alderton@NPRDC.NAVY.MIL (David Alderton) (01/13/90)
Hi group,
There are periodic rashes of interest in computing Coefficient Alpha
on this net (including one that I initiated) but no one ever mentioned
testing the significance of the Alpha estimate. Since I recently had
need of doing this, I modified some code for this purpose. Below is
code that (a) estimates Alpha (based on mean interitem correlations -- this
includes contributions from several people), and (b) tests the significance
of the estimate from an expectation of zero. The test statistic is an
F with (N - 1) and (N - 1)*(k - 1) degrees of freedom (N = people, k = items).
The F statistic is derived from (1 - E[Alpha]) / (1 - Alpha), where
E[Alpha] is the expected value, for this case it is the usual null hypothesis
value of 0 (but other values could be used), and Alpha is the observed value.
This test can be inferred from formula (4), page 95, in:
Felt, L.S., Woodruff, D.J., & Salih, F.A. (1987). Statistical
Inference for Coefficient Alpha. Applied Psychological
Measurement, 11, 93-103.
(The article is quite thorough and covers the single estimate case, with
confidence intervals, Alpha comparisons from independent and dependent
samples, the assumptions involved and their importance.)
Below is the code. This is set up for a 6 item test (random values),
the practice data set (alpha2.dat) has 40 "subjects." Following the code
is sample output.
Enjoy!
David.
=========================IBM 4381, CMS, V 5.18=============================
OPTIONS CENTER NOCAPS LS=72;
CMS FILEDEF ALPHA DISK ALPHA2 DAT A;
DATA ONE;
INFILE ALPHA;
INPUT K1-K6;
*note input items
PROC CORR DATA=ONE NOPRINT OUT=COR;
*compute type=corr data set
DATA FINAL (KEEP=N K SUMR MEANR ALPHA);
SET COR END=ENDIN;
RETAIN SUMR 0 N;
IF _TYPE_='N' THEN N=SUM(OF _NUMERIC_)/(N(OF _NUMERIC_)-1);
*gets n or number of people
IF _TYPE_='CORR' THEN SUMR+SUM(OF _NUMERIC_)-SUMR-N;
IF ENDIN=1 THEN DO;
K=N(OF _NUMERIC_)-2;
*gets number of items
MEANR = ((SUMR-K)/2)/((K**2-K)/2);
*computes average unique interitem correlations
ALPHA = (K*MEANR)/(1+(MEANR*(K-1)));
*computes coefficient alpha
OUTPUT;
END;
RUN;
DATA CALCF;
SET FINAL;
F = (1-0)/(1-ALPHA);
*calculates the F: Note that 0 is the null expectation that can be changed
FPROB = 1 - PROBF(OF F, N-1, (N-1)*(K-1));
*calculates the F probability
PROC PRINT DATA=CALCF;
VAR ALPHA N K F FPROB;
*prints relevant results
==============================Sample Output===============================
OBS ALPHA N K F FPROB
1 0.135156 40 6 1.15628 0.258396
==========================================================================
David L. Alderton, Ph.D.
Navy Personnel Research and Development Center
Aptitude Research Division
Code 131
San Diego, CA 92152-6800
(619 553-7647 or AUTOVON 553-7647)
arpanet: alderton@nprdc.navy.mil
=============================================================================
| The opinions expressed or implied are mine, are not official, and do not |
| necessarily reflect the views of the Navy Department or the US Government |
=============================================================================
DATA FINAL (KEEP=N K SUMR MEANR ALPHA);
SET COR END=ENDIN;
RETAIN SUMR 0 N;
IF _TYPE_='N' THEN N=SUM(OF _NUMERIC_)/(N(OF _NUMERIC_)-1);
*gets n or number of people
IF _TYPE_='CORR' THEN SUMR+SUM(OF _NUMERIC_)-SUMR-N;
IF ENDIN=1 THEN DO;
K=N(OF _NUMERIC_)-2;
*gets number of items
MEANR = ((SUMR-K)/2)/((K**2-K)/2);
*computes average unique interitem correlations
ALPHA = (K*MEANR)/(1+(MEANR*(K-1)));
*computes coefficient alpha
OUTPUT;
END;
RUN;
DATA CALCF;
SET FINAL;
F = (1-0)/(1-ALPHA);
*calculates the F: Note that 0 is the null expectation that can be changed
FPROB = 1 - PROBF(OF F, N-1, (N-1)*(K-1));
*calculates the F probability
PROC PRINT DATA=CALCF;
VAR ALPHA N K F FPROB;
*prints relevant results
==============================Sample Output===============================
OBS ALPHA N K F FPROB
1 0.135156 40 6 1.15628 0.258396
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From: David Alderton <alderton@NPRDC.NAVY.MIL>
Subject: F-test for Coefficient Alpha
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To: $PEER$ <SAS-L@OHSTVMA>
Hi group,
There are periodic rashes of interest in computing Coefficient Alpha
on this net (including one that I initiated) but no one ever mentioned
testing the significance of the Alpha estimate. Since I recently had
need of doing this, I modified some code for this purpose. Below is
code that (a) estimates Alpha (based on mean interitem correlations -- this
includes contributions from several people), and (b) tests the significance
of the estimate from an expectation of zero. The test statistic is an
F with (N - 1) and (N - 1)*(k - 1) degrees of freedom (N = people, k = items).
The F statistic is derived from (1 - E[Alpha]) / (1 - Alpha), where
E[Alpha] is the expected value, for this case it is the usual null hypothesis
value of 0 (but other values could be used), and Alpha is the observed value.
This test can be inferred from formula (4), page 95, in:
Felt, L.S., Woodruff, D.J., & Salih, F.A. (1987). Statistical
Inference for Coefficient Alpha. Applied Psychological
Measurement, 11, 93-103.
(The article is quite thorough and covers the single estimate case, with
confidence intervals, Alpha comparisons from independent and dependent
samples, the assumptions involved and their importance.)
Below is the code. This is set up for a 6 item test (random values),
the practice data set (alpha2.dat) has 40 "subjects." Following the code
is sample output.
Enjoy!
David.
=========================IBM 4381, CMS, V 5.18=============================
OPTIONS CENTER NOCAPS LS=72;
CMS FILEDEF ALPHA DISK ALPHA2 DAT A;
DATA ONE;
INFILE ALPHA;
INPUT K1-K6;
*note input items
PROC CORR DATA=ONE NOPRINT OUT=COR;
*compute type=corr data set
DATA FINAL (KEEP=N K SUMR MEANR ALPHA);
SET COR END=ENDIN;
RETAIN SUMR 0 N;
IF _TYPE_='N' THEN N=SUM(OF _NUMERIC_)/(N(OF _NUMERIC_)-1);
*gets n or number of people
IF _TYPE_='CORR' THEN SUMR+SUM(OF _NUMERIC_)-SUMR-N;
IF ENDIN=1 THEN DO;
K=N(OF _NUMERIC_)-2;
*gets number of items
MEANR = ((SUMR-K)/2)/((K**2-K)/2);
*computes average unique interitem correlations
ALPHA = (K*MEANR)/(1+(MEANR*(K-1)));
*computes coefficient alpha
OUTPUT;
END;
RUN;
DATA CALCF;
SET FINAL;
F = (1-0)/(1-ALPHA);
*calculates the F: Note that 0 is the null expectation that can be changed
FPROB = 1 - PROBF(OF F, N-1, (N-1)*(K-1));
*calculates the F probability
PROC PRINT DATA=CALCF;
VAR ALPHA N K F FPROB;
*prints relevant results
==============================Sample Output===============================
OBS ALPHA N K F FPROB
1 0.135156 40 6 1.15628 0.258396
==========================================================================
David L. Alderton, Ph.D.
Navy Personnel Research and Development Center
Aptitude Research Division
Code 131
San Diego, CA 92152-6800
(619 553-7647 or AUTOVON 553-7647)
arpanet: alderton@nprdc.navy.mil
=============================================================================
| The opinions expressed or implied are mine, are not official, and do not |
| necessarily reflect the views of the Navy Department or the US Government |
=============================================================================