Using the standard Wald confidence interval for a population proportion hypothesis test is a common mistake

2018 ◽  
Vol 41 (2) ◽  
pp. 65-68
Author(s):  
Shitao Yang ◽  
Ken Black
Keyword(s):  
Confidence Interval ◽  
Hypothesis Test ◽  
Population Proportion ◽  
Common Mistake

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.

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.

The Simulation and Analysis of the Large-Scale Intrusion Detection Model in Shuffle Networks

2014 ◽  
Vol 556-562 ◽  
pp. 2878-2881
Author(s):  
Ke Wei Li
Keyword(s):  
Intrusion Detection ◽  
Confidence Interval ◽  
Large Scale ◽  
Hypothesis Test ◽  
Network Intrusion Detection ◽  
Detection Rates ◽  
Feed Forward ◽  
High Loss ◽  
Network Intrusion ◽  
Feed Forward Network

There are some issues for the shuffle network intrusion detection, such as high loss detection rates and time-consuming procedures. This paper proposes a shuffle network intrusion detection method fusing the misuse behavior analysis and analyzes the network misuse behavior procedures. According to the damaged data flow balance features by network misuse behavior, the paper applies the hypothesis test in probability theory to evaluate whether the confidence interval excesses 0. If the confidence interval does not contain zero, it indicates the presence of feed-forward network intrusion; otherwise, there is no feed-forward network intrusion. The experimental results show that this method can effectively solve the multi-packet collaborative intrusion problems. Compared to traditional methods, the test speed and accuracy of the method is significantly improved.

scholarly journals The Support Interval

2018 ◽  
Author(s):  
Eric-Jan Wagenmakers ◽  
Quentin Frederik Gronau ◽  
Fabian Dablander ◽  
Alexander Etz
Keyword(s):  
Confidence Interval ◽  
Hypothesis Test ◽  
Credible Interval ◽  
Minimum Amount ◽  
Evidence Based ◽  
Support Interval ◽  
Bayesian Credible Interval ◽  
Parameter Values ◽  
Lindley’S Paradox ◽  
Bayesian Support

A frequentist confidence interval can be constructed by inverting a hypothesis test, such that the interval contains only parameter values that would not have been rejected by the test. We show how a similar definition can be employed to construct a Bayesian support interval. Consistent with Carnap’s theory of corroboration, the support interval contains only parameter values that receive at least some minimum amount of support from the data. The support interval is not subject to Lindley’s paradox and provides an evidence-based perspective on inference that differ from the belief-based perspective that forms the basis of the standard Bayesian credible interval.

The Support Interval

2019 ◽  
Author(s):  
Eric-Jan Wagenmakers ◽  
Quentin Frederik Gronau ◽  
Fabian Dablander ◽  
Alexander Etz
Keyword(s):  
Confidence Interval ◽  
Hypothesis Test ◽  
Credible Interval ◽  
Minimum Amount ◽  
Evidence Based ◽  
Support Interval ◽  
Bayesian Credible Interval ◽  
Parameter Values ◽  
Lindley’S Paradox ◽  
Bayesian Support

A frequentist confidence interval can be constructed by inverting a hypothesis test, such that the interval contains only parameter values that would not have been rejected by the test. We show how a similar definition can be employed to construct a Bayesian support interval. Consistent with Carnap’s theory of corroboration, the support interval contains only parameter values that receive at least some minimum amount of support from the data. The support interval is not subject to Lindley's paradox and provides an evidence-based perspective on inference that differs from the belief-based perspective that forms the basis of the standard Bayesian credible interval.

scholarly journals Field Significance of Regression Patterns

2011 ◽  
Vol 24 (19) ◽  
pp. 5094-5107 ◽  
Author(s):  
Timothy DelSole ◽  
Xiaosong Yang
Keyword(s):  
Confidence Interval ◽  
Hypothesis Test ◽  
Significance Test ◽  
Spatial Filter ◽  
Climate Index ◽  
Boreal Winter ◽  
Ratio Test ◽  
Test Statistic ◽  
Canonical Correlations ◽  
The Cross

Regression patterns often are used to diagnose the relation between a field and a climate index, but a significance test for the pattern “as a whole” that accounts for the multiplicity and interdependence of the tests has not been widely available. This paper argues that field significance can be framed as a test of the hypothesis that all regression coefficients vanish in a suitable multivariate regression model. A test for this hypothesis can be derived from the generalized likelihood ratio test. The resulting statistic depends on relevant covariance matrices and accounts for the multiplicity and interdependence of the tests. It also depends only on the canonical correlations between the predictors and predictands, thereby revealing a fundamental connection to canonical correlation analysis. Remarkably, the test statistic is invariant to a reversal of the predictors and predictands, allowing the field significance test to be reduced to a standard univariate hypothesis test. In practice, the test cannot be applied when the number of coefficients exceeds the sample size, reflecting the fact that testing more hypotheses than data is ill conceived. To formulate a proper significance test, the data are represented by a small number of principal components, with the number chosen based on cross-validation experiments. However, instead of selecting the model that minimizes the cross-validated mean square error, a confidence interval for the cross-validated error is estimated and the most parsimonious model whose error is within the confidence interval of the minimum error is chosen. This procedure avoids selecting complex models whose error is close to much simpler models. The procedure is applied to diagnose long-term trends in annual average sea surface temperature and boreal winter 300-hPa zonal wind. In both cases a statistically significant 50-yr trend pattern is extracted. The resulting spatial filter can be used to monitor the evolution of the regression pattern without temporal filtering.

Explorations in statistics: the bootstrap

2009 ◽  
Vol 33 (4) ◽  
pp. 286-292 ◽  
Author(s):  
Douglas Curran-Everett
Keyword(s):  
Statistical Theory ◽  
Confidence Interval ◽  
Hypothesis Test ◽  
Empirical Approach ◽  
Experimental Result ◽  
Sample Mean ◽  
Sample Statistic

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This fourth installment of Explorations in Statistics explores the bootstrap. The bootstrap gives us an empirical approach to estimate the theoretical variability among possible values of a sample statistic such as the sample mean. The appeal of the bootstrap is that we can use it to make an inference about some experimental result when the statistical theory is uncertain or even unknown. We can also use the bootstrap to assess how well the statistical theory holds: that is, whether an inference we make from a hypothesis test or confidence interval is justified.

scholarly journals Prevalence of antibodies to Toxoplasma gondii in horses in the province of Kars, Turkey

2012 ◽  
Vol 49 (No. 1) ◽  
pp. 9-13 ◽  
Author(s):  
A. Akca ◽  
C. Babur ◽  
Arslan MO ◽  
Y. Gicik ◽  
M. Kara ◽  
...  
Keyword(s):  
Toxoplasma Gondii ◽  
Confidence Interval ◽  
Serum Samples ◽  
Population Proportion ◽  
Eastern Turkey ◽  
North Eastern

This study investigates the seroprevalence of Toxoplasma gondii in horses from seven villages in the province of Kars in north-eastern Turkey. A total of 189 serum samples from clinically healthy, local crossbred horses were tested for anti-T. gondii antibodies using the Sabin-Feldman dye test. Antibodies to T. gondii were found in 39 (20.6%) horses, with specific titres of 1 : 16 (27), 1 : 64 (11) and 1 : 256 (1). The 95% confidence interval for the population proportion ranged from 13.3 to 27.9%. The number of seropositive horses in Yucelen village (40%) was considerably higher than in other villages, whereas in the villages of Caglayan (8%) and Cerme (10.5%) the seroprevalence was lower than elsewhere. However, the differences in seroprevalence between the seven villages were not statistically significant (P > 0.05). In contrast, the overall seroprevalence in the province of Kars was significantly higher than that reported previously in studies carried out on army and private horse stud farms elsewhere in Turkey (P < 0.05). The relevance of these findings to the epizootiology of toxoplasmosis in Kars and Turkey is discussed.

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