Assumptions of Multivariate Analytical Techniques

The question is to determine if the level of education significantly affect income, cost of home, and family income among postal workers after adjusting for starting salary. With the level of education identified as the independent variable (IV), income, cost of home and family income as dependent variables (DV), and starting salary as covariate variable, the data was review to make sure that it can be analyzed and one-way MANCOVA statistical technique was determined as the appropriate test to be conducted.

As noted by Mertler and Vannatta (2013), there are three general assumptions in multivariate statistical technique namely, normality, linearity and homoscedasticity. In normality testing, a test for robustness of the data is conducted, to test for “the degree to which a statistical test is applicable even when the assumptions are not met.” (p.32). Univariate normality which is when a sample for a given variable is normally distribute must be conducted before testing for multivariate normality. A normal Q-Q plot is a graphical method used to examine univariate normality, using SPSS explore procedure option to test for normality with histograms. On the other hand, skewness and Kurtosis coefficients are utilized as the statistical options to test for univariate normality (Mertler and Vannatta, 2013). Mertler and Vannatta (2013) elucidates that Kolmogorov-Smirnov statistic can also be conducted to test the null hypothesis that a given sample population is distributed normally.

Assumptions of linearity assumes that there is a straight line between two variables. As such, it is critical in multivariate because many methods used for testing are based on linear combination of variables such as the Pearson’s r test which ignores any nonlinear relationship that may exist within variables (Mertler and Vannatta, 2013). Residual plots and bivariate scatterplots are used to assess the degree by which assumption of linearity is supported by given data sample (p.34).

Finally, the assumption of homoscedasticity. It is the assumption that the variability in scores for a continuous variable is the same across all values of another continuous variable (Mertler and Vannatta, 2013). Levene’s test of homogeneity of variance is used to statistically assess variables in the case univariate method. In levene’s test, the null hypothesis is rejected that the variances are equal if the significant level observed are small