getRCIfromSDandAlpha: Function returns RCI given baseline score SD, reliability and...

Description Usage Arguments Value Background History Author(s) References See Also Examples

View source: R/getRCIfromSDandAlpha.R

Description

Function returns RCI given baseline score SD, reliability and confidence sought

Usage

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getRCIfromSDandAlpha(SD, rel, conf = 0.95)

Arguments

SD

single number giving the baseline score standard deviation

rel

reliability of the measure, typically, and sensibly, Cronbach's alpha

conf

the expectation/confidence interval, almost always .95

Value

single number giving the RCI

Background

Like the CSC, the RCI comes out of the classic paper Jacobson, Follette & Revenstorf (1984). The thrust of the paper was about trying to bridge the gap between (quantitative) researchers who then, and still, tend to think in terms of aggregated data about change in therapy, and clinicians who tend to think about individual client's change.

The authors came up with two indices: the CSC, and the one here: the RCI or Reliable Change Index.

\loadmathjax \mjdeqn

RCI = \varphi(conf)\! \times\! \sqrt2\! \times SD\times\sqrt1 - rel

Where

The logic of the this is that this bit: \mjdeqn\sqrt2\! \times SD\times\sqrt1 - rel

is the standard error (SE) of a difference between two scores in Classical Test Theory (CTT) In fact the 1984 paper omitted the \(\sqrt(2)\) term and that was corrected by a subsequent letter from Christensen & Menoza (1986). If we accept the model of CTT in which all these distributions are Gaussian then multiplying the SE by \(\varphi(conf)\) gives you a range of scores that would include a proportion conf of change that would arise from unreliability of measurement alone.

There is a very widespread misunderstanding that the RCI is a generic benchmark, in fact it's a coverage expectation based on the SD of the baseline scores so it's a calculation to be done for any sample. Computing the RCI for your dataset allows you to designate change as "reliable improvement", "reliable deterioration" or "no reliable change". This is perhaps useful for three particular sets of clients:

There's also an issue that Jacobson and his colleagues were looking for criteria with which to categorise individual change, sadly, too often the RCSC paradigm seems to have become just another way aggregate scores but my counting.

History

Started before 5.iv.21

Author(s)

Chris Evans

References

See Also

Other RCSC functions: classifyScoresVectorByRCI(), getBootCICSC(), getCSC()

Examples

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## Not run: 

getRCIfromSDandAlpha(7.5, .8, conf = 0.95) # from Jacobson & Truax (1991)

## End(Not run)

cpsyctc/CECPfuns documentation built on April 15, 2021, 3:26 a.m.