Negative Cronbach's Alpha

[Zhen Gie]

Hi everyone,

Recently I did a pilot study on adapting (14 items) a published scale (23 items). I stumped into a negative alpha value of -0.77 and item deletion wouldn't make it any better either. Where and how do I proceed from this?

Link to the excel and output if anyone could help with this:
https://drive.google.com/drive/folders/1KKz1pTZLka9g4XPtZ9E9PkKc5cG1JMLc?usp=sharing

-Zhen

[Rich Ulrich]

I didn't know I could read that, but Firefox called up Google-docs
or some-such, and it worked.

I see the message at the bottom -
a. The value is negative due to a negative average covariance among
items. This violates reliability model assumptions. You may want to
check item codings.

I note:
Assumption 1, all items are "scored in the same direction" so that
an average correlation makes sense.
Assumption 2, all variances are approximately equal, so that
the items are weighted equally in the computation.

I copied from an answer I gave in 2021:
* *
Where do negative alphas come from? -- SPSS Reliability does
not know about "reversed scored" items; you need to be sure
that all variables which you pass to the Reliability program
are scored so that low numbers always represent "low" on
whatever you label the scale. (To fix: Scores may be "reflected"
by subtraction -- X in the range of 1-4 becomes X_rev in the
range of 4-1 after you subtract from 5). The resulting matrix
of correlations will be (almost entirely) positive values.
* *

(There will be positive r's, if you have a sensible 'scale'.)

Alpha is sort-of the average correlation, 'sort-of' because it is
computed from covariances while assuming COV's are of similar
magnitude. Your data has a wide range for variances, so implicit
weightings are not equal. /Apparently/ the negative covariances
are much larger than the positive.

I notice that your total sample N is 12, one less than the number
of items. That is why the squared multiple correlation is missing.

That "Cronbach's alpha if item is deleted" which is reported as -1.043
surprises me - as being, possibly, an impossible value for an alpha.
I'm not checking on the formulas, but I figure that the "if deleted"
computation is an approximation, and it could be screwed up by
your combination of small N and +/- covariances, with unequal
variances implicitly being weighted very differently when 'adjusted'
(while the computation assumes that variances are equal).

Unequal variances: From the statistics, I gather that your items
are scored from 0-3; the reduced SD is reported when the mean
0.50 and lower and for mean=2.92. I suggest that your more
robust estimate of alpha will be obtained by dropping those 5
variables. Or, add them together to get one score, after doing
the necessary reverse scoring.

It is also nice to have an N of 30 or more when looking at
individual correlations; but we work with what we have.

--
Rich Ulrich

[Rich Ulrich]

On Mon, 19 Jun 2023 19:37:09 -0400, Rich Ulrich
<rich....@comcast.net> wrote:

>I copied from an answer I gave in 2021:
>* *
>Where do negative alphas come from? -- SPSS Reliability does
>not know about "reversed scored" items; you need to be sure
>that all variables which you pass to the Reliability program
>are scored so that low numbers always represent "low" on
>whatever you label the scale. (To fix: Scores may be "reflected"
>by subtraction -- X in the range of 1-4 becomes X_rev in the
>range of 4-1 after you subtract from 5). The resulting matrix
>of correlations will be (almost entirely) positive values.
>* *

Maybe it is obvious which direction is "low" and maybe it
is not. If not, how should you proceed?

Even though the sample is tiny for a factor analysis, a FA should
run and produce at least one principle component. If it won't run
with the 13, drop the 5 items with low variance.

Assuming that these items to represent some 'universe' of
scores, all the items will load on the PC. About half the items
will have positive loadings, and half will have negative.
Consider that to be two sets; reverse-score one of the sets.

(Which set the program computes as negative is a accident of
the data and the implementation. I /think/ SPSS automatically
reverses all the signs displayed for a factor when a majority of items
were computed as negative. But I'm not sure of that.)

It doesn't matter which set gets reversed, except the 'high' end
probably illustrates what name you should give to the 'factor',
considering especially the highest few loadings.

--
Rich Ulrich