Data is extremely not normal, how to remedy?

• Check and remove outlier cases.
• Remove non-normal item from the model.
• Bootstrapping (i.e., re-sampling process in the existing data-set with replacement).

Multivariate Outlier

To test for multivariate outliers, Hair et al. (2010) and Byrne (2010) suggested to identify the extreme score on two or more constructs by using Mahalanobis distance (Mahalanobis D²). It evaluates the position of a particular case from the centroid of the remaining cases. Centroid is defined as the point created by the means of all the variables (Tabachnick & Fidell, 2007).

Based on a rule of thumb, the maximum Mahalanobis distance should not exceed the critical chi-square value, given the number of predictors as degree of freedom. Otherwise, the data may contain multivariate outliers (Hair, Tatham, Anderson, & Black, 1998)

Univariate Outlier

Step 2: Select Simple, and data in chart are Summaries of Separate Variables, and Define.

Bivariate Outlier

Step 1: At the Graph tab, select Legacy Dialogs, Scatter/Dot.

Step 2: Select Simple Scatter, and Define.

Step 2: Select the variables (Independent and dependent variable) and transfer to Y Axis and Y Axis Simple Scatter, and OK.

Below is the output.

Step 3: Double click at the chart to have the Chart Editor. Below will come out. Add reference line by clicking icon for Add a reference line from equation, and click Icon for Data Label Mode to mark the outlier cases.

Step 4: Close Chart Editor, and below is the output. Based on the output, case number 234 and 168 are outliers.

Multivariate Outlier

Step 1: At the Analyze Tab, Select Regression and Linear.

Step 2: Select any variable and assign as dependent variable. Select the main variables of the study and transfer them to independent(s). Click Save, and tick Mahalanobis. Continue and OK.

Step 3: Go to the Data View, and check the mahalanobis distance labelled as MAH_1

Step 4: Sort MAH_1 in descending order.

Step 5: Compare the mahalanobis distance and critical chi-square value (See Chi-square table here). Chi-square table shows that critical chi-square at the 4 degree of freedom and alpha 0.01 is 13.277.

Mahalanobis distance should not exceed the critical chi-square value, given the number of predictors as degree of freedom. Otherwise, the data may contain multivariate outliers (Hair, Tatham, Anderson, & Black, 1998).

Based on this data, all the MAH_1 values, which are greater than 13.277, are considered outlier.