Correlations Multivariate This correlation matrix is calculated by the method that you select in the launch window. Correlation Probability 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. CI of Correlation Shows the two-tailed confidence intervals of the correlations. This option is off by default. The default confidence coefficient is 95%. Use the Set α Level option to change the confidence coefficient. Inverse Correlations Shows or hides the inverse correlation matrix (Inverse Corr table). This option is off by default. 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. Partial Correlations Shows or hides the partial correlation table (Partial Corr), which shows the measure of the relationship between a pair of variables after adjusting for the effects of all the other variables. This option is off by default. This table is the negative of the inverse correlation matrix, scaled to unit diagonal. Covariance Matrix Shows or hides the covariance matrix which measures the degree to which a pair of variables change together. This option is off by default. Pairwise Correlations Shows or hides the Pairwise Correlations table, which lists the Pearson product-moment correlations for each pair of Y variables. This option is off by default. The correlations are calculated by the pairwise deletion method. The count values differ if any pair has a missing value for either variable. The Pairwise Correlations report also shows significance probabilities and compares the correlations in a bar chart. All results are based on the pairwise method. Hotelling’s T2 Test Allows you to conduct a one-sample test for the mean of the multivariate distribution of the variables that you entered as Y. Specify the mean vector under the null hypothesis in the window that appears by entering a hypothesized mean for each variable. The test assumes multivariate normality of the Y variables. The Hotelling’s T2 Test report gives the following: Variable Lists the variables entered as Y. Mean Gives the sample mean for each variable. Hypothesized Mean Shows the null hypothesis means that you specified. Test Statistic Gives the value of Hotelling’s T2 statistic. F Ratio Gives the value of the test statistic. If you have n rows and k variables, the F ratio is given as follows: Prob > F 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. Simple Statistics This menu contains two options that each show or hide simple statistics (mean, standard deviation, and so on) for each column. The univariate and multivariate simple statistics can differ when there are missing values present, or when the Robust method is used. Univariate Simple Statistics Shows statistics that are calculated on each column, regardless of values in other columns. These values match those produced by the Distribution platform. Multivariate Simple Statistics 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. These options are off by default. Nonparametric Correlations This menu contains three nonparametric measures: Spearman’s Rho, Kendall’s Tau, and Hoeffding’s D. These options are off by default. Set α Level You can specify any alpha value for the correlation confidence intervals. Four alpha values are listed: 0.01, 0.05, 0.10, and 0.50. Select Other to enter any other value. Scatterplot Matrix Shows or hides a scatterplot matrix of each pair of response variables. This option is on by default. Color Maps The Color Map menu contains three types of color maps. Color Map On Correlations Produces a cell plot that shows the correlations among variables on a scale from red (+1) to blue (-1). Color Map On p-values Produces a cell plot that shows the significance of the correlations on a scale from p = 0 (red) to p = 1 (blue). Cluster the Correlations Produces a cell plot that clusters together similar variables. The correlations are the same as for Color Map on Correlations, but the positioning of the variables may be different. These options are off by default. Parallel Coord Plot Shows or hides a parallel coordinate plot of the variables. This option is off by default. Ellipsoid 3D Plot Shows or hides a three-dimensional scatterplot with a 95% confidence ellipsoid. You are prompted to specify the three variables when you select this option. This option is off by default. Principal Components 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. Outlier Analysis Item Reliability This menu contains options that each shows or hides an item reliability report. The reports indicate how consistently a set of instruments measures an overall response, using either Cronbach’s α or standardized α. These options are off by default. Impute Missing Data Produces a new data table that duplicates your data table and replaces all missing values with estimated values. This option is available only if your data table contains missing values. Save Imputed Formula