Testing of Assumptions

In statistical analysis, all parametric tests assume some certain characteristic about the data, also known as assumptions.  Violation of these assumptions changes the conclusion of the research and interpretation of the results. Therefore all research, whether for a journal article, thesis, or dissertation, must follow these assumptions for accurate interpretation  Depending on the parametric analysis, the assumptions vary.

Researchers commonly find the following data assumptions in statistical research:

Assumptions of normality: Most parametric tests require meeting the assumption of normality. Normality refers to a bell-shaped distribution, with a mean of 0, a standard deviation of 1, and symmetry. To test this assumption, you can apply the following measures and tests:

Skewness and Kurtosis: To test the assumption of normal distribution, Skewness should be within the range ±2.  Kurtosis values should be within range of ±7.

Shapiro-Wilk’s W test: Most of the researchers use this test to test the assumption of normality.  Wilk’s test should not be significant to meet the assumption of normality.

Kolmogorov-Smirnov test: In the case of a large sample, most researchers use K-S test to test the assumption of normality.  This test should not be significant to meet the assumption of normality.

Graphical method for test of normality:

Q-Q plot: Most researchers use Q-Q plots to test the hypothesis of normality.  In this method, you plot the observed value and expected value on a graph. If the plotted values deviate more from a straight line, you conclude that the data is not normally distributed. Otherwise distribute data normally.

Assumptions of homogeneity of variance:

Levene’s test: To evaluate the hypothesis of homogeneity of variance, you use Levene’s test. Levene’s test assesses whether the groups have equal variances.  This test should not be significant to meet the assumption of equality of variances.

Homogeneity of variance-covariance matrices assumption:

Box’s M test: You use this test to evaluate the supposition of multivariate homogeneity of variance-covariance matrices.  An insignificant value of Box’s M test shows that those groups do not differ from each other and would meet the presumption.

Randomness: Most of the statistics assume that the sample observations are random.  To test the presumption of randomness, use the Run Test.

Multicollinearity: Multicollinearity occurs when the variables of interest are highly correlated, and high correlations should be avoided among them. To test for multicollinearity, you can use VIF and Condition indices, especially in regression analyses. A VIF value greater than 10 indicates the presence of multicollinearity, violating the assumption.