Summarise categorical or continuous data
# Calculate confidence limits for a sample proportion

This utility calculates confidence limits for a population proportion for a specified level of confidence.

Inputs are the sample size and number of positive results, the desired level of confidence in the estimate and the number of decimal places required in the answer.

The program outputs the estimated proportion plus upper and lower limits of the specified confidence interval, using 5 alternative calculation methods decribed and discussed in Brown, LD, Cat, TT and DasGupta, A (2001). Interval Estimation for a proportion. Statistical Science 16:101-133:

The Wald interval often has inadequate coverage, particularly for small n and values of p close to 0 or 1. Conversely, the Clopper-Pearson Exact method is very conservative and tends to produce wider intervals than necessary. Brown et al. recommends the Wilson or Jeffreys methods for small n and Agresti-Coull, Wilson, or Jeffreys, for larger n as providing more reliable coverage than the alternatives. Also note that the point estimate for the Agresti-Coull method is slightly larger than for other methods because of the way this interval is calculated.

This utility calculates confidence limits for a population proportion for a specified level of confidence.

Inputs are the sample size and number of positive results, the desired level of confidence in the estimate and the number of decimal places required in the answer.

The program outputs the estimated proportion plus upper and lower limits of the specified confidence interval, using 5 alternative calculation methods decribed and discussed in Brown, LD, Cat, TT and DasGupta, A (2001). Interval Estimation for a proportion. Statistical Science 16:101-133:

- Asymptotic (Wald) method based on a normal approximation;
- Binomial (Clopper-Pearson) "exact" method based on the beta distribution;
- "Wilson" Score interval;
- "Agresti-Coull" (adjusted Wald) interval; and
- "Jeffreys" interval.

The Wald interval often has inadequate coverage, particularly for small n and values of p close to 0 or 1. Conversely, the Clopper-Pearson Exact method is very conservative and tends to produce wider intervals than necessary. Brown et al. recommends the Wilson or Jeffreys methods for small n and Agresti-Coull, Wilson, or Jeffreys, for larger n as providing more reliable coverage than the alternatives. Also note that the point estimate for the Agresti-Coull method is slightly larger than for other methods because of the way this interval is calculated.

1-sample z-test for a population proportion

1-Stage Freedom analysis

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Analyse test repeatability

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Bioequivalence analysis - two-period, two-treatment crossover trial

Calculate Cluster-level sensitivity and specificity for range of sample sizes and cut-points for given cluster size and imperfect tests

Calculate confidence limits for a sample proportion

Calculate sample sizes for 2-stage freedom survey where individual cluster details are available

Calculate sample sizes for 2-stage freedom survey where individual cluster details are NOT available

Calculate sample sizes for 2-stage freedom survey with fixed cluster-level sensitivity

Calculate test Sensitivity and Specificity and ROC curves

Capture-Recapture analysis

Chi-squared test for contingency table from original data

Chi-squared test for homogeneity of a sample

Chi-squared test for r x c contingency table

Chi-squared test for trend

Cluster-level sensitivity and specificity with variable cut-points

Compare prevalence values

Compare two tests

Complex 2-stage risk-based surveillance - calculation of surveillance sample size

Complex 2-stage risk-based surveillance - calculation of surveillance sensitivity

Complex 2-stage risk-based surveillance - calculation of surveillance sensitivity based on herd testing data

Complex risk-based surveillance - calculation of surveillance sample size

Complex risk-based surveillance - calculation of surveillance sensitivity

Confidence of population freedom (NPV) for a surveillance system

Confidence of population freedom for multiple time periods

Contact

Design prevalence required to achieve target population (cluster or system) sensitivity

Diagnostic test evaluation and comparison

Estimate 95% confidence limits for a median

Estimate alpha and beta Parameters for Beta distributions from count data

Estimate confidence limits for a mean

Estimate parameters for multiple Beta probability distributions or summarise distributions for specified parameters

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Estimated true prevalence using one test with a Gibbs sampler

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Estimating prevalence

Estimation of alpha and beta parameters for prior Beta distributions

"EUFMD - Demonstration of FMD freedom": 2-stage risk-based surveillance with 1 herd-level risk factor, 1 animal-level risk factor and multiple surveillance components

FreeCalc: Analyse results of freedom testing

FreeCalc: Calculate sample size for freedom testing with imperfect tests

Get P and critical values for the Chi-squared distribution

Get P and critical values for the F distribution

Get P and critical values for the normal distribution

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Glossary

HerdPlus utilities

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HerdPlus: SeH and SpH comparison for varying herd sizes

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HerdPlus: SeH and SpH for optimised sample sizes for range of herd sizes

HerdPlus: SeH and SpH for range of sample sizes and cut-points for given herd size

HerdPlus: SeH and SpH for varying sample sizes

HerdPlus: SeH for fixed sample size and cut-point

HerdPlus: SeH for optimised sampling strategy

HerdPlus: SeH for varying design prevalence

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Pooled Prevalence

Pooled Prevalence Calculator - Demonstration analyses

Pooled Prevalence Calculator - Demonstration analyses - 1

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Pooled prevalence for fixed pool size and perfect tests

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Pooled prevalence for fixed pool size and tests with uncertain sensitivity and specificity

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References

Risk-based surveillance

Sample size calculation for fixed pool size and perfect tests

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Sample size calculations

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Sample size for demonstration of freedom (detection of disease) using pooled testing

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Sample size to detect a significant difference between 2 proportions

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Sample size to estimate a true prevalence with an imperfect test

Sample size to estimate a true prevalence with an imperfect test

Simple 2-stage risk-based surveillance - calculation of sample size

Simple 2-stage risk-based surveillance - calculation of surveillance sensitivity

Simple 2-stage risk-based surveillance - calculation of surveillance sensitivity based on herd testing data

Simple risk-based surveillance - calculation of minimum detectable prevalence

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Simple risk-based surveillance - calculation of surveillance sensitivity

Simple risk-based surveillance with differential sensitivity - calculation of sample size with two sensitivity groups

Simple risk-based surveillance with differential sensitivity - calculation of surveillance sensitivity

Simulate sampling for fixed pool size and assumed known test sensitivity and specificity

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Simulated true prevalence estimates from survey testing with an imperfect test

Statistical analysis of numeric data

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Summarise Beta probability distributions for specified alpha and beta parameters

Summarise Binomial probability distributions for specified sample size and probability

Summarise categorical or continuous data

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Summarise measures of association from a 2x2 table

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Survey Toolbox for livestock diseases

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Test evaluation against a gold standard

User guide - Home

User guide 1 - Introduction

User guide 2 - Overview

User guide 3 - Bayesian vs frequentist methods

User guide 4 - Pooled prevalence for fixed pool size and perfect tests

User guide 5 - Pooled prevalence for fixed pool size and tests with known sensitivity and specificity

User guide 6 - Pooled prevalence for fixed pool size and tests with uncertain sensitivity and specificity

User guide 7 - Pooled prevalence for variable pool size and perfect tests

User guide 8 - Pooled prevalence using a Gibbs sampler

User guide 9 - Estimated true prevalence using one test with a Gibbs sampler

User guide 10 - Estimated true prevalence using two tests with a Gibbs sampler

User guide 11 - Estimation of alpha and beta parameters for prior Beta distributions and summarisation of Beta distributions for specified alpha and beta parameters

User guide 12 - Sample size for fixed pool size and perfect test

User guide 13 - Sample size for fixed pool size and known test sensitivity and specificity

User guide 14 - Sample size for fixed pool size and uncertain test sensitivity and specificity

User guide 15 - Simulate sampling for fixed pool size

User guide 16 - Simulate sampling for variable pool sizes

User guide 17 - Important Assumptions

User guide 18 - Pooled prevalence estimates are biased!