[R] Significance test, Cronbach's Alpha
Chris Evans
chris at psyctc.org
Mon Jun 5 20:40:23 CEST 2006
Jonathan Baron sent the following at 05/06/2006 12:05:
... some snipped ...
> It is rare to see anyone report a test for alpha because it is
> usually used descriptively. If it isn't .7 or higher, people get
> upset, yet even .5 would be wildly significant in most cases.
>
> Jon
Feldt did a lot of good work on ANOVA models of alpha, well summarised
in his paper with Salih. Here are some functions. Please don't
ridicule my R style, I'm a psychotherapist first, researcher second, and
R enthusiast third. Amused advice on how to write better code warmly
received.
I'm sure that jackknifing or bootstrapping would give much more
distributionally robust CIs and p values but, as Jon's point above makes
so simply, the real problem is that people don't think through what
they're looking for from an alpha. I find there are situations in which
I'm genuinely interested in the null: is there some evidence of
covariance here?; and other situations where I want a high alpha because
I'm postulating that we have a useful measure, in the latter case, all
these totemistic values that are "acceptable", "excellent" etc. are
often misleading and a CI around the observed alpha and some exploration
of the factor structure, EFA or CFA, or IRT model explorations, will be
far more important than exactly what alpha you got.
Oops </FLAME> not quite sure where I should have put the starter on that!
I'll go back to enjoying the fact that I think this is the first time
I've posted something that might be useful to someone!
Very best all:
Chris
feldt1.return <- function(obs.a, n, k, ci = 0.95, null.a = 0)
{
if(obs.a > null.a)
f <- (1 - obs.a)/(1 - null.a)
else f <- (1 - null.a)/(1 - obs.a)
# allows for testing against a higher null
n.den <- (n - 1) * (k - 1)
n.num <- n - 1
null.p <- pf(f, n.num, n.den)
# set the upper and lower p values for the desired C.I.
p1 <- (1 - ci)/2
p2 <- ci + p1 # corresponding F values
f1 <- qf(p1, n.num, n.den)
f2 <- qf(p2, n.num, n.den) # confidence interval
lwr <- 1 - (1 - obs.a) * f2
upr <- 1 - (1 - obs.a) * f1
cat(round(lwr,2), "to",round(upr,2),"\n")
interval <- list(lwr,upr)
return(interval)
}
feldt1.lwr <- function(obs.a, n, k, ci = 0.95, null.a = 0)
{
if(obs.a > null.a)
f <- (1 - obs.a)/(1 - null.a)
else f <- (1 - null.a)/(1 - obs.a)
# allows for testing against a higher null
n.den <- (n - 1) * (k - 1)
n.num <- n - 1
null.p <- pf(f, n.num, n.den)
# set the upper and lower p values for the desired C.I.
p1 <- (1 - ci)/2
p2 <- ci + p1 # corresponding F values
f1 <- qf(p1, n.num, n.den)
f2 <- qf(p2, n.num, n.den) # confidence interval
lwr <- 1 - (1 - obs.a) * f2
return(lwr)
}
feldt1.upr <- function(obs.a, n, k, ci = 0.95, null.a = 0)
{
if(obs.a > null.a)
f <- (1 - obs.a)/(1 - null.a)
else f <- (1 - null.a)/(1 - obs.a)
# allows for testing against a higher null
n.den <- (n - 1) * (k - 1)
n.num <- n - 1
null.p <- pf(f, n.num, n.den)
# set the upper and lower p values for the desired C.I.
p1 <- (1 - ci)/2
p2 <- ci + p1 # corresponding F values
f1 <- qf(p1, n.num, n.den)
f2 <- qf(p2, n.num, n.den) # confidence interval
upr <- 1 - (1 - obs.a) * f1
return(upr)
}
--
Chris Evans <chris at psyctc.org>
Hon. Professor of Psychotherapy, Nottingham University;
Consultant Psychiatrist in Psychotherapy, Rampton Hospital;
Research Programmes Director, Nottinghamshire NHS Trust;
Hon. SL Institute of Psychiatry, Hon. Con., Tavistock & Portman Trust
**If I am writing from one of those roles, it will be clear. Otherwise**
**my views are my own and not representative of those institutions **
More information about the R-help
mailing list