R: The sample size weighted correlation may be used in...

cor.wt {psych} | R Documentation

## The sample size weighted correlation may be used in correlating aggregated data

### Description

If using aggregated data, the correlation of the means does not reflect the sample size used for each mean. cov.wt in RCore does this and returns a covariance matrix or the correlation matrix. The cor.wt function weights by sample size or by standard errors and by default return correlations.

### Usage

    cor.wt(data,vars=NULL, w=NULL,sds=NULL, cor=TRUE)

### Arguments

`data` | A matrix or data frame
`vars` | Variables to analyze
`w` | A set of weights (e.g., the sample sizes)
`sds` | Standard deviations of the samples (used if weighting by standard errors)
`cor` | Report correlations (the default) or covariances

### Details

A weighted correlation is just ∑ (wt_k * (x_ik - x_jk)) /sqrt[wt_k ∑(x^2_ik) wt_k ∑(x^2_jk)] where x_ik is a deviation from the weighted mean.

The weighted correlation is appropriate for correlating aggregated data, where individual data points might reflect the means of a number of observations. In this case, each point is weighted by its sample size (or alternatively, by the standard error). If the weights are all equal, the correlation is just a normal Pearson correlation.

Used when finding correlations of group means found using `statsBy`.

### Value

`cor` | The weighted correlation
`xwt` | The data as weighted deviations from the weighted mean
`wt` | The weights used (calculated from the sample sizes).
`mean` | The weighted means
`xc` | Unweighted, centered deviation scores from the weighted mean
`xs` | Deviation scores weighted by the standard error of each sample mean

### Note

A generalization of `cov.wt` in core R

### Author(s)

William Revelle

### See Also

See Also as `cov.wt`, `statsBy`

### Examples

    means.by.age <- statsBy(sat.act,"age")
    wt.cors <- cor.wt(means.by.age)
    lowerMat(wt.cors$r)  #show the weighted correlations
    unwt <- lowerCor(means.by.age$mean)
    mixed <- lowerUpper(unwt,wt.cors$r)  #combine both results
    cor.plot(mixed,TRUE,main="weighted versus unweighted correlations")
    diff <- lowerUpper(unwt,wt.cors$r,TRUE)
    cor.plot(diff,TRUE,main="differences of weighted versus unweighted correlations")

[Package psych version 1.7.3.21 Index]