Background: The Government of Turkey has initiated a series of major health reforms in 2003 with an objective of increasing access to health care services and improving efficiency of public and private hospitals. This study attempts to understand the technical efficiency of public and private hospitals in Turkey to better guide hospital reform. Methods: We use data from 1079 public and private hospitals and translog stochastic production frontier was adopted to estimate technical inefficiency of hospitals. Results: Results indicate that there is no statistically significant difference in the degree of inefficiency of hospitals by geographic location or its level of economic development. Efficiency scores vary significantly across hospital types with Ministry of Health (MoH) General Hospitals being the most efficient followed by MoH teaching hospitals. Better performance of MoH hospitals may be due to successful implementation of 2003 health reforms in Turkey, which intended to improve resource utilization within and across MoH hospitals. Among MoH hospital types, integrated county hospitals were the least efficient. Since the hospital outcome measure did not include the value of medical training, efficiency scores of university hospitals became relatively low. Wide variability of efficiency scores of private general hospitals implies the existence of both highly efficient and inefficient hospitals in the private sector. Conclusions: Efficiency differences of various hospital types can beleveraged to guidefuturereforms by emphasizingthe strengths of general hospitals and improving the referral system from county hospitals to general hospitals. Encouraging resource sharing across hospitals, as being done by the 2011 reforms, should further improve hospital efficiency. Promoting private hospitals may not necessarily be efficiency enhancing due to high variability of private hospitals in terms of efficiency scores. Similarly, implementation of common productivity standards and quality control measures are likely to improve hospital technical efficiency scores further. Keywords: Hospital efficiency, Stochastic frontier model, Health transformation program, Public and private hospitals, Turkey Background alternative strategies must be devised for improving effi- Efficiency analysis in health care sector has attracted sig- ciency in resource use . In modern health care system, nificant interest in recent decades due to escalating health health sector consists of many different types of facilities care costs [1, 2]. Better understanding of health facility and organizations and system-wide efficiency measurement efficiency is important for ensuring effective use of health often requires estimation of efficiency for each of the major resources, especially in countries where public involvement sectors like insurance providers, hospitals, nursing homes, in health care provision is high. Since public sector health primary care facilities, etc. . facilities, in many cases, do not compete in the marketplace, Turkey’s health care system has gone through significant structural changes in the last few decades. In 2015, public * Correspondence: VHeboyan@augusta.edu expenditure was about 79% of total national health care Department of Clinical and Digital Health Sciences, College of Allied Health expenditure of the country . Greater involvement of the Sciences, Augusta University, 987 St. Sebastian Way, EC 4314, Augusta, GA government in health sector allowed better coordination 30912, USA Full list of author information is available at the end of the article © The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Yildiz et al. BMC Health Services Research (2018) 18:401 Page 2 of 16 of service provision and improved access to services. with national priorities in health. Since the government Turkey also saw very rapid improvements in population became the major source of funding, the MoH could health since 1980s. Significant improvements were reported influence and manage use of resources (in both public in almost all health outcome measures. Life expectancy at and private hospitals) and implement more effectively birth has increased from about 65 years in 1990 to 78 years health care service standards. in 2013–15 . However, these accomplishments have not This research is an attempt to understand efficiency of been equally distributed geographically and, despite the hospital sector in the provision of services in Turkey. The rapid improvements, Turkey still lags behind most of the analysis assumes that efficiency of any production unit is Organization for Economic Cooperation and Development affected by its specific goal and objectives and therefore, (OECD) countries in terms of health outcomes and health factors affecting efficiency will be different for different care resource availability (Tables 1 and 2). hospital types. For empirical analysis, hospitals in Turkey In 2003, the Government of Turkey initiated a set of were grouped into categories based on ownership (MoH, major health reforms, the Health Transformation Program university, private) and teaching status/type (teaching, (HTP), with an objective of increasing access to health general, integrated). No single health policy can be equally care services and improving efficiency of hospitals through effective in improving resource allocation in all these (i) implementation of General Health Insurance (GHI), (ii) different hospital types. Therefore, it is important to establishing autonomous hospital structures, (iii) im- understand the relative efficiency in healthcare resource proving qualifications of health professionals and their utilization for each of the hospital types so that the work motivation, and (iv) deployment of an effective MoH can develop targeted policy options. health information system . The reforms integrated The primary objective of this study is to estimate tech- social security schemes under the Social Insurance nical inefficiency of Turkish hospitals and to analyze the Institution (SII), transferred public hospitals from the role of various hospital-specific and region-specific factors insurance agency to the Ministry of Health (MoH), insti- affecting the efficiency scores. The adoption of health care tuted a performance-based supplementary payment system service standards and alignment of goals and objectives of (P4P), and implemented family medicine model of health all hospitals with national priorities should reduce variabil- care delivery . ity of efficiency levels. For estimating the efficiency scores, These reforms gave the Ministry and newly established this study uses hospital data of MoH Health Services Public Hospital Administration of Turkey (PHAT) the General Directorate. Stochastic Frontier Analysis (SFA) authority to align hospital mission, goals, and objectives approach of Aigner, Lovell, and Schmidt  and Meeusen and van der Broeck  were used for estimating the efficiency scores and single-step estimation approach Table 1 Basic Health Indicators for Turkey and OECD34 suggested by Battese and Coelli [11, 12](discussedin averages, 2013 (or nearest year) detail in section “Methods”)was applied toidentifythe Indicator OECD34 Turkey Rank factors affecting efficiency. average (out of 34 OECD A number of studies have attempted to estimate efficiency countries) of Turkish hospitals but most focused on either a single Life expectancy at birth 80.5 76.6 31 hospital category [13–15]and/ora smallsubsetof hospitals Infant mortality 3.8 10.2 34 [16, 17], primarily utilizing Data Envelopment Analysis (per 1000 live births) (DEA). For example, Sahin et al.  analyzed the oper- Total expenditure 8.9 5.1 34 on health, % GDP ational performance of the MoH general public hospitals in the aftermath of HTP. Authors indicate that the HTP Total expenditure on health, 3453 941 34 per capita, US$ PPP reforms improved hospital productivity during 2005–08. Narci et al.  examined the competition and technical Physicians, per 1000 3.3 1.8 34 population efficiency among public and private general hospitals in Nurses, per 1000 9.1 1.8 34 Turkey. Results showed that only 17% of these hospitals population were technically efficient, but they did not observe any Hospital beds, 4.8 2.7 31 statistically significant relationship between market compe- per 1000 population tition and efficiency. None of the reviewed studies exam- MRI units per 1 million 14.1 10.5 20 ined relative efficiency of hospitals by considering all the population public and private facilities taken together. Moreover, recent CT scanners per million 24.4 14.2 25 health sector reform initiatives are supposed to improve population hospital efficiency and the analysis with recent data should A lower number indicates higher ranking b be able to indicate how the hospital efficiency has changed Out of 32 OECD countries Source: OECD  over the years. Yildiz et al. BMC Health Services Research (2018) 18:401 Page 3 of 16 Table 2 Geographic variations in health outcomes, availability of health resources and utilization of hospital services in Turkey, 2012 Centraleast Central Northeast Istanbul Southeast Aegean East East West West West Mediterranean Anatolia Anatolia Anatolia Anatolia Marmara Black Sea Marmara Black Sea Anatolia Perinatal 10.9 7.1 10.9 6.7 11.3 7.5 7.5 7.0 7.8 8.4 6.7 7.6 Mortality per 1000 live birth Neonatal 6.5 3.9 6.3 3.2 6.2 3.5 3.7 3.8 3.9 3.9 3.0 3.7 Mortality per 1000 live birth Post-neonatal 4.6 3.3 4.1 2.2 4.4 2.3 2.2 3.0 2.5 3.0 2.5 3.3 Mortality per 1000 live birth Mortality under 16.7 10.8 13.9 8.2 16.1 8.7 9.0 9.9 9.1 9.9 8.3 10.8 5 years per 1000 live birth Maternal 25.5 25.9 32.2 15.1 14.7 13.6 7.7 21.5 7.8 17.2 12.7 10.7 Mortality per 1000 live birth Poverty rate (%), 13.4 12.4 13.2 9.6 12.8 11.6 10.8 11.1 13.0 12.0 12.9 13.7 50% poverty risk threshold Number of 26.7 28.4 28.8 23.3 19.7 27.2 26.1 33.1 27.4 30.3 35.8 23.8 hospital beds per 10,000 Number of 2.9 2.9 2.0 3.3 3.1 3.1 3.0 2.9 2.4 2.8 3.8 3.3 ICU beds per 10,000 Per Capita visits 4.5 4.9 4.7 4.2 4.1 4.9 4.8 5.8 5.0 5.4 5.0 4.6 to hospitals Physicians 144 159 142 192 121 183 156 159 150 152 266 155 per 100,000 population Nurses 257 277 253 191 184 279 254 339 278 296 302 242 per 100,000 population Surgical 49.5 63.4 57.2 56.3 49.6 58.0 59.1 59.8 44.4 53.6 73.8 64.7 operations per 1000 population Surgical 3.1 5.0 3.5 6.8 2.8 6.4 6.8 6.0 3.5 5.4 8.9 5.5 operations per 1000 population (Group A) Number of MRI 31.8 19.9 23.4 28.0 24.5 22.5 22.9 25.8 18.7 25.8 24.8 23.0 exams per 1000 population in hospitals Bed 65.4 60.8 65.0 70.1 67.9 67.5 67.8 62.2 67.8 62.2 68.5 68.6 Occupancy Ratio Source: General Directorate of Health Research  Surgical operations are classified into groups A to E based on the severity of the operations This study is the first in Turkey that analyzes efficiency the ‘zero-value’ problem in production function analyses of the hospital sector by using information on all general (modified production function) and uses the simultaneous hospitals, both public and private. In addition, this study estimation of efficiency scores and determinants of effi- has made an attempt to link health sector reform policies ciency to obtain unbiased estimates. and hospital efficiency. In terms of estimation technique, The paper is structured as follows. Section “Health this paper adopts an empirical approach to account for system in Turkey” provides a brief overview of the Yildiz et al. BMC Health Services Research (2018) 18:401 Page 4 of 16 health system in Turkey. Section “Methods” describes population in their catchment areas. Public university the methodology, and model specification. Sources of hospitals also serve tertiary needs of the population in data are presented in section “Results”. The results are addition to medical training and teaching responsibilities. presented in section “Discussion” and concluding remarks Specialty hospitals, both public and private, have spe- and policy recommendations are provided in Section cialized focus such as emergency and traumatology, “Conclusions”. physical therapy and rehabilitation, chest and cardiovascu- lar diseases, ophthalmology, obstetric and child health, cardiology, etc. Health system in Turkey A number of reform initiatives were adopted in Turkey Turkish health system has gone through rapid changes since 2003 within the HTP framework. Since the beginning since the adoption of Health Transformation Program of HTP, the MoH has been successful in expanding health (HTP) in 2003 which was designed to change delivery of service delivery and quality  with significant invest- services, financing of the system, organizational set-up, ments in (i) new infrastructures for providing better quality level of health expenditure, health infrastructure, and health services (e.g. new hospitals), (ii) medical technolo- mechanism of resource allocation. The improvements in gies (e.g. total number of computerized tomography and health outcomes and health facility performance in recent magnetic resonance devices), (iii) increasing number of years are often attributed to the strategies and policies beds and intensive care unit beds, (e.g. intensive care unit implemented under the HTP . beds in MoH hospitals increased from 869 in 2002 to One principal objective of the HTP was to address the 10,321 in 2012), and (iv) increasing availability of medical issues related to fragmentation of health care provision and personnel (e.g. number of Specialist Physicians increased financing. Two governmental agencies became responsible from 45,457 to 70,103 and nurses increased from 72,393 to for provision and financing of health care. At the national 134,906 over 2002 to 2012) . level, General Health Insurance Scheme (GHIS) was intro- As part of the wider health system reform, hospital ser- duced in 2008 which now covers 99.5% of population. vice coordination was decentralized to give local authorities Turkey had the second lowest private health insurance financial and administrative autonomy . The reform coverage (5.6% in 2013) among all the OECD countries has reorganized the MoH and rural hospital structure by . Provision of healthcare services is primarily controlled uniting 843 MoH hospitals into 87 Public Hospital Unions by the MoH including the Ministry of Defense (MoD) (PHUs) and devolved important tasks to these PHUs in health facilities that were recently transferred to the 2012. The PHAT was delegated the authority of establish- MoH management. Private providers are integrated into ing financial and administrative regulations for public hos- the system through contractual agreements with the social pitals and carrying out annual monitoring and assessment health insurers . of public hospital and PHUs for improving effectiveness, For empirical analysis, we have categorized hospitals quality, and efficiency . in Turkey based on ownership, teaching status, size and As a result of this reorganization, the MoH assumed scope of services rendered. If ownership is used for the responsibility of preparing and implementing hospital categorization, for 2012, hospitals in Turkey (1483 total) service delivery standards (public, university, and private can be grouped into MoH hospitals (832 hospitals), hospitals) and human resource planning for the entire university hospitals (65 hospitals), private hospitals (541 health system. In addition, MoH approves private hospital hospitals), MoD hospitals (42 hospitals), and local ad- start-ups and determines quotas of doctors and their ministration hospitals (3 hospitals). The scale and scope specialties for the private sector . To better under- of services rendered are also different among the stand the effect of these policy changes on efficient use hospital types with significant geographic variability of resources, it is important to estimate relative effi- (Table 2)(, p., 143). ciency of hospitals by ownership, size and geographic The MoH hospital category can further be subdivided location. into: MoH teaching hospitals, responsible for residency Consistent with health sector reform policies, public training and tertiary level care, the MoH general hospitals, health expenditure as share of national health expenditure providing secondary level care with intensive care units increased from 68.1% in 2001 to 74.9% in 2011. Although and emergency services and integrated hospitals which the public funding for health care has not reached the provide limited essential patient care services in low OECD average yet, such a rapid increase in public funding population-density rural areas in partnership with local reflects significant injection of new resources in the health general hospitals. sector. General government expenditure on health as a Private university hospitals primarily provide medical percentage of total government expenditure has increased education and training for residents, while the private from 9.5% in 2001 to 12.8% in 2011. Total expenditure on hospitals serve the secondary and tertiary level needs of health as a percentage of Gross Domestic Product (GDP) Yildiz et al. BMC Health Services Research (2018) 18:401 Page 5 of 16 has also increased from 5.2 to 6.7% over 2001 to 2011 output that can be produced with available inputs at a (Table 3). given technology (or the minimum inputs required to pro- duce the outputs with a given technology). Technically ef- Methods ficient producers operate on their production frontier, Estimation methodology whereas those who operate below the frontier are la- In the economics literature, there are two broad categories beled as inefficient. The econometric implication of of analytic approaches to estimate the cost or production such reformulation is the decomposition of the error frontiers and associated efficiencies: parametric and non- term into a traditional symmetric random noise and a parametric methods. The former uses econometric new inefficiency component (, p. 42). approaches to estimate the functional forms and the latter There are two classes of econometric techniques used uses observed data to estimate the frontier without placing for efficiency analysis: corrected ordinary least squares conditions on the functional form . The Stochastic (COLS) and stochastic frontier analysis (SFA). The latter Frontier Analysis (SFA) and DEA are the most prominent is based on the specification of a stochastic production forms of the parametric and non-parametric approaches, frontier proposed by Aigner et al.  and Meeusen and respectively. Both of these approaches have their strengths van der Broeck . It allows the firms to be technically and weaknesses and the empirical literature has used both inefficient relative to their own frontier rather than to approaches without a clear argument for either approach. some norm. This alleviates the concerns associated with Jacobs et al.  provide a detailed individual and compara- the estimation of deterministic production frontiers where tive examination of these approaches. In this study, we are the parameters are computed rather than estimated, adopting the SFA approach to address the research making hypothesis testing impossible . Both COLS objectives and also provide comparative basis for studies and SFA are specified by the general production frontier utilizing alternative approaches. of the form : Production function analysis implicitly assumes that all firms, on the average, are technically efficient and the lny ¼ x β−u ð1Þ average production function reflects the underlying i technical efficiency. However, Kumbhakar and Lovell th  suggested that “not all producers are technically effi- where, y is the output of the i firm; the x is a Kx1 vector i i cient” and, therefore, it becomes desirable to move away containing the logarithms of inputs; β is a vector of from traditional average production functions to frontiers unknown parameters; and u is a non-negative random (p. 3). The production frontier defines the maximum variable representing technical inefficiency. Table 3 Changes in health care financing in Turkey, 1995–2011 № Indicator 1995–2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 1 Total expenditure on health as a 4.13 5.16 5.36 5.34 5.37 5.45 5.81 6.04 6.07 6.75 6.67 6.66 percentage of gross domestic product 2 General government expenditure on 10.52 9.54 9.07 9.73 10.75 11.28 11.95 12.13 12.79 12.79 12.79 12.79 health as a percentage of total government expenditure 3 General government expenditure on 67.85 68.07 70.68 71.92 71.25 67.84 68.34 67.83 73.02 75.14 74.79 74.94 health as a percentage of total expenditure on health 4 Private expenditure on health as a 32.15 31.93 29.32 28.08 28.75 32.16 31.66 32.17 26.98 24.86 25.21 25.06 percentage of total expenditure on health 5 External resources for health as a 0.80 0.27 0.01 0.12 0.01 0.01 0.03 0.09 0.07 0.01 0.00 .. percentage of total expenditure on health 6 Out-of-pocket expenditure as a 91.42 71.55 67.68 65.75 66.91 70.78 69.4 67.82 64.41 64.41 64.41 64.41 percentage of private expenditure on health 7 Private prepaid plans as a percentage .. .. .. .. 5.63 5.91 5.99 6.11 7.31 7.31 7.31 7.31 of private expenditure on health 8 Social security expenditure on health 43.55 54.46 57.51 59.91 60.85 56.08 56.63 54.44 57.04 57.04 57.04 57.04 as a percentage of general government expenditure on health Source: WHO  “..”: data not available Yildiz et al. BMC Health Services Research (2018) 18:401 Page 6 of 16 The difference between COLS (and its variants) and literature, SFA results have been found to be robust SFA is in their interpretation of the error term; COLS across distributional assumptions on inefficiency term. assumes that the entire error term is the inefficiency and Furthermore, considering the critique of Newhouse SFA assumes that the error term is a combination of a  and remedy proposed by Stevenson , Rosko random error term and an inefficiency term . There-  concluded that the assumption of truncated normal fore, in the presence of inefficiency and random shocks distribution appear appropriate for the inefficiency (υ ), empirically estimable frontier production function term. Following Battese et al.  and Coelli and Battese can be written as: , we assume that the inefficiency term u follows truncated (at zero) normal distribution with mean μ 0 i lny ¼ x β þ v −u ð2Þ i i i and variance σ . In the empirical work, most researchers have opted for or estimation of production frontier (Eq. 3) and inefficiency effects (Eq. 4) in a two-stage approach, where the first lny ¼ β þ β lnx þ v −u ðÞ Cobb‐Douglas stage involves estimation of the stochastic frontier and ji i i 0 j j¼1 the second stage estimates factors affecting technical in- k k X XX 1 efficiency. This approach, Battese and Coelli argued, lny ¼ β þ β lnx þ β ji i 0 j jh violates the identically distributed assumption of ineffi- j¼1 h¼1 ciency effects in the stochastic frontier model. Kumbhakar et al. , Reifschneider and Stevenson , Huang and lnx lnx þ v −u ðÞ Translog ji hi i i Lui , and Battese and Coelli  proposed single-stage, ð3Þ simultaneous estimation of the parameters. “This one-stage approach is less objectionable from a statistical point of where, (v - u ) is the decomposed error term in which v i i i view and is expected to lead to more efficient inference with allows for randomness across firms and captures the respect to the parameters involved” (, p., 105). For effect of measurement error, other statistical noise, and empirical modeling, this paper has used single-stage random shocks outside the firm’s control and u captures simultaneous estimation approach. the effect of inefficiency . This study adopts the stochastic frontier approach Zero-value problem with one-stage simultaneous estimation strategy sug- Often production functions involve explanatory variables gested by Battese and Coelli [11, 12]toestimatethe that have zero values making logarithmic transforma- technical efficiency scores for Turkish public and pri- tions of production functions impossible. For example, vate hospitals. An extensive review of SFA applica- in a health center, nurses and other paramedics may tions to hospitals (in US) can be found in Rosko and provide health care services without the presence of any Mutter . physician or a hospital may not have some particular Battese and Coelli notethatmosttheoretical equipment (e.g. an x-ray machine or CT scan). Battese stochastic frontier production functions do not explicitly and Batteseetal.  argue that confining the ana- model the technical inefficiency effects using appropriate lysis to those who utilize positive amounts of inputs explanatory variables, which usually are neither output may not be the most appropriate method of estimation nor input variables. To address this concern, we specify a as it implies excluding producers from the analysis with model with inefficiency term (mean μ and variance σ )as at least one zero input value. the dependent variable and z , a set of variables affecting The so-called ‘zero-value’ problem in estimation of technical inefficiency. The last term, ω represents the production functions has been addressed in various ways. stochastic error term (Eq. 3). Some have suggested assigning an arbitrary small value to the zero-value, while others have tried to fit other func- μ ¼ γ þ γ z þ ω ð4Þ m i 0 m tional forms that did not violate the zero input levels such Estimation of stochastic frontier requires specifying as quadratic equation model. Moss argues that the the distributional characteristics of both components of former is conditioned by the choice of the small number, the residual. It is commonly assumed that v is normally while the latter is unacceptable from a purely theoretical distributed with zero mean and constant variance. Jacobs perspective and has implications for global concavity of et al. (, p. 54–56) suggests that inefficiency estimates the production function. If the cases with zero-values are are sensitive to the choice of distribution for u and no substantial in the sample (Battese ), substituting with economic criteria are available to guide this choice. A an arbitrary small value may result in biased estimates. review of recent literature on SFA by Rosko and Mutter The recommendations are either to use bootstrapping to  has showed that, in both general and health care construct an alternative sample or to use dummy variable Yildiz et al. BMC Health Services Research (2018) 18:401 Page 7 of 16 associated with zero-value observations to generate lnðÞ output ¼ β þ β lnbed þ β lnclinicians þ β lndoctors i 0 1 2 3 unbiased estimates for the production functions. This study þ β lndevices þþβ lnicubeds 4 5 adopts the approach by Battese , where the input þ β lnadmin þ β devices d þ β icubeds d 6 7 8 variable that contains zero values is modified as: 2 2 þþβ 0:5lðÞ nbed þ β 0:5lðÞ nclinicians 11 22 2 2 þ β 0:5lðÞ ndoctors þþβ 0:5lðÞ ndevices 33 44 x ¼ lnðÞ max½ x ; D ð5Þ i i 2 2 þ β 0:5lðÞ nicubeds þ β 0:5lðÞ nadmin 55 66 þþβðÞ lnbed lnclinicians th where, x is the i explanatory variable that contains þ βðÞ lnbed lndoctors zero-value observations and D is defined as: 13 þ βðÞ lnbed lndevices þþβðÞ lnbed lnicubeds 1if x ¼ 0 D ¼ ð6Þ 0if x > 0 þ βðÞ lnbed lnadmin þ βðÞ lnclinicians lndoctors þþβðÞ lnclinicians lndevices þ βðÞ lnclinicians lnicubeds Data source and empirical model specification þþβðÞ lnclinicians lnadmin Data þ βðÞ lndoctors lndevices This study has used cross-sectional data obtained 34 from the MoH Health Services General Directorate of þ βðÞ lndoctors lnicubeds Turkey for the year 2012. The data set consists of a þþβðÞ lndoctors lnadmin comprehensive sample of 1394 hospitals (843 MoH þ βðÞ lndevices lnicubeds hospitals, 62 University hospitals and 489 private hos- þ βðÞ lndevices lnadmin pitals). Since the purpose of the analysis is to esti- mate efficiency scores for acute care general hospitals, þþβðÞ lnicubeds lnadminþ error 93 specialty hospitals were dropped from the data set. ð7Þ Some of the hospitals in the data set had no beds at where β is the intercept; β , β , β , β , β , β , β , and β all and these hospitals were also dropped (134 hospi- 0 1 2 3 4 5 6 7 8 are the first order derivatives; β , β , β , β , β , and tals) and finally 88 hospitals were dropped for sub- 11 22 33 44 55 β are the second order derivatives; and β , β , β , stantial missing data. Therefore, the final dataset had 66 12 13 14 β , β , β , β , β , β , β , β , β , β , β , and 1079 hospitals with different ownerships (398 private, 15 16 23 24 25 26 34 35 36 45 46 β are cross second order derivatives. Since Eq. 7 is in 56 university, and 625 MoH hospitals) and types (98 56 double log form, the estimated coefficients are the elas- teaching and 981 general). ticities between dependent and independent variables. When using the translog functional form, to truly assess the effect of each input, the marginal effects of inputs are Functional form of interest rather than the values of the input coefficients. The literature identifies the Cobb-Douglas and trans- We calculate the marginal effects for each input using the log as the two leading functional forms employed in following equation: the literature to specify and estimate production func- tions in hospital inefficiency studies [39–41]. They both k k XX ∂ lnðÞ y have their own merits and drawbacks. Some researchers e ¼ ¼ β þ β lnx ð8Þ j h j jh ∂ ln x are in favor of using the translog functional form, espe- j j¼1 h¼1 cially for larger samples, while others support the use The technical inefficiency term for this model is esti- of Cobb-Douglas functional form [39, 40, 42, 43]. We mated as (using Eq. 3): have performed the generalized likelihood ratio test to identify the proper functional form to use for our data. μ ¼ γ þ γðÞ type þ γðÞ incomeþ γðÞ region 3 i 0 1 2 3 The test results reject the null hypothesis that þ ω ð9Þ Cobb-Douglas is the appropriate model to use at 0.05 level of significance, implying that the translog functional form Apriori expectations are that general hospitals (type) is more suitable for our analysis. Therefore, the produc- will have higher efficiency than the teaching hospitals tion frontier is empirically modeled as a modified trans- and the MoH hospitals will have higher efficiency scores log function that accounts for the zero-value problem. than non-MoH hospitals. The level of the economic The function is presented below: development (income) in the province where the hospital Yildiz et al. BMC Health Services Research (2018) 18:401 Page 8 of 16 is located is hypothesized to affect the inefficiency devices does not have ‘substantial’ number of observations because socio-economic and cultural characteristics affect with zero value, to ensure consistency in our modeling access and utilization of healthcare services. Finally, approach, we modified both variables using the approach regional differences (region) are likely to affect hospital indicated in Eq. 5 to address the ‘zero-value’ problem. efficiency due to specific spatial factors. Efficiency scores among MoH hospital types or between MoH and private Results hospitals will help policy makers to identify possible inter- The maximum likelihood estimates (MLE) of the logarith- ventions in order to improve resource use of hospitals. mic modified translog stochastic production frontier and The analysis will also be able indicate whether increased inefficiency effects are presented in Tables 6 and 8, market competition by encouraging establishment of respectively. Table 6 reports the set of parameters that private hospitals will help improve efficiency of hospital explain the impact of production factors on healthcare sector in general. output. Results show that the number of non-doctor For comparative analysis of efficiency scores, hospitals health professionals (lnclinicians), ICU beds (lnicubeds),and should be compared with the most efficient hospitals administrative staff (lnadmin) are statistically significant at within the sample. Although the size of the hospitals may 5% level and have the expected positive sign. ICU beds had be associated with different scale and scope of health the largest impact on the output followed by clinicians and services, comparing relative efficiency of hospitals with administrative staff. The dummy variable controlling for the the corresponding efficiency frontier should not bias ‘zero value’ problem in devices is statistically significant and the results. Small size hospitals are compared with the negative implying that hospitals without “devices” exhibit efficient units within the same size groups as the pro- lower outputs. duction function identifies the most efficient outcomes Only the second order coefficient for ICU beds was for all hospital sizes in the sample. Therefore, estimating statistically significant and combined with statistically one production function should not necessarily be a prob- significant and positive first order ICU beds coefficient, lem unless significant part of outputs were not measured implies that hospitals investing in additional ICU beds in the data set. will be able to generate output at an increasing rate. Several In Eq. 7, the dependent variable (output) is a measure interaction terms were statistically significant indicating of aggregate hospital output which was derived by using that the usage levels of the inputs are inter-dependent on Eq. 10. Eq. 10 aggregates multiple outputs of hospitals each other. using output-specific weights, the average market prices, Output elasticities of each of the input variables at p, of hospital services. Since public funding is such a big their mean values were calculated using Eq. 8 and reported component of hospital expenditure, the prices of hospital in Table 7. The estimates were − 0.04, 0.20, 0.33, 0.12, 1.18, services set by the SSI  are considered the relevant and 0.06 for beds, clinicians, doctors, devices, ICU beds, prices to use to derive the measure of aggregate output. and staff, respectively. All, except beds were statistically significant at 1% level. ICU beds appear to be the most 5 7 X X important factor in the hospital production and exhibits output ¼ surgeries p þ beds rate 365 p iq iq i ij j q increasing returns to scale (RTS), while all other statisti- j¼1 q¼1 cally significant inputs exhibit decreasing returns to scale. þ inpatient p þðÞ delivery p i inpatient im m Next, in order of importance, are the doctors and clinicians m¼1 (e.g. nurses). Overall, hospitals in the sample exhibit in- 5 2 X X creasing RTS; a 1% increase in all inputs would increase þ ðÞ tech pþ ðÞ visits p il ih l h hospital production by 1.9%. l¼1 h¼1 Parameter estimates for the inefficiency term are pre- ð10Þ sented in Table 8. Results indicate no statistically significant Price index for each output type is generated by assign- difference in the inefficiency of the hospitals by level of eco- ing a base value of 1.00 to the least expensive transaction/ nomic development (income) of the locality. Geographically output – doctor, ER, and inpatient bed prices. This aggre- (region), only two regions, West Anatolia and Central East gation approach allows estimation of a one output frontier Anatolia, show statistically different (lower) efficiencies production function for multi-output production units. compared to the reference group of the Istanbul region. Independent variables in Eq. 7 are related to hospital Meanwhile, significant differences, as expected, are present infrastructure, technology, and human resources. Tables 4 for various hospital types. For example, the MoH General and 5 list the variables used in empirical modelling with Hospitals are found to be the most efficient hospital type. associated summary statistics. In our sample, variables The statistical difference in the inefficiency among icubeds and devices have 316 (29.3%) and 4 (0.4%) obser- hospital types and higher efficiency of MoH General vations with zero values, respectively. Even though variable Hospitals can be explained by their high utilization rate Yildiz et al. BMC Health Services Research (2018) 18:401 Page 9 of 16 Table 4 Description of variables used in empirical models and summary statistics Variable Description Mean SD Min Max Variables in Frontier Model output Hospital composite output (see Eq. 9) 14.3 M 29.0 M 2885 287 M bed Number of inpatient hospital beds 144 215 2 1816 doctors Number of doctors except residents 55 83 1 1030 clinicians Number of non-doctor health professionals 174 231 7 2006 (nurses, midwives, technicians, etc.) devices Number of X-Ray, MR, CT, ECG, Doppler 12 17 0 458 devices_d Dummy to control for zero-value problem admin Number of administrative staff 39 53 1 489 icubeds Intensive Care Unit (ICU) Beds 17 25 0 230 icubeds_d Dummy to control for zero-value problem Variables in Inefficiency term model type Hospital ownership type (%) MoH General 42.02 MoH Integrated County Hospitals 11.97 MoH Teaching 3.99 Private General 36.83 Private University 1.21 Public University 3.99 income Per capita income proxied by Regional per capita Gross Domestic Product Less than $5000 4.36 $ 5001–10,000 12.64 $ 10,001–15,000 28.94 $ 15,001–20,000 39.33 $ 20,001 and above 13.73 region Statistical regions and percent of hospitals in each region Istanbul 15.31 West Marmara 5.94 Aegean 12.8 East Marmara 8.91 West Anatolia 8.91 Mediterranean 11.41 Central Anatolia 5.94 West Black Sea 7.88 East Black Sea 4.92 North East Anatolia 3.53 Central East Anatolia 6.22 South East Anatolia 8.26 (patient volume). Many of the public sector general hos- Reported value of γ (0.97) is close to 1 indicating that pitals are the only source of hospital care in relatively much of the variation in the composite error term is due small districts. Moreover, central planning of resource to the inefficiency component (, p., 250) and only 3% is allocation and use of human resources may have affected due to random errors. Hence, hospital inefficiency is highly efficiency levels of these hospitals. important in explaining the variability of hospital output. Yildiz et al. BMC Health Services Research (2018) 18:401 Page 10 of 16 Table 5 Summary statistics for output elements and corresponding price indices Variable Description Mean SD Min Max Price index operations Number of annual surgical operations Type A 332 667 0 6485 266.53 Type B 1190 1887 0 14,757 75.73 Type C 1797 2490 0 20,611 37.60 Type D 1639 2776 0 25,107 23.13 Type E 2921 7284 0 109,748 11.07 icubeds Number of beds in the ICU units Adult level 1 70,254 163,681 0 1,617,388 16.67 Adult level 2 75,591 175,739 0 2,385,640 30.00 Adult level 3 117,145 316,273 0 3,403,698 50.00 Neonatal level 1 16,690 64,281 0 903,375 16.67 Neonatal level 2 28,028 95,935 0 1,151,502 30.00 Neonatal level 3 52,077 160,709 0 1,292,319 50.00 Pediatric 11,885 66,458 0 949,000 30.00 inpatient Number of inpatient-day (inpatient bed) utilization at each hospital. 33,072 58,193 0 470,287 1.00 Rate Average percentage of daily occupancy rates of the beds at the ICU units. Adult 32.18 34.07 0 100 na Neonatal 19.22 30.95 0 100 na Pediatric 3.39 15.79 0 100 na delivery Number of annual child deliveries Normal 328 589 0 7381 6.67 Operation 22 107 0 1595 12.00 C-section 396 527 0 4692 12.00 Tech Number of annual utilization of the diagnostics equipment ECG 365 601 0 5352 4.80 MR 653 1047 0 7371 4.80 BT 701 1244 0 10,220 4.00 Doppler 2120 6172 0 180,153 2.00 X-ray 4044 6324 0 54,205 1.00 Visits Number of annual visits to ER 75,351 90,152 0 736,292 1.00 Doctors 267,580 320,679 1685 2,405,443 1.00 “na” - not applicable Surgical operations are classified into groups A to E based on the severity of the operations Figure 1 shows the frequency distribution of technical the scores. Therefore, some of the private hospitals are efficiency scores for all six types of hospitals. The very efficient while others are very inefficient. efficiency scores of all three MoH Hospitals and Public The public and private University hospitals focus signifi- University Hospitals are skewed towards the right indicating cant amount of their resources towards clinical trainings that a higher proportion of these hospitals are among the and medical education. Educational mission often requires high efficiency groups. Distribution of efficiency scores for conducting additional clinical tests and diagnostics for private hospital types show equal distribution along the the benefit of learners implying that teaching hospitals efficiency plane. The distribution for Private Hospitals shows are likely to use higher level of resources than non- a distinctive bimodal pattern with wide variability of teaching hospitals for producing the same level of output. Yildiz et al. BMC Health Services Research (2018) 18:401 Page 11 of 16 Table 6 Frontier estimation results – translog production function Variable Coef. Std. Error Z P > z 95% Conf. Interval Frontier Model: dependent variable = log(output) Inpatient hospital beds (log) −0.3904 0.2548 −1.5300 0.1250 −0.8899 0.1090 Non-doctor clinicians (log) 1.1531 0.3090 3.7300 0.0000 0.5474 1.7587 Doctors (log) − 0.4522 0.2831 −1.6000 0.1100 −1.0071 0.1027 Devices (log) 0.2977 0.2337 1.2700 0.2030 −0.1602 0.7557 Devices dummy (=1 if no device) −0.6614 0.2165 −3.0600 0.0020 −1.0857 − 0.2372 ICU beds (log) 2.5584 0.1710 14.9600 0.0000 2.2232 2.8937 ICU beds dummy (=1 if no beds) −0.0167 0.1205 −0.1400 0.8900 −0.2528 0.2194 Administrative staff (log) 0.3217 0.1278 2.5200 0.0120 0.0713 0.5722 lnbed 0.0328 0.0436 0.7500 0.4510 −0.0526 0.1183 lnclinicians −0.1171 0.0752 −1.5600 0.1190 −0.2645 0.0302 lndoctors 0.0903 0.0726 1.2400 0.2130 −0.0519 0.2325 lndevices 0.0221 0.0270 0.8200 0.4130 −0.0308 0.0750 lnicubeds 0.1862 0.0259 7.1800 0.0000 0.1354 0.2371 lnadmin 0.0194 0.0196 0.9900 0.3210 −0.0189 0.0578 lnbed ×lnclinicians 0.1086 0.1035 1.0500 0.2940 −0.0942 0.3113 lnbed ×lndoctors −0.1246 0.1150 −1.0800 0.2790 −0.3500 0.1009 lnbed ×lndevices −0.0157 0.0941 −0.1700 0.8670 −0.2002 0.1687 lnbed ×lnicubeds −0.0876 0.0578 −1.5200 0.1290 −0.2008 0.0256 lnbed ×lnadmin 0.0598 0.0542 1.1000 0.2700 −0.0464 0.1660 lnclinicians ×lndoctors 0.2428 0.1102 2.2000 0.0280 0.0269 0.4587 lnclinicians ×lndevices −0.0267 0.1076 −0.2500 0.8040 −0.2377 0.1842 lnclinicians ×lnicubeds −0.2386 0.0606 −3.9400 0.0000 −0.3574 −0.1198 lnclinicians ×lnadmin −0.2112 0.0566 −3.7300 0.0000 −0.3221 −0.1002 lndoctors ×lndevices −0.1513 0.1005 −1.5100 0.1320 −0.3483 0.0457 lndoctors ×lnicubeds −0.1510 0.0571 −2.6400 0.0080 −0.2629 −0.0391 lndoctors ×lnadmin 0.0583 0.0691 0.8400 0.3990 −0.0771 0.1938 lndevices ×lnicubeds 0.0362 0.0457 0.7900 0.4280 −0.0533 0.1257 lndevices ×lnadmin 0.1196 0.0521 2.3000 0.0220 0.0176 0.2216 lnicubeds ×lnadmin −0.0522 0.0327 −1.6000 0.1100 −0.1162 0.0118 Constant 8.5814 0.5541 15.4900 0.0000 7.4953 9.6675 Therefore, university hospitals may become less efficient than other general hospitals. A number of research studies also found relatively low efficiency scores for teaching Table 7 Output elasticities of input variables hospitals (e.g. (p. 116) [45–47]). It is interesting that MoH Inputs Coef. Teaching hospitals show relative high efficiency scores Inpatient hospital beds −0.0399 even though teaching and learning functions are import- ant for these hospitals. Unlike the university hospitals, the Non-doctor clinicians 0.2036 principal objective of MoH teaching hospitals is to provide Doctors 0.3308 hospital services rather than teaching. These hospitals are Devices 0.1212 directly under financial and administrative oversight of ICU beds 1.1816 the MoH and implementation of cost containment Administrative staff 0.0646 strategies, centralized resource reallocation approach, Total 1.8618 and other related policies probably helped in improving individual input coefficients significant at 1% their efficiency scores. Yildiz et al. BMC Health Services Research (2018) 18:401 Page 12 of 16 Table 8 Frontier estimation results – inefficiency equation Inefficiency term model Coef. Std. Error Z P > z 95% Conf. Interval Hospital type (reference = MoH General Hospitals) MoH Integrated County −0.3087 1.0999 −0.2800 0.7790 −2.4644 1.8471 MoH Teaching −10.2968 6.2776 −1.6400 0.1010 −22.6007 2.0070 Private General 5.7161 1.5593 3.6700 0.0000 2.6598 8.7723 Private University 5.3802 1.7796 3.0200 0.0030 1.8923 8.8682 Public University 1.9877 1.3731 1.4500 0.1480 −0.7036 4.6790 Provincial per capita income (reference = less than $5000) $ 5001–10,000 1.1581 1.4513 0.8000 0.4250 −1.6864 4.0026 $ 10,001–15,000 0.1728 1.0065 0.1700 0.8640 −1.7999 2.1455 $ 15,001–20,000 0.2287 1.1706 0.2000 0.8450 −2.0657 2.5231 Over $20,000 0.7793 1.2776 0.6100 0.5420 −1.7247 3.2834 Regions (reference = Istanbul) West Marmara 0.0169 0.8593 0.0200 0.9840 −1.6673 1.7010 Aegean 0.3144 0.7433 0.4200 0.6720 −1.1424 1.7712 East Marmara 0.9828 0.7174 1.3700 0.1710 −0.4232 2.3888 West Anatolia 1.3406 0.6433 2.0800 0.0370 0.0798 2.6014 Mediterranean −0.5174 0.6444 −0.8000 0.4220 −1.7805 0.7456 Central Anatolia 1.5293 0.9611 1.5900 0.1120 −0.3543 3.4130 West Black Sea −0.0208 1.0204 −0.0200 0.9840 −2.0209 1.9792 East Black Sea −2.3229 1.7857 −1.3000 0.1930 −5.8228 1.1770 North East Anatolia −0.2497 1.7456 −0.1400 0.8860 −3.6711 3.1717 Central East Anatolia 2.2611 1.0253 2.2100 0.0270 0.2515 4.2708 South East Anatolia 0.0522 1.3654 0.0400 0.9690 −2.6240 2.7284 Constant −7.2108 2.6058 −2.7700 0.0060 −12.3182 −2.1035 ln ðσ Þ 1.0157 0.2782 3.6500 0.0000 0.4704 1.5610 exp(γ)/[exp(γ) + 1] 3.6915 0.2975 12.4100 0.0000 3.1085 4.2745 2 2 2 2.7613 0.7683 1.6006 4.7638 σ ¼ σ þ σ S v v 2 2 γ ¼ σ =σ 0.9757 0.0071 0.9572 0.9863 u v σ 2.6942 0.7672 1.1905 4.1978 σ 0.0672 0.0086 0.0503 0.0840 Figure 2 illustrates the average technical efficiency to provide basic health services and to function as the (ATE) scores of various hospital types. The ATE score social safety net facility in relatively remote and rural for all hospitals was 0.63 and ranged from 0.01 to 0.94 areas. These hospitals regularly refer more serious cases with a median of 0.73. About one third of these hospitals to general or teaching hospitals after initial consultation had a technical efficiency score between 0.80 and 1.00 or urgent care. They serve basic surgery needs and non- and another one third had a score between 0.60 and risk deliveries. They transfers higher risk patients to 0.80. The MoH hospital types reported the highest ATE general hospitals after stabilizing their health condition. scores with the MoH Teaching Hospitals leading the The MoH allocates a sufficient number of doctors to these group. Public university hospitals follow the MoH hospitals hospitals. However, they are not as ‘busy’ as they would in ATE score. Private hospitals reported the lowest ATE have been in other types of hospitals. Hence, we have a score. Within the MoH hospitals, the Integrated hospitals situation where fewer inpatient and outpatient patients are serve low population density rural provinces. As can be served by greater number of doctors and other healthcare seen from Fig. 2, the integrated hospitals exhibit lower professionals, thus, contributing towards lower efficiency. ATE than the MoH Teaching hospitals. This is not Private hospitals report the lowest ATE scores and surprising because the primary role of these hospitals is their technical efficiencies follow a bimodal distribution Yildiz et al. BMC Health Services Research (2018) 18:401 Page 13 of 16 Fig. 1 Distribution of Technical Efficiency Scores by Hospital Type (Fig. 1). This is also consistent with the nature of private private hospitals tend to fill gaps in hospital services but hospital market in Turkey. Private hospitals in Turkey metropolitan private hospitals serve customers from can be subdivided into two types – smaller hospitals higher socioeconomic groups. With increasing income with limited service availability and highly specialized of the population, private hospitals are becoming more large scale chain hospitals. The lower end of efficiency popular in urban areas and since these hospitals have score distribution among private hospitals represents to compete with MoH general hospitals for patients, mainly the small hospitals while the higher efficiency remaining efficient is important to maintain or increase hospitals are the larger comprehensive hospitals. Rural the market share. Fig. 2 Mean Technical Efficiency Scores and 95% Confidence Interval by Hospital Type Yildiz et al. BMC Health Services Research (2018) 18:401 Page 14 of 16 Discussion The estimation approach incorporates a number of new The relative efficiency scores of hospital types indicate empirical aspects for deriving the efficiency scores for that overall efficiency of hospital sector of Turkey can be multi-product firms. The production and technical efficiency improved by encouraging more effective use of resources. functions are estimated simultaneously and a modification In fact, increasing market share of public hospitals will also has been introduced to account for zero-value inputs in the improve efficiency of resource use. Since the small private logarithmic production function. Assuming that relative hospitals are the least efficient, policy makers should iden- prices of various hospital outputs remain more or less tify strategies to improve efficiency of these hospitals. The constant across hospitals, Hicksian aggregation principle integrated public hospitals may be able to improve technical can be used to derive the composite index of output. All efficiency by becoming better integrated with local private significant estimates in the regression model had expected clinics and other hospitals in rural communities. signs. Technical efficiency of hospitals varied across hos- Affiliation system, which was implemented by the MoH pital types but not across level of economic development in 2011 , facilitates collaboration between University of the region in which the hospitals are located. The ana- and MoH hospitals by utilizing each other’s resources. lysis also indicates that technical efficiency scores of MoH Newly established university hospitals have the opportunity hospitals are better than those for other hospital types. to use MOH hospitals’ relatively better infrastructures It is interesting to note that not all private hospitals are while MoH hospitals benefit from the expertise and efficient and many are highly inefficient. Small private specialization of university hospitals. In the long-run, hospitals are the least efficient hospital category among all this approach may help improve efficiency of both Public the hospital-types in Turkey. The MoH general hospitals University and MoH Teaching hospitals. Similar arrange- were the most efficient hospital category, often better than ments between MoH, private university, and private the urban private hospitals. The efficiency scores of rural hospitals should also be useful in improving efficiency MoH hospitals are relatively low but these hospitals are of both private university hospitals and other general designed as the safety net units in rural areas. private hospitals. Additional efficiency improvements As expected, the University hospitals, both private are expected as a result of 2012 reform that established and public, were less efficient than other non-university the PHUs through the unification of MoH hospitals of hospitals, except for Private General Hospitals. The various categories. The unifications are accompanied by university hospitals have the important social objective implementation of a set of common cost containment of training health professionals and specialists and and quality control measures, implying that hospitals therefore, unless the value of medical trainings is taken will become more homogeneous in terms of efficiency. into account as additional output, these facilities will The reforms initiated by Government of Turkey aimed show low efficiency scores. In that sense, low efficiency at improving technical efficiency of all hospitals, especially scores of university hospitals may not necessarily be the secondary and tertiary hospitals. Our findings from interpreted as indication of inefficient use of resources. 2012 indicate significant variability in the efficiency scores The values these hospitals create in terms of training of hospitals. The expectation is that this variability in effi- may more than offset the additional resources used. ciency scores across hospitals will reduce over the years if Interestingly, the MoH teaching hospitals turned out to be the reform initiatives are successful. Our findings may be quite efficient in relative terms. The health sector reform used as the baseline to evaluate the effect of these hospital in Turkey has emphasized better management of MoH sector reforms on hospital efficiency. Future research hospitals and it is possible that improved management studies can re-estimate efficiency scores to see how the practices have enhanced relative efficiency scores of MoH variability of scores changed over the years with an teaching hospitals as well. expectation that the range and variability of hospital Turkey considers highly specialized private hospital efficiency scores will decline over time. The continued sector an important component of overall health care reforms are explicitly aiming at improving efficiency by system and the results suggest that encouraging estab- encouraging sharing of resources to maximize hospital lishment of private specialized hospitals will improve production and to improve operational efficiency. If overall efficiency. To promote investments in large-scale reforms are successful, we should see improvements in private hospitals, the Government of Turkey will be creat- overall efficiency scores and reductions in the variability ing “health zones” throughout the country to attract foreign of the scores across hospitals of different types and sizes. direct investment [23, 49]. Conclusions Endnotes This study has estimated the technical inefficiency A variation of COLS called Modified OLS (MOLS) scores for public and private hospitals using a recent was proposed by Afrait  and Richmond , which and comprehensive hospital dataset available for Turkey. is very similar to the two-step COLS procedure. Yildiz et al. BMC Health Services Research (2018) 18:401 Page 15 of 16 11. Battese GE, Coelli TJ. A stochastic frontier production function incorporating LR ¼ −2½ lnðLðH Þ=LðH ÞÞ∼Χ where L(H ) is the 0 1 0 ðnÞ a model for technical inefficiency effects. Armidale: Department of likelihood value of the restricted estimate, L(H )is Econometrics. University of New England; 1993. the likelihood value of for the unrestricted estimate, 12. Battese GE, Coelli TJ. A model for technical inefficiency effects in a stochastic frontier production function for panel data. Empir Econ. 1995; and n is the number of restrictions imposed by the 20(2):325–32. null hypothesis . 13. 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