psychmeta (version 2.3.4)

wt_dist: Weighted descriptive statistics for a vector of numbers

Description

Compute the weighted mean and variance of a vector of numeric values. If no weights are supplied, defaults to computing the unweighted mean and the unweighted maximum-likelihood variance.

Usage

wt_dist(x, wt = rep(1, length(x)), unbiased = TRUE,
  df_type = c("count", "sum_wts"))
wt_mean(x, wt = rep(1, length(x)))
wt_var(x, wt = rep(1, length(x)), unbiased = TRUE,
  df_type = c("count", "sum_wts"))

Arguments

x

Vector of values to be analyzed.

wt

Weights associated with the values in x.

unbiased

Logical scalar determining whether variance should be unbiased (TRUE) or maximum-likelihood (FALSE).

df_type

Character scalar determining whether the degrees of freedom for unbiased estimates should be based on numbers of cases ("count"; default) or sums of weights ("sum_wts").

Value

A weighted mean and variance if weights are supplied or an unweighted mean and variance if weights are not supplied.

Details

The weighted mean is computed as $${\overline{x}}_w=\frac{{\mathrm{\Sigma }}_{i=1}^k{x}_i{w}_i}{{\mathrm{\Sigma }}_{i=1}^k{w}_i}$$ where x is a numeric vector and w is a vector of weights.

The weighted variance is computed as $$va{r}_w(x)=\frac{{\mathrm{\Sigma }}_{i=1}^k{(x_i-{\overline{x}}_w)}^2{w}_i}{{\mathrm{\Sigma }}_{i=1}^k{w}_i}$$ and the unbiased weighted variance is estimated by multiplying $va{r}_w(x)$ by $\frac{k}{k-1}$.

Examples

# NOT RUN {
wt_dist(x = c(.1, .3, .5), wt = c(100, 200, 300))
wt_mean(x = c(.1, .3, .5), wt = c(100, 200, 300))
wt_var(x = c(.1, .3, .5), wt = c(100, 200, 300))
# }