The following statements create the data set Fish1
from the Fish
data set used in Chapter 108: The STEPDISC Procedure in SAS/STAT 14.1 User's Guide. The cubic root of the weight (Weight3
) is computed as a onedimensional measure of the size of a fish.
* Fish Measurement Data *  The data set contains 35 fish from the species Bream caught in   Finland's lake Laengelmavesi with the following measurements:   Weight (in grams)   Length3 (length from the nose to the end of its tail, in cm)   HtPct (max height, as percentage of Length3)   WidthPct (max width, as percentage of Length3)  **; data Fish1 (drop=HtPct WidthPct); title 'Fish Measurement Data'; input Weight Length3 HtPct WidthPct @@; Weight3= Weight**(1/3); Height=HtPct*Length3/100; Width=WidthPct*Length3/100; datalines; 242.0 30.0 38.4 13.4 290.0 31.2 40.0 13.8 340.0 31.1 39.8 15.1 363.0 33.5 38.0 13.3 430.0 34.0 36.6 15.1 450.0 34.7 39.2 14.2 500.0 34.5 41.1 15.3 390.0 35.0 36.2 13.4 450.0 35.1 39.9 13.8 500.0 36.2 39.3 13.7 475.0 36.2 39.4 14.1 500.0 36.2 39.7 13.3 500.0 36.4 37.8 12.0 . 37.3 37.3 13.6 600.0 37.2 40.2 13.9 600.0 37.2 41.5 15.0 700.0 38.3 38.8 13.8 700.0 38.5 38.8 13.5 610.0 38.6 40.5 13.3 650.0 38.7 37.4 14.8 575.0 39.5 38.3 14.1 685.0 39.2 40.8 13.7 620.0 39.7 39.1 13.3 680.0 40.6 38.1 15.1 700.0 40.5 40.1 13.8 725.0 40.9 40.0 14.8 720.0 40.6 40.3 15.0 714.0 41.5 39.8 14.1 850.0 41.6 40.6 14.9 1000.0 42.6 44.5 15.5 920.0 44.1 40.9 14.3 955.0 44.0 41.1 14.3 925.0 45.3 41.4 14.9 975.0 45.9 40.6 14.7 950.0 46.5 37.9 13.7 ;
The following statements request a correlation analysis and compute Cronbach’s coefficient alpha for the variables Weight3
, Length3
, Height
, and Width
:
ods graphics on; title 'Fish Measurement Data'; proc corr data=fish1 nomiss alpha plots=matrix; var Weight3 Length3 Height Width; run;
The ALPHA option computes Cronbach’s coefficient alpha for the analysis variables.
The "Simple Statistics" table in Output 2.6.1 displays univariate descriptive statistics for each analysis variable.
Output 2.6.1: Simple Statistics
The "Pearson Correlation Coefficients" table in Output 2.6.2 displays Pearson correlation statistics for pairs of analysis variables.
Output 2.6.2: Pearson Correlation Coefficients
Pearson Correlation Coefficients, N = 34 Prob > r under H0: Rho=0 


Weight3  Length3  Height  Width  
Weight3 





Length3 





Height 





Width 




Since the data set contains only one species of fish, all the variables are highly correlated. Using the ALPHA option, the CORR procedure computes Cronbach’s coefficient alpha in Output 2.6.3. The Cronbach’s coefficient alpha is a lower bound for the reliability coefficient for the raw variables and the standardized variables. Positive correlation is needed for the alpha coefficient because variables measure a common entity.
Output 2.6.3: Cronbach’s Coefficient Alpha
Because the variances of some variables vary widely, you should use the standardized score to estimate reliability. The overall standardized Cronbach’s coefficient alpha of 0.985145 provides an acceptable lower bound for the reliability coefficient. This is much greater than the suggested value of 0.70 given by Nunnally and Bernstein (1994).
The standardized alpha coefficient provides information about how each variable reflects the reliability of the scale with standardized variables. If the standardized alpha decreases after removing a variable from the construct, then this variable is strongly correlated with other variables in the scale. On the other hand, if the standardized alpha increases after removing a variable from the construct, then removing this variable from the scale makes the construct more reliable. The "Cronbach Coefficient Alpha with Deleted Variables" table in Output 2.6.4 does not show significant increase or decrease in the standardized alpha coefficients. See the section Cronbach’s Coefficient Alpha for more information about Cronbach’s alpha.
Output 2.6.4: Cronbach’s Coefficient Alpha with Deleted Variables
Cronbach Coefficient Alpha with Deleted Variable  

Deleted Variable 
Raw Variables  Standardized Variables  
Correlation with Total 
Alpha  Correlation with Total 
Alpha  
Weight3  0.975379  0.783365  0.973464  0.977103 
Length3  0.967602  0.881987  0.967177  0.978783 
Height  0.964715  0.655098  0.968079  0.978542 
Width  0.934635  0.824069  0.937599  0.986626 