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assumptions of parametric test

Parametric Tests
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.
The following are the data assumptions commonly found: in statistical research:
Assumptions of normality: Most of the parametric tests require that the assumption of normality be met.  Normality means that the distribution of the test is normally distributed (or bell-shaped)means 0 mean, with 1 standard deviation and a symmetric bell-shaped curve.  To test the assumption of normality, the following measures and tests can be applied:
·         Skewness and Kurtosis: To test the assumption of normal distribution, Skewness should be within the range ±2.  Kurtosis values should be within the 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 the 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 assumption of normality.  In this method, observed value and expected value are plotted on a graph.  If the plotted value varies more from a straight line, then the data is not normally distributed. Otherwise, data will be normally distributed.
Assumptions of homogeneity of variance:
·         Levine’s test: To test the assumption of homogeneity of variance, Levine’s test is used.  Levine’s test is used to asses if 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: This test is used to test the multivariate homogeneity of variance-covariance matrices assumption.  An insignificant value of Box’s M test shows that those groups do not differ from each other and would meet the assumption
Randomness: Most of the statistics assume that the sample observations are random.  Run Test is used to test the assumption of randomness.
Multicollinearity: Multicollinearity means that the variables of interest are highly correlated, and high correlations should not be present among variables of interest.  To test the assumption of multicollinearity, VIF and Condition indices can be used, especially in regression analyses.  A value of VIF >10 indicates multicollinearity is present and the assumption is violated.

Normality Analysis 

Normality tests are used to determine if a data set is well-modeled by a normal distribution and to compute how likely it is for a random variable underlying the data set to be normally distributed. Normality analysis was conducted to determine whether data meets the assumption of parametric tests or not. Shapiro-Wilk test was used to assess normality in this study because the sample size was less than 2000 (Royston, 1992). Histograms, the value of skewness, kurtosis, mean and median were also explored for assessing the normality of distribution. 
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