Explorations in statistics: confidence intervals

2009 ◽  
Vol 33 (2) ◽  
pp. 87-90 ◽  
Author(s):  
Douglas Curran-Everett
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Hypothesis Test ◽  
Statistical Information ◽  
Experimental Result ◽  
P Value ◽  
Population Parameter ◽  
True Value ◽  
Level Of Confidence ◽  
The Mean

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This third installment of Explorations in Statistics investigates confidence intervals. A confidence interval is a range that we expect, with some level of confidence, to include the true value of a population parameter such as the mean. A confidence interval provides the same statistical information as the P value from a hypothesis test, but it circumvents the drawbacks of that hypothesis test. Even more important, a confidence interval focuses our attention on the scientific importance of some experimental result.

scholarly journals Assessment of decrease in renal function associated with hypothyroidism

2021 ◽  
Vol 12 (1) ◽  
pp. 275-286
Author(s):  
Ayesha Ammar ◽  
Kahkashan Bashir Mir ◽  
Sadaf Batool ◽  
Noreen Marwat ◽  
Maryam Saeed ◽  
...  
Keyword(s):  
Renal Function ◽  
Confidence Interval ◽  
Creatinine Clearance ◽  
Confidence Intervals ◽  
Standard Error ◽  
Radioactive Iodine ◽  
T Test ◽  
Euthyroid State ◽  
Significant Difference ◽  
The Mean

Objective: Study was aimed to see the effects of hypothyroidism on GFR as a renal function. Material and methods: Total of Fifty-eight patients were included in the study. Out of those forty-eight patients were female and the rest were male. Out of fifty eight patients, fifty three patients were of thyroid cancer in which hypothyroidism was due to discontinuation of thyroxine before the administration of radioactive iodine for Differentiated thyroid cancer.Moreover, remaining five patients were post radioactive iodine treatment (for hyperthyroidism) hypothyroid. All of the patients were above eighteen years of age with TSH value > 30µIU/ml. Pregnant and lactating females were excluded.Renal function tests (urea/creatinine, creatinine clearance) and serum electrolytes followed by Tc-99m-DTPA renal scan for GFR assessment (GATES’ method) were carried out in all subjects twice during the study, One study during hypothyroid state (TSH > 30 µIU/ml) and other during euthyroid state (TSH between 0.4 to 4µ IU/ml). The results of Student’s t-test showed significant difference in renal functions (Urea, creatinine, creatinine clearance, GFR values) in euthyroid state and hypothyroid state (p-value <0.05). RESULTS: In case of creatinine the paired t test reveal the mean 1.014±0.428, with standard error of 0.669 within 95% confidence interval, for creatinine clearance 80.11±14.12 with standard error of 1.94 within 95% confidence intervals, for urea the mean 28±12.13 with standard error of 1.607 within 95% confidence intervals and for GFR for individual kidney is 38.056±8.56 with standard error of 1.3717 within 95% confidence interval. There was no difference in the outcome of the 2 groups. Conclusion: Hypothyroidism impairs renal function to a significant level and hence needs to be prevented and corrected as early as possible.

scholarly journals How to tell about errors not boringly: methodological analysis of expounding the basis of data processing

2020 ◽  
Vol 2020 (2 (131)) ◽  
pp. 104-115
Author(s):  
Oksana Lozovenko ◽  
Yevgeny Sokolov
Keyword(s):  
Confidence Interval ◽  
Experimental Research ◽  
Basic Skills ◽  
A Priori ◽  
Teaching Experience ◽  
Measured Quantity ◽  
General View ◽  
True Value ◽  
Training Interval ◽  
The Mean

The authors continue to report about results they have obtained in the process of creating a special introductory one-semester Laboratory Physics course «Search for Physics laws». It is known that the teaching experience and the results of the performed tests show that most students do not acquire the basic skills for conducting an experimental research. This course was built on the basis of the algorithm of systematic construction of students’ skills for carrying out an experimental research. The authors have used Galperin’s stepwise teaching procedure which was developed on the assumption that learning any kind of knowledge involves different kinds of actions. The authors have analysed different ways of how to expound the basic ideas of data analysis, and shown their connection with the point, syncretic and training-interval paradigms. Action diagrams are provided for each type of expounding. As an example of using the training-interval paradigm for teaching first-year students of a technical university, a specially designed lab session is presented in the article. The topic of the session is “The concept of a confidence interval”. Laboratory Work 1 “The Buffon-de Morgan Experiment”. This lab session meets several important requirements: a) the number of computations is minimised; b) a directly measurable quantity is considered; c) students are provided with a “fulcrum” in the form of a priori known true value of a quantity. A general view on measuring physics quantities is summarised in four quite unexpected for students “unpleasant axioms”: 1) none of measured values coincides with the true value of a quantity; 2) the mean of measured values does not coincide with the true value of a quantity; 3) even if, by a lucky chance, one of measured values or the mean coincided with the true value of a quantity, we would never know about it; 4) a confidence interval catches the true value of a measured quantity only in 68% of cases. The authors claim that the presented lab lesson allows demonstrating the equity of these “axioms” clearly and vividly, and that the organised laboratory sessions in the new way are significantly more successful in improving students’ basic skills of error analysis than traditional laboratory sessions.

scholarly journals Coverage versus Confidence

2021 ◽  
Vol 23 ◽  
Author(s):  
Peyton Cook
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Coverage Probability ◽  
Negative Binomial ◽  
Asymptotic Confidence Interval ◽  
Population Proportion ◽  
Coverage Probabilities ◽  
The Mean

This article is intended to help students understand the concept of a coverage probability involving confidence intervals. Mathematica is used as a language for describing an algorithm to compute the coverage probability for a simple confidence interval based on the binomial distribution. Then, higher-level functions are used to compute probabilities of expressions in order to obtain coverage probabilities. Several examples are presented: two confidence intervals for a population proportion based on the binomial distribution, an asymptotic confidence interval for the mean of the Poisson distribution, and an asymptotic confidence interval for a population proportion based on the negative binomial distribution.

scholarly journals The Shortest Confidence Interval for the Mean of a Normal Distribution

2018 ◽  
Vol 7 (2) ◽  
pp. 33
Author(s):  
Traoré Boubakar ◽  
Diabaté Lassina ◽  
Touré Belco ◽  
Fané Abdou
Keyword(s):  
Confidence Interval ◽  
Normal Distribution ◽  
Confidence Intervals ◽  
Mathematical Statistics ◽  
Standard Normal Distribution ◽  
Pivotal Quantity ◽  
Construction Technique ◽  
Standard Normal ◽  
The Mean ◽  
Shortest Confidence Intervals

An interesting topic in mathematical statistics is that of the construction of the confidence intervals. Two kinds of intervals which are both based on the method of pivotal quantity are the shortest confidence interval and the equal tail confidence intervals. The aim of this paper is to clarify and comment on the finding of such intervals and to investigation the relation between the two kinds of intervals. In particular, we will give a construction technique of the shortest confidence intervals for the mean of the standard normal distribution. Examples illustrating the use of this technique are given.

scholarly journals Beyond Psychology: Prevalence of p-value and confidence interval misinterpretation across different fields

2019 ◽  
Author(s):  
Xiaokang Lyu ◽  
Yuepei Xu ◽  
Xiaofan Zhao ◽  
Xi-Nian Zuo ◽  
Hu Chuan-Peng
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Biomedical Research ◽  
Scientific Community ◽  
Scientific Literature ◽  
P Value ◽  
Raw Data ◽  
Research Fields ◽  
Research Gap ◽  
Two Indices

P-value and confidence intervals (CIs) are the most widely used statistical indices in scientific literature. Several surveys revealed that these two indices are generally misunderstood. However, existing surveys on this subject fall under psychology and biomedical research, and data from other disciplines are rare. Moreover, the confidence of researchers when constructing judgments remains unclear. To fill this research gap, we survey 1,479 researchers and students from different fields in China. Results reveal that for significant (p &lt; .05, CI doesn’t include 0) and non-significant (p &gt; .05, CI includes 0) conditions, most respondents, regardless of academic degrees, research fields, and stages of career, could not interpret p-value and CI accurately. Moreover, the majority of them are confident about their (inaccurate) judgments (see osf.io/mcu9q/ for raw data, materials, and supplementary analyses). Therefore, misinterpretations of p-value and CIs prevail in the whole scientific community, thus the need for statistical training in science.

scholarly journals Visualization Strategies for Regression Estimates with Randomization Inference

2019 ◽  
Author(s):  
Marshall A. Taylor
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Regression Models ◽  
Statistical Significance ◽  
Permutation Tests ◽  
P Value ◽  
P Values ◽  
Alpha Level ◽  
Significance Levels ◽  
Nonprobability Sample

Coefficient plots are a popular tool for visualizing regression estimates. The appeal of these plots is that they visualize confidence intervals around the estimates and generally center the plot around zero, meaning that any estimate that crosses zero is statistically non-significant at at least the alpha-level around which the confidence intervals are constructed. For models with statistical significance levels determined via randomization models of inference and for which there is no standard error or confidence intervals for the estimate itself, these plots appear less useful. In this paper, I illustrate a variant of the coefficient plot for regression models with p-values constructed using permutation tests. These visualizations plot each estimate's p-value and its associated confidence interval in relation to a specified alpha-level. These plots can help the analyst interpret and report both the statistical and substantive significance of their models. Illustrations are provided using a nonprobability sample of activists and participants at a 1962 anti-Communism school.

Confidence Interval for Site Index Using Curves Based on Stem Analyses

1971 ◽  
Vol 1 (4) ◽  
pp. 241-245 ◽  
Author(s):  
L. Heger
Keyword(s):  
Confidence Interval ◽  
Sample Size ◽  
Confidence Intervals ◽  
White Spruce ◽  
Site Index ◽  
Stand Age ◽  
Average Quality ◽  
Breast Height ◽  
True Value ◽  
Index Level

A method was described for the derivation of confidence intervals for site index using site-index curves based on stem analyses. The method allows assessment of effects on index estimates due to stand age, index level, sample size of heights used in entering the curves, index age, and sample size underlying the curves. Of these effects, the first three were evaluated for a set of curves based on stem analyses of white spruce (Piceaglauca (Moench) Voss) and on index age of 50 years at breast height (BH). With sample averages of 20 heights, about 95% of index estimates were within ±5 ft (1.52 m) of the true value in spruce 25–100 years old at BH on both average quality and extreme quality sites. To ensure this precision in spruce younger than 15 years at BH, 50 heights were required on the average sites and more than 50 on extreme sites.

Research on the Confidence Interval of Indirect Detection

2011 ◽  
Vol 418-420 ◽  
pp. 532-535
Author(s):  
Hai Bin Chen ◽  
Nan Ge ◽  
Xiao Jun Tong
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Concrete Strength ◽  
Interval Estimation ◽  
Point Estimation ◽  
Indirect Detection ◽  
Detection Methods ◽  
Theoretical Formula ◽  
True Value ◽  
Practical Engineering

Abstract. Using the correlation between the measure value and measured value in the indirect detection, the whole presumption method and theoretical formula of the confidence intervals for measured value are put forward. Based on the different detection methods, the confidence interval of high confidence and high accuracy can be given by the proposed method according to random measurement results. Through the Monte Carlo simulation, using the deducing method and the related theory, it may be concluded that the true value is included within the confidence interval which is obtained by this method. The traditional method can only get the point estimation but not give the confidence intervals in the practical engineering. According to the method, the interval estimation of concrete strength can be give. Moreover, this method is used not only in test concrete strength, especially in the evaluation of earthquake, but also in strength detecting for bridges, the pressure vessel, aircraft wing etc.

scholarly journals Parameter Estimation of Inverse Rayleigh Distribution under Competing Risk Model for Masked data

2015 ◽  
Vol 20 (2) ◽  
pp. 122-127 ◽  
Author(s):  
M.S. Panwar ◽  
Bapat Akanshya Sudhir ◽  
Rashmi Bundel ◽  
Sanjeev K. Tomer
Keyword(s):  
Sample Size ◽  
Mean Square Error ◽  
Confidence Intervals ◽  
Risk Model ◽  
Life Time ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Mean Square ◽  
True Value ◽  
The Mean

This paper tries to derive maximum likelihood estimators (MLEs) for the parameters of the inverse Rayleigh distribution (IRD) when the observed data is masked. MLEs, asymptotic confidence intervals (ACIs) and boot-p confidence intervals (boot-p CIs) for the lifetime parameters have been discussed. The simulation illustrations provided that as the sample size increases the estimated value approaches to the true value, and the mean square error decreases with the increase in sample size, and mean square error increases with increase in level of masking, the ACIs are always symmetric and the boot-p CIs approaches to symmetry as the sample size increases whereas the mean life time due to the local spread of the disease is less than that due to the metastasis spread in case of real data set.Journal of Institute of Science and Technology, 2015, 20(2): 122-127

Statistical and Clinical Interpretation of Research Results

2007 ◽  
Vol 97 (2) ◽  
pp. 165-170 ◽  
Author(s):  
Garry T. Allison
Keyword(s):  
Clinical Trials ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Publication Bias ◽  
Clinical Studies ◽  
Statistical Power ◽  
P Value ◽  
Clinical Implications ◽  
Clinical Interpretation ◽  
Research Results

There is a well-known phenomenon of publication bias toward manuscripts that report statistically significant differences. The clinical implications of these statistically significant differences are not always clear because the magnitude of the changes may be clinically meaningless. This article relates the critical P value threshold to the magnitude of the actual observed change and provides a rationale for reporting confidence intervals in clinical studies. Strategies for improving statistical power and reducing the magnitude of the confidence interval range for clinical trials are also described. (J Am Podiatr Med Assoc 97(2): 165–170, 2007)

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