope and diminishes their reliability and accuracy, making them less suitable to monitor (statistical) reliable change (Jacobson & Truax, 1991) (Obbarius et al., 2017). This will help to limit the proliferation of measurementbased care and may enhance the quality of mental healthcare (Fortney et al., 2017;Kilbourne et al., 2018).
Another part of the literature builds on the key to a proper understanding of what we aim for with common metrics: the difference between equating or merely expressing scores on a common metric, which should not be confused with each other. Equating test scores assumes that the same construct is being measured (Kolen & Brennan, 2014). In contrast, expressing scores on a common metric does not imply this assumption and merely aims to align test results with a common metric for the measurement of constructs that remain distinct, even if they are expressed on the same metric. For example, a T score of 60 for depression does not denote the same thing as a T score of 60 for anxiety, as the two constructs differ. In fact, given the considerable differences in content of various depression instruments, such as the CES-D and the BDI, similar T scores on these measures may not denote the same thing (Fried, 2017). Consequently, T scores for different constructs should not be directly compared, beyond the fact that they express how extraordinary the score is in comparison to a reference group such as the general population.
While such scores carry crucial information, we caution against comparing or equating T scores (or percentile scores, for that matter) stemming from different constructs. For a person who scores T = 65 on depression and T = 55 on anxiety, the proper interpretation and message would be that the depression score deviates more from the general population mean (1.5 SD) than the anxiety score (0.5 SD) or the depression score is more exceptional than the anxiety score. This differs slightly but meaningfully from the erroneous inference that the patient is more depressed than anxious.
Confusion between common metrics and common constructs may arise from the research literature on the PROMIS measures and PROMIS T score metric. Various legacy measures have been linked to PROMIS measures and can be converted with crosswalk tables into the preferred metric of PROMIS (T scores). This research is usually done per construct, such as, depression , anxiety , pain  and physical functioning , all titled 'Establishing a common metric for …'.
The aim of these studies was equating test results from various measures and mapping them per construct on the T score metric.
For PROMIS measures this implies that all are scaled on a common metric: US population-based T scores. Moreover, for convenience, scores on PROMIS measures all share the same direction (a higher score represents more of the measured construct, such as depression, pain, mobility, functioning, or quality of life), and are similarly colour coded in graphical output (green is normal, red is severe, see Figure 2). However, using the same metric does not imply that the same construct is measured. The metric merely expresses conveniently for each construct the exceptionality of the score (e.g., depression), but it does not imply that these scores are comparable across constructs. For more studies using this approach, see, for example, for depression (Wahl et al., 2014), physical functioning (Oude Voshaar et al., 2019), personality pathology (Zimmermann et al., 2020), psychological distress (Batterham et al., 2018) and fatigue .
Finally, it is important to note that converting scale scores to T scores does not imply that the original scores are lost. The sum scores metric can still be calculated and reported in research, for instance, to compare scores with previously published research findings that used the traditional way of scoring.
To conclude, use of common metrics, particularly populationbased T scores and clinical percentile ranks, may aid to harmonize measurement practices in clinical psychology research, will be helpful for a proper interpretation of test results, enhance the communication about tests results among professionals and ease explanation of their meaning to patients in mental healthcare. To bring this about, a first step is to provide easy ways to express test results as T scores, for instance, in user manuals for assessment instruments with cross walk tables and formulas. Also, nowadays many self-report questionnaires are administered via computer or smart phone, and expressing results in T scores can be accomplished easily within the software.
Next steps are educating professionals, helping them gain experience with T scores and asking them to help educate their clients on the meaning of T scores. The common use of IQ scores and understanding by the general public on what IQ scores convey shows the feasibility of this approach. We hope that our paper stimulates the use of T sores as the main way to give meaning to (neuro-)psychological test results.