"It is important to verify that the data are not too far from normal as extremely non-normal data prove problematic in the assessment of the parameters’ significance. Specifically, extremely non-normal data inflate standard errors obtained from bootstrapping and thus decrease the likelihood that some relationships will be assessed as significant"

(Hair et al., 2016)

What is Normality?

• Refers to the shape of data distribution for individual variable.
• If variation from normal distribution is large, all resulting statistical tests are invalid, because F & t-statistics assume normality (Hair et al., 2010).
• Normality can have serious effects in small samples (<50), but the impact effectively diminishes when sample sizes > 200.

How to Test for Normality?

• Histogram: Compare the observed data values with a distribution approximating normal distribution.
• Normal Probability Plot: Compare the cumulative distribution of actual data values with the cumulative distribution of a normal distribution.
• Skewness and Kurtosis Statistics.
• Shapiro-Wilks (sample < 2000).
• Kolmogorov-Smirnov (sample > 2000).

Skewness

The degree of symmetry in the variable distribution.

Threshold: -2 ≤ skewness ≤ 2 (Curran et al., 1996; West et al., 1995; Gliselli et al., 1981).

Kurtosis

The degree peakedness/flatness in the variable distribution.

Threshold: -7 ≤ Kurtosis ≤ 7 (Curran et al., 1996; West et al., 1995).

Univariate Normality: Skewness & Kurtosis

Step 1: At the Analyze tab, select Descriptive Statistics, Descriptives

Step 2: Select the variable to be assessed and transfer to the box labelled Variable(s)

Step 3: Click Options, and tick Kurtosis dan Skewness. Click Continue. At the Descriptive dialogue box, click OK.