Testing

Before you begin to analyze your data, it is important to check the assumptions associated with each statistical procedure. Many of the procedures in SPSS assume that the scores on each of the variables have a normal distribution. This is due to the fact that most of the statistics, such as the t statistic, the F statistic and r statistic (Pearson correlation coefficient) are all derived theoretically from a normal distribution.

SPSS provides three methods for assessing normality:

• Graphical methods – this involves examining histogram, Q-Q plot and box plot
• Descriptive methods – this involves examining mean, median, mode, skew and kurtosis
• Tests of Normality

Two tests are given by SPSS: Kolmogorov-Smirnov’s test and Shapiro-Wilk’s test. Shapiro-Wilk’s test is recommended for sample size up to 2000. For sample size larger than 2000, use Kolmogorov-Smirnov’s test. If the p-value given under the Sig. column is smaller than 0.05, then the normality assumption is violated.

A researcher should use all three methods to assess normality. If data distribution is found to be non-normal but skewed positively or negatively, several transformations can be used to correct skew and these are called normalizing transformations.

Normalizing Transformations

A. For positively-skewed distribution, suggested transformations are:

• Square root
  Formula: new variable = SQRT(old variable)
• Natural logarithm
  Formula: new variable = LN(old variable)
• Inverse
  Formula: new variable = 1/(old variable)

B. For negatively-skewed distribution, suggested transformation are:

• Reflect and square root
  Formula: new variable = SQRT(K - old variable)
• Reflect and natural logarithm
  Formula: new variable = LN(K - old variable)
• Reflect and inverse
  Formula: new variable = 1/(K - old variable),

where K = (the largest value) + 1.

The transformed variables should again be assessed for normality. If none of the transformations work, stay cool because SPSS provides alternative non-parametric procedures.

References

Garson, G.D. (2010). SPSS Tutorial. URL: http://faculty.chass.ncsu.edu/garson/PA765/assumpt.htm#normal

Pallant, J. (2007). SPSS survival manual (3rd edn). Two Penn Plaza, New York, NY: McGraw-Hill.