Two‐sample Problems in Statistical Data Modelling

Abstract

Abstract. A common problem in mathematical statistics is to check whether two samples differ from each other. From modelling point of view it is possible to make a statistical test for the equality of two means or alternatively two distribution functions. The second approach allows to represent the two-sample test graphically. This can be done by adding simultaneous confidence bands to the probability-probability (P − P ) or quantile-quantile (Q − Q) plots. In this paper we compare empirically the accuracy of the classical two-sample t-test, empirical likelihood method and several bootstrap methods. For a real data example both Q − Q and P − P plots with simultaneous confidence bands have been plotted using the smoothed empirical likelihood and smoothed bootstrap methods.

Association of Endotoxemia with Low-Grade Inflammation, Metabolic Syndrome and Distinct Response to Lipopolysaccharide in Type 1 Diabetes

“…In this study, 74 patients with T1DM were included. In the T1D group, the median diabetes duration was 21 (13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32) years and 31 subjects had MS. Compared to patients without MS, subjects with MS had a higher BMI, waist/height ratio and prevalence of diabetic complications and used antihypertensive and lipid-lowering medications more frequently.…”

“…In brief, patients with diabetes and controls did not differ in anthropometric measures and gender distribution. Compared to subjects in the control group, patients with diabetes were older (control: 35 (30)(31)(32)(33)(34)(35)(36)(37)(38)(39)(40)(41)(42)(43)(44) years; T1D: 43 (34-51), p = 0.013); had higher HbA1c levels (control: 5.2 (5.0-5.5), T1D: 7.7 (6.9-9.3), p < 0.001); had a higher prevalence of MS (control: 4 (12.1%), T1D: 31 (41.9%), p = 0.005), hypertension (control: 7 (21.2%), T1D: 35 (27.0%), p = 0.019) CVD (control: 0 (0%), T1D: 9 (12.2%), p = 0.086) and autoimmune thyroid disease (control: 1 (3%), T1D: 19 (25.7%), p = 0.012); and had a higher level of albuminuria (control: 0.32 (0.11-0.76), T1D: 0.32 (0.11-0.76), p = 0.013) and lower level of insulin sensitivity as assessed using eGDR (control: 7.1 (5.5-7.7), T1D: 3.3 (1.6-5.7), p < 0.001).…”

“…In this work, we utilized several novel approaches of statistical analysis in addition to conventionally used methods; for example, for data normalization between the plates, a transformation based on the two-sample location-scale model was used [28,29]. For two-distribution comparisons, we used the smoothed empirical likelihood method for the probability-probability (PP) plot [30][31][32]. In addition, the empirical likelihood method for the equality test of all deciles of two distributions, which allows for obtaining information about the differences or similarities of two samples, was applied for data analysis [33].…”

Badanie dokładności opracowania sytuacyjnego wielkoskalowych map cyfrowych

“…W klasycznych metodach estymacji przyjmowane jest założenie o typie rozkła-du gęstości prawdopodobieństwa wystąpienia elementów próby empirycznej, co bez analizy probabilistycznej typu rozkładu może prowadzić do błędnego oszacowania przedziałów ufności wyznaczanych parametrów [61]. Ponadto klasyczne procedury badań statystycznych są wrażliwe na wydłużone rozkłady analizowanych zbiorów i wystąpienie w nich wartości odstających [52]. W związku z powyższym, w ramach przeprowadzonych badań [19] poszukiwano rzeczywisty rozkład zbiorów empirycznych oraz zastosowano metody statystyki nieparametrycznej i metody odporne na występowanie elementów odstających w zbiorach błędów punktów kontrolnych ocenianych map cyfrowych.…”

Association of endotoxaemia with low grade inflammation, metabolic syndrome and distinct response to lipopolysaccharide in type 1 diabetes

“…Page 3/17 28,29 . Third, in this work we also use the empirical likelihood method for the equality test of all deciles of two distributions, which naturally includes the important median comparison as well.…”