Cronbach Alpha

[Bill Wu]

I used both Spearman Brown Prophecy formula and also used the sum of item variance over total variance formula to calculate the Cronbach Alpha.

For a larger data set 6 items 20 cases, the results turned out the same. Then I tried to demonstrate if two items are highly related, then alpha should be very close to 1.

The following data turned out very different results.

 

V1  v2

40   60

36   56

80   100

55   76

 

By using average correlation coefficients the result is 1 but using variance approach the result is totally different.

The data set does not have any meaning but why this happened? My questions are

1.       Does SPSS use average correlation coefficient approach to calculate alpha?

2.       Why sometimes the results match and others does not.

 

Thanks.

 

Bill

 

 

    

[Swank, Paul R]

Spearman Brown uses a different model than does coefficient alpha. Coefficient alpha is the average of all Guttman-Flanagan split halves, not Spearman Brown. The Spearman Brown assumes parallel items whereas the Guttman-Flanagan assumes essentially tau equivalent items.

 

Dr. Paul R. Swank, Professor

Health Promotion and Behavioral Sciences

School of Public Health

University of Texas Health Science Center Houston

 

From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Wu, Yow Wu
Sent: Thursday, October 18, 2012 12:28 PM
To: [hidden email]
Subject: Cronbach Alpha

 

I used both Spearman Brown Prophecy formula and also used the sum of item variance over total variance formula to calculate the Cronbach Alpha.

For a larger data set 6 items 20 cases, the results turned out the same. Then I tried to demonstrate if two items are highly related, then alpha should be very close to 1.

The following data turned out very different results.

 

V1  v2

40   60

36   56

80   100

55   76

 

By using average correlation coefficients the result is 1 but using variance approach the result is totally different.

The data set does not have any meaning but why this happened? My questions are

1.       Does SPSS use average correlation coefficient approach to calculate alpha?

2.       Why sometimes the results match and others does not.

 

Thanks.

 

Bill

 

 

    

[Rich Ulrich]

SPSS gives you more than one version of alpha, and
gives them different labels.

I think you can find computation formulas in the
documentation.

--
Rich Ulrich

---

Date: Thu, 18 Oct 2012 13:27:52 -0400
From: [hidden email]
Subject: Cronbach Alpha
To: [hidden email]

I used both Spearman Brown Prophecy formula and also used the sum of item variance over total variance formula to calculate the Cronbach Alpha.

For a larger data set 6 items 20 cases, the results turned out the same. Then I tried to demonstrate if two items are highly related, then alpha should be very close to 1.

The following data turned out very different results.

 

V1  v2

40   60

36   56

80   100

55   76

 

By using average correlation coefficients the result is 1 but using variance approach the result is totally different.

The data set does not have any meaning but why this happened? My questions are

1.       Does SPSS use average correlation coefficient approach to calculate alpha?

2.       Why sometimes the results match and others does not.

 

Thanks.

 

Bill

 

 

    

[Baker, Harley]

Actually, I get the same results by all formulas. With the original variance formula:

1. Var for item01 (40, 36, 80, 55) = 297.6875
2. Var for item02 (60, 56, 100, 76) = 299
3. Test variance = (100, 92, 180, 131) = 1193.1875
4. Number of items = 2;

So alpha = [k/(k-1)](1 – sum of item vars/test var)

  = 2*(1 – 596.6875/1193.1875)

 = 2*(1 - .5000)

 = 2*(.5)

 = 1.0 (to rounding error)

This is the same as SPS gets and also if you use either the Spearman-Brown formula based on the covariance approach or on the averaged correlation approach.

Harley

Dr. Harley Baker

Professor of Psychology

Madera Hall 2413

California State University Channel Islands

One University Drive

Camarillo, CA 93012

805.437.8997

[hidden email]

From: <Wu>, Yow Wu <[hidden email]>
Reply-To: "Wu, Yow Wu" <[hidden email]>
Date: Thursday, October 18, 2012 10:27 AM
To: "[hidden email]" <[hidden email]>
Subject: Cronbach Alpha

I used both Spearman Brown Prophecy formula and also used the sum of item variance over total variance formula to calculate the Cronbach Alpha.

For a larger data set 6 items 20 cases, the results turned out the same. Then I tried to demonstrate if two items are highly related, then alpha should be very close to 1.

The following data turned out very different results.

 

V1  v2

40   60

36   56

80   100

55   76

 

By using average correlation coefficients the result is 1 but using variance approach the result is totally different.

The data set does not have any meaning but why this happened? My questions are

1.       Does SPSS use average correlation coefficient approach to calculate alpha?

2.       Why sometimes the results match and others does not.

 

Thanks.

 

Bill