Summarizing data

2010 ◽  
pp. 173-187
Author(s):  
Janet L. Peacock ◽  
Philip J. Peacock
Keyword(s):  
Categorical Data ◽  
Quantitative Data ◽  
Geometric Mean ◽  
Interquartile Range ◽  
Harmonic Mean ◽  
Summary Measure

Why summarize data? 174 Types of data 176 Quantitative data 178 Categorical data 180 Summarizing quantitative data 182 Calculation of mean, SD 184 Calculation of median, interquartile range 186 Geometric mean, harmonic mean, mode 188 Choosing a summary measure for quantitative data 190 Summarizing categorical data ...

Prevalence of Hypersensitivity in Teeth Affected by Molar-Incisor Hypomineralization (MIH)

2019 ◽  
Vol 53 (4) ◽  
pp. 424-430 ◽  
Author(s):  
Fernanda Raposo ◽  
Ana Cristina de Carvalho Rodrigues ◽  
Érica Negrini Lia ◽  
Soraya Coelho Leal
Keyword(s):  
Categorical Data ◽  
Quantitative Data ◽  
Analogue Scale ◽  
Confounding Factor ◽  
Multiple Comparisons ◽  
Air Blast ◽  
Low Intensity ◽  
Carious Lesions ◽  
Molar Incisor Hypomineralization ◽  
New Criterion

Aim: This study aimed to investigate the prevalence of hypersensitivity in molar-incisor hypomineralization (MIH)-affected molars through a census carried out in 8-year-old schoolchildren. Methods: Examinations were conducted by a calibrated examiner, using the Nyvad criteria for caries diagnosis and a new criterion for MIH assessment. For hypersensitivity assessment, all MIH-affected molars were included. Nonaffected molars from the same child were used as controls. Air blast reaction was measured using the Visual Analogue Scale (VAS) and the Schiff Cold Air Sensitivity Scale (SCASS) scale, while tactile hypersensitivity was scored using VAS only. Statistical analysis was performed using the Kruskal-Wallis test followed by Dunn’s multiple comparisons test for quantitative data. χ2 was used for the comparison of categorical data. Results: In total, 631 children were assessed, of whom 102 had MIH-affected molars (16.1%). Of these, 51.7 and 8.7% presented enamel and dentin carious lesions, respectively. Regarding the number of teeth, 239 molars were MIH affected (59.8%), with 188 (78.7%) being classified as mild (opacities only), 20 (8.4%) as moderate (posteruptive enamel breakdown), and 31 (13%) as severe (posteruptive breakdown involving dentin/atypical restorations). Hypersensitivity was recorded in only one control molar, while the prevalence of hypersensitivity in MIH-affected molars was 34.7%, being of low intensity and more prevalent in moderate (55%) and severe cases (51.6 %) than in mild cases (29.8%, p = 0.008). An association between hypersensitivity and the presence of mild and moderate cases was observed. Although the same association was observed for severe cases, it was not considered a reliable information as 90% of the MIH-affected molars with posteruptive breakdown involving dentin were affected by carious lesions. It is known that dental caries is a confounding factor for the presence of hypersensitivity. Conclusions: Hypersensitivity was significantly higher in MIH-affected molars than in nonaffected molars, being associated with MIH teeth presenting opacities and posteruptive enamel breakdown.

scholarly journals Transmuted Modified Inverse Weibull distribution: Properties and application

2019 ◽  
pp. 667-677
Author(s):  
Muhammad Shuaib Khan
Keyword(s):  
Weibull Distribution ◽  
Geometric Mean ◽  
Life Time ◽  
Harmonic Mean ◽  
Potential Usefulness ◽  
Parameter Distribution ◽  
Estimation Of Parameters ◽  
Real Dataset ◽  
Special Cases ◽  
Inverse Weibull Distribution

This paper examines the potential usefulness of the transmuted modified inverse Weibull distribution. This four-parameter distribution holds eleven life time distributions as special cases. Theoretical properties of the transmuted modified inverse Weibull distribution are studied; which includes the quantile, median, entropy, mean deviations, mean, geometric mean and harmonic mean. The estimation of parameters is obtained by using the method of maximumlikelihood. An application to real dataset is provided to show the better fit of the transmuted modified inverse Weibull distribution.

scholarly journals Use of metformin to prolong gestation in preterm pre-eclampsia: randomised, double blind, placebo controlled trial

BMJ ◽  
2021 ◽  
pp. n2103
Author(s):  
Catherine A Cluver ◽  
Richard Hiscock ◽  
Eric H Decloedt ◽  
David R Hall ◽  
Sonja Schell ◽  
...  
Keyword(s):  
Confidence Interval ◽  
Extended Release ◽  
Controlled Trial ◽  
Geometric Mean ◽  
Interquartile Range ◽  
Geometric Mean Ratio ◽  
Double Blind ◽  
Double Blind Placebo ◽  
Median Difference ◽  
Trial Drug

Abstract Objective To evaluate whether extended release metformin could be used to prolong gestation in women being expectantly managed for preterm pre-eclampsia. Design Randomised, double blind, placebo controlled trial. Setting Referral hospital in Cape Town, South Africa. Participants 180 women with preterm pre-eclampsia between 26+0 to 31+6 weeks’ gestation undergoing expectant management: 90 were randomised to extended release metformin and 90 to placebo. Intervention 3 g of oral extended release metformin or placebo daily, in divided doses, until delivery. Main outcome measure The primary outcome was prolongation of gestation. Results Of 180 participants, one woman delivered before taking any trial drug. The median time from randomisation to delivery was 17.7 days (interquartile range 5.4-29.4 days; n=89) in the metformin arm and 10.1 (3.7-24.1; n=90) days in the placebo arm, a median difference of 7.6 days (geometric mean ratio 1.39, 95% confidence interval 0.99 to 1.95; P=0.057). Among those who continued to take the trial drug at any dose, the median prolongation of gestation in the metformin arm was 17.5 (interquartile range 5.4-28.7; n=76) days compared with 7.9 (3.0-22.2; n=74) days in the placebo arm, a median difference of 9.6 days (geometric mean ratio 1.67, 95% confidence interval 1.16 to 2.42). Among those who took the full dosage, the median prolongation of gestation in the metformin arm was 16.3 (interquartile range 4.8-28.8; n=40) days compared with 4.8 (2.5-15.4; n=61) days in the placebo arm, a median difference of 11.5 days (geometric mean ratio 1.85, 95% confidence interval 1.14 to 2.88). Composite maternal, fetal, and neonatal outcomes and circulating concentrations of soluble fms-like tyrosine kinase-1, placental growth factor, and soluble endoglin did not differ. In the metformin arm, birth weight increased non-significantly and length of stay decreased in the neonatal nursery. No serious adverse events related to trial drugs were observed, although diarrhoea was more common in the metformin arm. Conclusions This trial suggests that extended release metformin can prolong gestation in women with preterm pre-eclampsia, although further trials are needed. It provides proof of concept that treatment of preterm pre-eclampsia is possible. Trial registration Pan African Clinical Trial Registry PACTR201608001752102 https://pactr.samrc.ac.za/ .

Empirical Investigation of Alternative Measures of Central Tendency

2020 ◽  
Author(s):  
William H Black ◽  
Lari B Masten
Keyword(s):  
Geometric Mean ◽  
Predictive Performance ◽  
Arithmetic Mean ◽  
Harmonic Mean ◽  
Central Tendency ◽  
Business Valuation ◽  
Alternative Measures ◽  
Data Points ◽  
Using Data ◽  
Performance Results

There is ongoing controversy in the business valuation literature regarding the preferability of the arithmetic mean or the harmonic mean when estimating ratios for use in business valuation. This research conducts a simulation using data reported from actual market transactions. Successive random samples were taken from data on valuation multiples and alternative measures of central tendency were calculated, accumulating more than 3.7 million data points. The measures (arithmetic mean, median, harmonic mean, geometric mean) were compared using hold-out sampling to identify which measure provided the closest approximation to actual results, evaluated in terms of least squares differences. Results indicated the harmonic mean delivered superior predictions to the other measures of central tendency, with less overstatement. Further, differences in sample size from 5 to 50 observations were evaluated to assess their impact on predictive performance. Results showed substantial improvements up to sample sizes of 20 or 25, with diminished improvements thereafter.

scholarly journals Unification Theories: Means and Generalized Euler Formulas

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 144
Author(s):  
Radu Iordanescu ◽  
Florin Felix Nichita ◽  
Ovidiu Pasarescu
Keyword(s):  
Geometric Mean ◽  
Arithmetic Mean ◽  
Harmonic Mean ◽  
Current Paper ◽  
Baxter Equation ◽  
Quadratic Mean ◽  
Euler’S Formula ◽  
Associative Structures ◽  
Generalized Mean

The main concepts in this paper are the means and Euler type formulas; the generalized mean which incorporates the harmonic mean, the geometric mean, the arithmetic mean, and the quadratic mean can be further generalized. Results on the Euler’s formula, the (modified) Yang–Baxter equation, coalgebra structures, and non-associative structures are also included in the current paper.

scholarly journals Comparison of different ways of computing grades in continuous assessment into the final grade

2017 ◽  
Vol 8 ◽  
pp. 1
Author(s):  
Juan A. Marin-Garcia ◽  
Julien Maheut ◽  
Julio J. Garcia Sabater
Keyword(s):  
Learning Outcomes ◽  
Geometric Mean ◽  
Arithmetic Mean ◽  
Harmonic Mean ◽  
Alternative Methods ◽  
Continuous Assessment ◽  
Final Grade ◽  
Weighted Arithmetic ◽  
Student’S Performance ◽  
The Subject

<p>We present the results of comparing various ways of calculating students' final grades from continuous assessment grades. Traditionally the weighted arithmetic mean has been used and we compare this method with other alternatives: arithmetic mean, geometric mean, harmonic mean and multiplication of the percentage of overcoming of each activi-ty. Our objective is to verify, if any of the alternative methods, agree with the student’s performance proposed by the teacher of the subject, further discriminating the grade be-tween high and low learning outcomes and reducing the number of approved opportunists.</p><p> </p><p>[Comparación del efecto de diferentes modos de agregar las califica-ciones de evaluación continua en la nota final]</p>

scholarly journals Raritas and RaritasVox: Programs for counting high diversity categorical data with highly unequal abundances

2018 ◽  
Author(s):  
David Lazarus ◽  
Johan Renaudie ◽  
Dorina Lenz ◽  
Patrick Diver ◽  
Jens Klump
Keyword(s):  
Graphical User Interface ◽  
Categorical Data ◽  
Quantitative Data ◽  
Source Code ◽  
Flexible Structure ◽  
Command Line ◽  
File Format ◽  
Occurrence Data ◽  
Rare Category ◽  
High Diversity

Acquiring data on the occurrences of many types of difficult to identify objects are often still made by human observation, e.g. in biodiversity and paleontologic research. Existing computer counting programs used to record such data have various limitations, including inflexibility and cost. We describe a pair of new open-source programs for this purpose - Raritas and RaritasVox, which share a similar graphical user interface for mouse based counting, and file output format. Raritas is written in Python and can be run as a standalone app for recent versions of either MacOS or Windows, or from the command line as easily customized source code. RaritasVox in addition supports voice based counting but is written in Java and is more complex to install or modify. Both programs explicitly support a rare category count mode which makes it easier to collect quantitative data on rare categories, e.g. rare species which are important in biodiversity surveys. Lastly, as to our knowledge no standards exist yet, we describe a new stratigraphic occurrence data (SOD) unitary file format which combines extensive metadata and a flexible structure for recording occurrence data of species or other categories in a series of samples.

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