STATISTICAL EVALUATION OF EXAMINATION TESTS IN MATHEMATICS FOR ECONOMISTS

Examination results are rather important for many students with regard to their future profession development. Results of exams should be carefully inspected by the teachers to help improve design and evaluation of tests and education process in general. Analysis of examination papers in mathematics taken by students of basic mathematics course at University of Economics in Prague is reported. The first issue addressed is identification of significant dependencies between performance in particular problem areas covered in the test and also between particular items and total score in test or ability level as a latent trait. The assessment is first performed with Spearman correlation coefficient, items in the test are then evaluated within Item Response Theory framework. The second analytical task addressed is a search for groups of students who are similar with respect to performance in test. Cluster analysis is performed using partitioning around medoids method and final model selection is made according to average silhouette width. Results of clustering, which may be also considered in connection with setting of the minimum score for passing the exam, show that two groups of students can be identified. The group which may be called "well-performers" is the more clearly defined one

MULTIPLE CHOICE QUESTION TESTS FOR ENTRANCE EXAMINATIONS - A PROBABILISTIC APPROACH

In this paper we shall analyze multiple choice question tests for entrance examinations from probability point of view. Multiple choice question tests are used for example for entrance examinations at Prague University of Economics, we shall analyze these tests at the Faculty of Business Administration. We shall report on probability methods, which can be used for modelling of these tests. In this case model of binomial distribution can be used for answering the following questions (under assumption of random choice of answers): what is the probability, that the number of correct answers exceeds given number, what is expected number of correct answers, etc. Results of this analysis can be used for consideration of the appropriateness of these tests

Calculation of Acceptance Sampling Plans for Inspection by Variables

Analysis of several acceptance sampling procedures is performed and improvement of the procedures is sug- gested in this thesis. The issue of an efficient calculation of exact (P1, P2) single sampling plans for sampling by variables and exact LTPD and AOQL single sampling plans for sampling by variables when the rejected lots are inspected is addressed. The calculation of the plans is done using exact formula for operating characteristic of acceptance sampling plan and the new plans have better characteristics compared to the plans computed in a usual way using just approximately valid formula for operating characteristic. The tables of plans calculated according to procedures suggested in this thesis are provided for a couple of input parameters combinations. Tools designed for working with acceptance sampling plans, tools for analysis and calculation of acceptance sampling plans is one of the outputs of this thesis. R language and environment for statistical computations was chosen for implementation. The tools are satisfactorily efficient and may be easily used even for acceptance sampling plans tables computation. Newly defined functions in R are supplied including their source code and basic documentation so that acceptance sampling plans can be computed as demanded in case that the particular input parameters set is out of the scope covered in the tables of plans provided here

Calculation of Acceptance Sampling Plans for Inspection by Variables

Cílem práce je provést analýzu některých přejímacích postupů a navrhnout jejich vylepšení. Práce je zaměřena na efektivní výpočet přesných přejímacích plánů (P1, P2) při jednovýběrové přejímce měřením a kombinovaných opravných přejímacích plánů LTPD a AOQL Při výpočtech se pracuje s přesným vztahem pro operativní charakteristiku přejímacího plánu a nové plány mají lepší vlastnosti než plány spočtené podle obvyklého postupu s využitím přibližného vztahu pro operativní charakteristiku. Plány spočtené podle postupu v práci navrženého jsou pro některé vybrané hodnoty vstupních parametrů tabelovány. K výsledkům práce patří nástroje určené pro práci s přejímacími plány, nástroje pro určování a analýzu přejímacích plánů. Pro praktickou realizaci výpočtů bylo zvoleno statistické výpočetní prostředí R. Vytvořené prostředky v prostředí R jsou dostatečně efektivní a použitelné i pro tabelaci přejímacích plánů. Nové funkce jsou v této práci uvedeny včetně jejich definice v jazyce R (zdrojový kód) a základní dokumentace a s jejich využitím je tak možné snadno spočítat přejímací plány podle požadavků i v případě, že zvolená kombinace hodnot parametrů není pokryta v tabulkách uvedených v této práci.Analysis of several acceptance sampling procedures is performed and improvement of the procedures is sug- gested in this thesis. The issue of an efficient calculation of exact (P1, P2) single sampling plans for sampling by variables and exact LTPD and AOQL single sampling plans for sampling by variables when the rejected lots are inspected is addressed. The calculation of the plans is done using exact formula for operating characteristic of acceptance sampling plan and the new plans have better characteristics compared to the plans computed in a usual way using just approximately valid formula for operating characteristic. The tables of plans calculated according to procedures suggested in this thesis are provided for a couple of input parameters combinations. Tools designed for working with acceptance sampling plans, tools for analysis and calculation of acceptance sampling plans is one of the outputs of this thesis. R language and environment for statistical computations was chosen for implementation. The tools are satisfactorily efficient and may be easily used even for acceptance sampling plans tables computation. Newly defined functions in R are supplied including their source code and basic documentation so that acceptance sampling plans can be computed as demanded in case that the particular input parameters set is out of the scope covered in the tables of plans provided here

Rectifying acceptance sampling plans

Tuto habilitační práci tvoří soubor pěti uveřejněných vědeckých prací doplněný sjednocujícím komentářem. Zařazené práce přinášejí původní výsledky v oblasti plánů pro kombinované opravné statistické přejímky typu AOQL a LTPD minimalizujícím střední náklady kontroly při průměrném podílu neshodných (tj. požadavkům nevyhovujících) výrobků. Nové výsledky umožňují efektivní výpočet plánů a snížení nákladů přejímky.This habilitation thesis addresses selected problems of statistical acceptance sampling, namely the design, calculation and economic evaluation of the rectifying LTPD and AOQL sampling plans minimizing the mean inspection cost per lot of the process average quality. The thesis is based on five publications which bring efficient calculation of the acceptance sampling plans and lower cost of inspection

Technological relatedness, knowledge space and smart specialisation: The case of Germany

The level of technological specialisation in the regions of Germany is assessed in this paper, as well as how such specialisation has evolved over time. Further, in three selected regions (Munich, Düsseldorf and Oberes Elbtal/Osterzgebirge), the knowledge space is explored in detail and compared to existing smart specialisation strategies. Average relatedness and knowledge space based upon EPO patent applications are used to measure the specialisation and technology trajectories of the German regions. Between three periods 1988-1992, 1998-2002 and 2008-2012, the specialisation of Germany based on EPO patent applications increased by 10%, despite a decline in many regions. Machinery and transportation industries have increased their significance. The assessment of regional smart specialisation strategies in the three German states shows that the methodology in terms of the identification of prospective industries is largely variegated and insufficiently developed. More attention should also be given to the choice of an appropriate geographical level of aggregation for analysis. Knowledge relatedness and knowledge complexity could be used as methodological tools for selecting prospective industries in smart specialisation strategies.9510

Technological relatedness, knowledge space and smart specialisation :the case of Germany

The level of technological specialisation in the regions of Germany is assessed in this paper, as well as how such specialisation has evolved over time. Further, in three selected regions (Munich, Düsseldorf and Oberes Elbtal/Osterzgebirge), the knowledge space is explored in detail and compared to existing smart specialisation strategies. Average relatedness and knowledge space based upon EPO patent applications are used to measure the specialisation and technology trajectories of the German regions. Between three periods 1988-1992, 1998-2002 and 2008-2012, the specialisation of Germany based on EPO patent applications increased by 10%, despite a decline in many regions. Machinery and transportation industries have increased their significance. The assessment of regional smart specialisation strategies in the three German states shows that the methodology in terms of the identification of prospective industries is largely variegated and insufficiently developed. More attention should also be given to the choice of an appropriate geographical level of aggregation for analysis. Knowledge relatedness and knowledge complexity could be used as methodological tools for selecting prospective industries in smart specialisation strategies.9510

Progranulin Is Associated with Disease Activity in Patients with Rheumatoid Arthritis

Objective. Progranulin (PGRN) is implicated in the pathogenesis of rheumatoid arthritis (RA). The aim of this study was to assess the relationship between PGRN and disease activity in RA. Methods. PGRN levels were evaluated in patients with RA (n=47) and OA (n=42) and healthy controls (n=41). Immunohistochemical analysis of PGRN in synovial tissues was performed. The association between PGRN and C-reactive protein (CRP), disease activity score (DAS28-CRP), and health assessment questionnaire (HAQ) was studied. Results. Circulating PGRN was elevated in patients with RA and OA compared to healthy controls (227.1±100.2 and 221.5±102.5 versus 128.1±34.7 ng/mL; P<0.001). Synovial fluid levels of PGRN were higher in patients with RA compared to OA (384.5±275.3 versus 241.4±165.2 ng/mL; P=0.002). PGRN expression was significantly upregulated in the synovial tissue of RA patients particularly in the inflammatory infiltrates. Serum PGRN levels correlated with DAS28 (r=0.327, P=0.049) and HAQ score (r=0.323, P=0.032), while synovial fluid PGRN correlated only with HAQ (r=0.310, P=0.043) in patients with RA. PGRN levels were not associated with CRP or autoantibodies. Conclusions. This study demonstrates increased PGRN expression at local sites of inflammation and association between PGRN levels, disease activity, and functional impairment in patients with RA