Confidence Interval for the Weighted Mean

This function computes the confidence interval (CI) for the weighted sample mean.

Usage

ciwm(x, weights, ..., confidence = 0.95, distribution = "normal", n)

Arguments

x: vector of measurements
weights: vector of weights
...: further arguments to sewm
confidence: the desired confidence level
distribution: sampling distribution of the estimate. Use normal if the population has unknown mean and known variance (or if n is large), t if population has unknown mean and variance
n: sample size, used to compute the degrees of freedom if distribution = "t"

Value

list containing three elements

m: sample mean
sem: standard error of the mean
ci: confidence interval for the sample mean

Details

The confidence interval of the weighted sample mean provides additional information about the variability of the population parameter estimate. It is defined as

$$CI = mean \pm \textit{critical value} \times \textit{standard error of the mean (SEM)}$$

where $mean = \frac{\sum_{i=1}^{n} w_{i} x_{i}}{\sum_{i=1}^{n} w_{i}}$ is the weighted mean.

References

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5723800/

Author

Alessandro Barberis