Modeling and Multivariate Methods - SAS

458 Correlations and Multivariate Techniques Chapter 17
Computations and Statistical Details
p = number of variables (columns)
α = α th quantile
β= beta distribution
Multivariate distances are useful for spotting outliers in many dimensions. However, if the variables are
highly correlated in a multivariate sense, then a point can be seen as an outlier in multivariate space without
looking unusual along any subset of dimensions. In other words, when the values are correlated, it is
possible for a point to be unremarkable when seen along one or two axes but still be an outlier by violating
the correlation.
Caution: This outlier distance is not robust because outlying points can distort the estimate of the
covariances and means so that outliers are disguised. You might want to use the alternate distance command
so that distances are computed with a jackknife method. The alternate distance for each observation uses
estimates of the mean, standard deviation, and correlation matrix that do not include the observation itself.
Cronbach’s α
Cronbach’s α is defined as
α =
k
c
v
-
----------------------------------
1 + ( k – 1)
c
v
-
where
k = the number of items in the scale
c = the average covariance between items
v = the average variance between items
If the items are standardized to have a constant variance, the formula becomes
kr ()
α = --------------------------- where
1 + ( k – 1)r
r = the average correlation between items
The larger the overall α coefficient, the more confident you can feel that your items contribute to a reliable
scale or test. The coefficient can approach 1.0 if you have many highly correlated items.