ASSESSING NORMALITY USING STATISTICAL TECHNIQUES

Kolmogrorov-Smirnov (a)

Statistic          df                    Sig.

    .057          999                  .200*

* This is lower bound of the true signifcance 

(a) Lilliefors Significance Correction  

SCORE

You set the null hypothesis that there is no significant difference between the distribution of the population and the  sample

                                                Ho:   H1   =    H2

See Figure 3.3 and note that the significant level observed is .200. Since the significance level is greater than .05, then you can assume that the sample is normally distributed.

In other words, you DO NOT REJECT the null hypothesis and conclude that the normal distribution assumed for your population can also be assumed for your sample.

Besides using graphical techniques, you could also use statistical procedures to determine whether a particular sample is normally distributed. You could use the Kolmogorov-Smirnov statistic with a Lilliefors significance level for testing normality. SPSS gives the following output (see Table below).

Table showing the Kolmogorov-Smirnov statistic for assessing normality

Table of Contents

INTRODUCTION

  MEAN

  STANDARD 

  DEVIATION

HYPOTHESIS

TESTING 

T-TEST FOR

INDEPENDENT GROUPS

T-TEST FOR

DEPENDENT MEANS 

ONEWAY ANOVA  

TWO-WAY ANALYSIS OF

Variance

  (ANOVA)

MULTIVARIATE

ANALYSIS OF

VARIANCE

  (MANOVA)

CHI-SQUARE

LINEAR

CORRELATION

LINEAR

REGRESSION

MULTIPLE

REGRESSION

RELIABILITY 

  ANALYSIS

FACTOR 

  ANALYSIS