The validity of a scale varies as a function of the number of items in the scale, their average intercorrelation, and their average validity. The asymptotic limit of a scales validity for any particular criterion is just the average validity divided by the square root of the average within scale item correlation. `predicted.validity`

will find the predicted validity for a set of scales (defined by a keys.list) and the average item validity for various criteria.

The function will find (and report) scale reliabilities (using `reliability`

) and average item validities (using `item.validity`

)

```
predicted.validity(x, criteria, keys, scale.rel = NULL, item.val = NULL)
item.validity(x,criteria,keys)
```

x

A data set

criteria

Variables to predict from the scales

keys

A keys.list that defines the scales

scale.rel

If not specified, these will be found. Otherwise, this is the output from `reliability`

.

item.val

If not specified, the average item validities for each scale will be found. Otherwise use the output from `item.validity`

The predicted validities given the scales specified

The average item validities for each scale with each criterion

The various statistics reported by the `reliability`

function

A matrix of the asymptotic validities

When predicting criteria from a set of items formed into scales, the validity of the scale (that is, the correlations of the scale with each criteria) is a function of the average item validity (r_y), the average intercorrelation of the items in the scale (r_x), and the number of items in the scale (n). The limit of validity is r_y/sqrt(r_x).

Criteria will differ in their predictability from a set of scales. These asymptotic values may be used to help the decision on which scales to develop further.

Revelle, William. (in prep) An introduction to psychometric theory with applications in R. Springer. Working draft available at https://personality-project.org/r/book/

Revelle, W. and Condon, D.M. (2019) Reliability from alpha to omega: A tutorial. Psychological Assessment, 31, 12, 1395-1411. https://doi.org/10.1037/pas0000754. https://psyarxiv.com/2y3w9/ Preprint available from PsyArxiv

```
# NOT RUN {
pred.bfi <- predicted.validity(psychTools::bfi[,1:25], psychTools::bfi[,26:28],
psychTools::bfi.keys)
pred.bfi
# }
```

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