The impact of uneven filling two-way contingency tables on the critical value of the test statistics

2016 ◽  
Vol 61 (4) ◽  
pp. 1-16
Author(s):  
Piotr Sulewski ◽  
Antoni Drapella
Keyword(s):  
Statistical Modeling ◽  
Contingency Tables ◽  
Critical Value ◽  
Small Sample ◽  
Test Statistics ◽  
Chi Square ◽  
Independent Verification ◽  
Power Of The Test ◽  
The Impact ◽  
Measures Of Inequality

The article concerns two-way (2×2) contingency tables. When the H0— hypothesis of independence of features is correct, very often — because of the small sample — the distribution of the test statistics differ from the chi-square. Quantile of the chi-square is therefore not a correct critical value. With the current performance of computers, designation of critical value by statistical modeling of Monte Carlo method is not a problem, but a problem is H0 modeling. The H0 modeling is generating such arrays, which feature value assigned rows are independent of the characteristics of the assigned columns. Suitable for such modeling are tables — uniform of the same probability of belonging to cells and uneven having equal probability in all rows of a given column or in all columns of a given row. Analysis of the results of statistical modeling revealed that even when H0 is right, the distribution of the test statistics significantly depends on the uneven array. The article shows that in order to maximize the power of the test should be set critical value, taking into account measures of inequality array. The final result of the study is offered the reader a ready tool for independent verification of the H0 hypothesis.

scholarly journals Conditional Inference in Small Sample Scenarios Using a Resampling Approach

Stats ◽  
2021 ◽  
Vol 4 (4) ◽  
pp. 837-849
Author(s):  
Clemens Draxler ◽  
Andreas Kurz
Keyword(s):  
Power Function ◽  
Small Sample Size ◽  
R Package ◽  
Small Sample ◽  
Conditional Inference ◽  
Test Statistics ◽  
Chi Square ◽  
Large Sample Theory ◽  
Chi Square Test ◽  
True Values

This paper discusses a non-parametric resampling technique in the context of multidimensional or multiparameter hypothesis testing of assumptions of the Rasch model. It is based on conditional distributions and it is suggested in small sample size scenarios as an alternative to the application of asymptotic or large sample theory. The exact sampling distribution of various well-known chi-square test statistics like Wald, likelihood ratio, score, and gradient tests as well as others can be arbitrarily well approximated in this way. A procedure to compute the power function of the tests is also presented. A number of examples of scenarios are discussed in which the power function of the test does not converge to 1 with an increasing deviation of the true values of the parameters of interest from the values specified in the hypothesis to be tested. Finally, an attempt to modify the critical region of the tests is made aiming at improving the power and an R package is provided.

scholarly journals The Influence of Decontamination Procedures on the Surface of Two Polymeric Liners Used in Prosthodontics

Polymers ◽  
2021 ◽  
Vol 13 (24) ◽  
pp. 4340
Author(s):  
Katarzyna Mańka-Malara ◽  
Maciej Trzaskowski ◽  
Dominika Gawlak
Keyword(s):  
New York ◽  
Soft Tissues ◽  
Small Sample Size ◽  
Polymeric Materials ◽  
Small Sample ◽  
Chi Square ◽  
Exact Test ◽  
Materials Used ◽  
Cleaning Methods ◽  
The Impact

Polymeric liners are materials commonly used in prosthodontics to reshape denture surfaces contacting the soft tissues of the oral cavity. The aim of the study was to determine the impact of different cleaning methods on two polymeric materials used in prosthodontics as non-adhesive permanent liners. The material for the research consisted of samples made from Mollosil Plus (Detax, Ettlingen, Germany)—direct polysiloxan liner; and Plastitanium (Pressing Dental, San Marino, Republic of San Marino)—an injection-molded liner. A total of 198 samples were made, 99 of each assessed material. They were exposed to different cleaning methods—a toothbrush, a toothbrush and soap, a toothbrush and toothpaste (BlendaMed, Procter&Gamble, Cincinnati, OH, USA), a toothpaste and denture cleaning paste (Protefix Hygiene Denture Paste, Queisser Pharma, Germany), denture cleansing tablets (Protefix Hygiene Cleaning Tablets, Queisse Pharma, Germany), and a disinfecting spray (Aftermat, Port Jefferson Station, New York City, NY, USA)—for 1 min, 5 min, 10 min, and 15 min. The image acquisition was performed with scanning electron microscopy and samples were analyzed for the homogeneity of their surfaces—the presence of holes, grooves, precipitate, and small and large separating pieces of the material marking departures from this homogeneity. For each type of damage, one point was given. Continuous data from two groups were compared with Mann–Whitney U testing. Due to a small sample size and distribution of variables other than normal, to compare more than two groups, Kruskal–Wallis testing with post hoc analysis (Dunn test with Bonferroni correction) was used. Categorical data were compared with the chi-square test and the Fisher’s exact test. The Mollosil Plus material should be decontaminated with the use of a toothbrush or toothbrush with soap, while Plastitanium material should be disinfected. Plastitanium samples are more susceptible to damage during the decontamination procedures than Mollosil Plus.

9 Impact of Methadone Initiation in Intubated Burn Patients: A Retrospective Review

2021 ◽  
Vol 42 (Supplement_1) ◽  
pp. S12-S12
Author(s):  
Sarah Zavala ◽  
Gabrielle Wasilewski ◽  
Anisha Sharma ◽  
Olga Bulakh ◽  
Joseph Fahmy ◽  
...  
Keyword(s):  
Pain Management ◽  
Small Sample Size ◽  
Total Body Surface Area ◽  
Small Sample ◽  
Burn Patients ◽  
Average Daily Dose ◽  
Nominal Data ◽  
Chi Square ◽  
Daily Dose ◽  
The Impact

Abstract Introduction Methadone can be used to wean opiates and reduce length of mechanical ventilation (MV) in critical care and burn patients. The objective of this study was to assess the impact of methadone use on ventilator-free days and clinical outcomes in burned patients requiring MV. Methods This was a retrospective study of adult patients admitted to a burn center for initial management of burn injuries who required MV for at least 48 hours between September 2013 and November 2019. Patients were excluded from the study if they had prior methadone use, total body surface area (TBSA) of less than 5%, or expired within the first 28 days of admission. The primary endpoint was the difference in ventilator-free days among those who received methadone compared to those who did not. Secondary endpoints include length of stay, mortality, sedative agent and average daily dose, analgesic agent and average daily dose, and incidence of delirium. Baseline demographics were compared using descriptive statistics. Nominal data was compared using Chi-square test. Continuous data was analyzed using student’s t-test or Mann-Whitney U test, as appropriate. Multivariate regression was used to identify variables for possible association with MV duration. Results A total of 83 patients were included in the study; 52 received methadone and 31 were controls. Patients were generally well-matched between groups, however patients receiving methadone were younger (45.3 vs 56.2 years, p = 0.002) and had a larger TBSA (30.4 vs 19.1%, p = 0.001). Patients who received methadone had fewer ventilator free days of the first 28 (9.5 vs 15.0 days, p = 0.009) and a longer ICU stay (57.2 vs 35.8 days, p = 0.025). There was no difference between groups in terms of mortality, reintubations, and incidence of delirium. Patients who received methadone had longer duration of analgesia (20.7 vs 12.0 days, p = 0.011) and sedation (19.0 vs 12.4 days, p = 0.026) while on MV. Conclusions This study found that methadone use contributed to fewer ventilator-free days and longer ICU stays, which was unexpected but worth discussing. There are several limitations to this study. This study occurred during a time period in which the pain management and sedation strategies of this burn unit were evolving, and strategies may not have been consistent between providers. The study included a small sample size and baseline demographics demonstrated significant differences in age and TBSA between the two groups. Additionally, pain scores were not collected as part of this study, which would have provided better insight into the effectiveness of pain management. The use of methadone as an adjunct for pain control remains undetermined.

STATISTICAL METHODS IN MEDICAL RESEARCH: I. QUALITATIVE STATISTICS (ENUMERATION DATA)

1948 ◽  
Vol 26e (1) ◽  
pp. 1-166 ◽  
Author(s):  
Donald Mainland
Keyword(s):  
Standard Deviation ◽  
Experimental Design ◽  
Random Sampling ◽  
Contingency Tables ◽  
Laboratory Data ◽  
Statistical Treatment ◽  
Small Sample ◽  
Confidence Limits ◽  
Chi Square ◽  
Contingency Test

This article is designed to help investigators in applying to qualitatively classified clinical and laboratory data the appropriate statistical treatment—tests of significance in binomial and multinomial distributions, estimation of confidence limits, analysis of contingency tables, and estimation of sample sizes required for further investigation. Section A is a brief introduction (definitions and principles). Section B comprises 40 examples classified so that the investigator can choose data and problems comparable to his own. Questions that arise in the examples, regarding experimental design (especially random sampling) and the interpretation of the tests, are discussed in Section C (Notes).Because the standard deviation of the binomial and the chi square contingency test are often used without appreciation of the risk entailed, tables, which can be used also in nonmedical investigation, are presented: binomial confidence limits (with graphs) and exact probabilities for small-sample fourfold contingency tables. For samples not covered by the tables, precautions and rules regarding the use of chi square have been derived from more than five hundred comparisons between chi square and the exact method. To help in the exact computation of probabilities where that is necessary, four-decimal logarithms of factorials of numbers up to 1000 are given.

Reconnoitering the Impact of Education on Observance of Purdah (Veil)

2021 ◽  
Vol 39 (- 1) ◽  
Author(s):  
Imran ◽  
Shahid Iqbal
Keyword(s):  
Multivariate Analysis ◽  
Positive Relationship ◽  
Survey Methodology ◽  
Family Values ◽  
Test Statistics ◽  
Traditional Values ◽  
Chi Square ◽  
Dependent Variables ◽  
The Impact ◽  
The Relationship

The study was designed to explore perceptions of different stakeholders regarding the impact of education on the observance of Purdah in the wake of modernization. To examine the phenomena, the Survey methodology was used for investigation. The quantitative data was obtained through a five-point Likert scale questionnaire from different sampled groups i.e. intellectuals, lawyers, politicians, community leaders, and literary persons. The data was analyzed through univariate, bivariate, and multivariate analyses. The association between independent and dependent variables was measured through Chi-square (χ2) whereas multivariate analysis was employed while controlling marital status. The overall findings signposted a non-significant and positive relationship between increased schooling breaks down traditional values and norms, including family values and change in observance of Purdah. On another hand, a significant and positive relationship was identified between education as one of the important indicators of modernization in Pakhtun society and the dependent variable. Similarly, the relationship between modernization leads to the emergence of different types of education systems in Pakistan, and the observance of Purdah was noticed as significant and positive. The overall test statistics of the multivariate analysis revealed a highly significant, positive, and non-spurious relationship.

scholarly journals Evaluation of Test Statistics for Detection of Outliers and Shifts

2020 ◽  
Vol 4 (2) ◽  
pp. 54-75
Author(s):  
Amena Urooj ◽  
Zahid Asghar
Keyword(s):  
Time Series ◽  
Sample Size ◽  
Structural Breaks ◽  
Time Series Data ◽  
Model Identification ◽  
Small Sample ◽  
Critical Values ◽  
Series Data ◽  
Test Statistics ◽  
The Impact

Existence of outliers and structural breaks having mutually unknown nature, in time series data, offer challenges to data analysts in model identification, estimation and validation. Detection of these outliers has been an important area of research in time series since long. To analyze the impact of these structural breaks and outliers on model identification, estimation and their inferential analysis, we use two data generating processes: MA(1) and ARMA(1,1). The performance of the test statistics for detecting additive outlier(AO), innovative outlier(IO), level shift(LS) and transient change(TC) is investigated using simulation strategy through power of a test, empirical level of significance, empirical critical values, misspecification frequencies and sampling distribution of estimators for the two models. The empirical critical values are found higher than the theoretical cut-off points, empirical power of the test statistics is not satisfactory for small sample size, large cut-off points and large model coefficient. We have explored confusion between LS, AO, TC and IO at different critical values(c) by varying sample size. We have also collected empirical evidence from time series data for Pakistan using 3-stage iterative procedure to detect multiple outliers and structural breaks. We find that neglecting shocks lead to wrong identification, biased estimation and excess kurtosis. JEL Classification Codes: C15, C18, C63, C32, C87, C51, C52, C82 AMS Classification Codes: 62, 65, 91, DI, 62-08, 62J20, 00A72, 91-08, 91-10, 91-11 62P20, 91B82, 91B84, 62M07, 62M09, 62M10, 62M15, 62M20

An influence of social isolation on the level of physical activity as well as on well-being and mental state of people during the coronavirus COVID-19 pandemic

2019 ◽  
Vol 129 (4) ◽  
pp. 127-131
Author(s):  
Agnieszka Parfin ◽  
Krystian Wdowiak ◽  
Marzena Furtak-Niczyporuk ◽  
Jolanta Herda
Keyword(s):  
Physical Activity ◽  
Social Isolation ◽  
Small Sample Size ◽  
Statistical Tests ◽  
Population Group ◽  
Well Being ◽  
Small Sample ◽  
Subjective Well Being ◽  
Tract Infections ◽  
The Impact

AbstractIntroduction. The COVID-19 is the name of an infectious disease caused by a new strain of coronavirus SARS-CoV-2 (Severe Acute Respiratory Syndrome Coronavirus 2). It was first diagnosed in December 2019 in patients in Wuhan City, Hubei Province, China. The symptoms are dominated by features of respiratory tract infections, in some patients with a very severe course leading to respiratory failure and, in extreme cases to death. Due to the spread of the infection worldwide, the WHO declared a pandemic in March 2020.Aim. An investigation of the impact of social isolation introduced due to the coronavirus pandemic on selected aspects of life. The researchers focused on observing changes in habits related to physical activity and their connections with people’s subjective well-being and emotional state.Material and methods. The study was carried out within the international project of the group „IRG on COVID and exercise”. The research tool was a standardized questionnaire.Results. Based on the data collected and the analysis of the percentage results, it can be observed that the overwhelming majority of people taking up physical activity reported a better mood during the pandemic. However, statistical tests do not confirm these relationships due to the small sample size.Conclusions. Isolation favours physical activity. Future, in-depth studies, by enlarging the population group, are necessary to confirm the above observations.

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