Shows the Correlation Probability report, which is a matrix of p-values. Each p-value corresponds to a test of the null hypothesis that the true correlation between the variables is zero. This is a test of no linear relationship between the two response variables. The test is the usual test for significance of the Pearson correlation coefficient.
The default confidence coefficient is 95%. Use the Set α Level option to change the confidence coefficient.
The diagonal elements of the matrix are a function of how closely the variable is a linear function of the other variables. In the inverse correlation, the diagonal is 1/(1 – R2) for the fit of that variable by all the other variables. If the multiple correlation is zero, the diagonal inverse element is 1. If the multiple correlation is 1, then the inverse element becomes infinite and is reported missing.
The Hotelling’s T2 Test report gives the following:
Gives the value of the test statistic. If you have n rows and k variables, the F ratio is given as follows:
The p-value for the test. Under the null hypothesis the F ratio has an F distribution with n and n - k degrees of freedom.
Shows statistics that correspond to the estimation method selected in the launch window. If the REML, ML, or Robust method is selected, the mean vector and covariance matrix are estimated by that selected method. If the Row-wise method is selected, all rows with at least one missing value are excluded from the calculation of means and variances. If the Pairwise method is selected, the mean and variance are calculated for each column.
Set α Level
Four alpha values are listed: 0.01, 0.05, 0.10, and 0.50. Select Other to enter any other value.
The Color Map menu contains three types of color maps.
Principal components is a technique to take linear combinations of the original variables. The first principal component has maximum variation, the second principal component has the next most variation, subject to being orthogonal to the first, and so on. For details, see the chapter Principal Components.
The Nonparametric Correlations menu offers three nonparametric measures:
is based on the number of concordant and discordant pairs of observations. A pair is concordant if the observation with the larger value of X also has the larger value of Y. A pair is discordant if the observation with the larger value of X has the smaller value of Y. There is a correction for tied pairs (pairs of observations that have equal values of X or equal values of Y).
Clusters of Correlations
When you look for patterns in the scatterplot matrix, you can see the variables cluster into groups based on their correlations. Clusters of Correlations shows two clusters of correlations: the first two variables (top, left), and the next four (bottom, right).
Colors each ellipse. Use the Ellipses Transparency and Ellipse Color menus to change the transparency and color.
Shows either horizontal or vertical histograms in the label cells. Once histograms have been added, select Show Counts to label each bar of the histogram with its count. Select Horizontal or Vertical to either change the orientation of the histograms or remove the histograms.
Sets the α-level used for the ellipses. Select one of the standard α-levels in the menu, or select Other to enter a different one.
The Outlier Analysis menu contains options that show or hide plots that measure distance in the multivariate sense using one of these methods:
T2 statistic
In Example of an Outlier, Point A is an outlier because it is outside the correlation structure rather than because it is an outlier in any of the coordinate directions.
Example of an Outlier
T2 Statistic
The T2 plot shows distances that are the square of the Mahalanobis distance. This plot is preferred for multivariate control charts. The plot includes the value of the calculated T2 statistic, as well as its upper control limit. Values that fall outside this limit might be outliers. See T2 Distance Measures for more information.
You can save any of the distances to the data table by selecting the Save option from the red triangle menu for the plot.
Note: There is no formula saved with the jackknife distance column. This means that the distance is not recomputed if you modify the data table. If you add or delete columns, or change values in the data table, select Analyze > Multivariate Methods > Multivariate again to compute new jackknife distances.
Item reliability indicates how consistently a set of instruments measures an overall response. Cronbach’s α (Cronbach 1951) is one measure of reliability. Two primary applications for Cronbach’s α are industrial instrument reliability and questionnaire analysis.
Cronbach’s α is based on the average correlation of items in a measurement scale. It is equivalent to computing the average of all split-half correlations in the data table. The Standardized α can be requested if the items have variances that vary widely.
Note: Cronbach’s α is not related to a significance level α. Also, item reliability is unrelated to survival time reliability analysis.
To look at the influence of an individual item, JMP excludes it from the computations and shows the effect of the Cronbach’s α value. If α increases when you exclude a variable (item), that variable is not highly correlated with the other variables. If the α decreases, you can conclude that the variable is correlated with the other items in the scale. Nunnally (1979) suggests a Cronbach’s α of 0.7 as a rule-of-thumb acceptable level of agreement.
See Cronbach’s α for details about computations.
To impute missing data, select Impute Missing Data from the red triangle menu for Multivariate. A new data table is created that duplicates your data table and replaces all missing values with estimated values.