ASSESSING NORMALITY USING GRAPHICAL METHODS

Assessing normality means determining whether the sample of students, teachers, parents or principals you are studying are normally distributed. For example, when you administer a questionnaire to a group of school principals, you want to be sure that your sample of 250 principals is normally distributed. WHY? The assumption of normality is a prerequisite for many inferential statistical techniques (such as the t-test, Anova, multiple-regression). There are two main ways of determining the normality of distribution.

• Using graphical methods (such as histograms, stem-and-lead plots and boxplots)
  

• Using statistical procedures.(such as the Kolmogorov-Smirnov statistic and the Shapiro-Wilks statistics)
  

Frequency

When you draw a sample from a population that is normally distributed, it does not mean that your sample will necessarily have a distribution that is exactly normal. Samples vary, so the distribution of each sample may also vary. However, if a sample is reasonably large and it comes froma normal population, its distribution should look more or less normal.

See the Graph which is a histogram showing the distribution of scores obtained on a Scientific Literacy Test administered to a sample of 1000 students.

• The values on the vertical axis indicate the freqency or number of cases.
  

• The values on the horizontal axis are midpoints of value ranges. For example, the first bar is 20 and the second bar is 25, indicating that each bar covers a range of 5.
  

The histogram for the sample looks about normal. This is supported by the fact that the:

• mean is 45.0 while the
  

• median is 45.3 which is very close.
  

a) ASSESSING NORMALITY USING THE HISTOGRAM

Table of Contents

The Normal Distribution

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SPSS Procedures for Assessing Normality:

There are several procedures to obtain the different graphs and statistics to assess normality, nut the EXPLORE procedure is the most convenient when both graphs and statistics are required.

• Select the Analyse menu
  

• Click on Descriptive Statistics and then Explore ....to open the Explore dialogue box
  

• Select the variable you require and click on the button to move this variable into the Dependent List: box
  

• Click on the Plots...command pushbutton to obtain the Explore: Plots sub dialogue box
  

• Click on the Histogram check box and the Normality plots with tests check box, and  ensure that the Factor levels together radio button is selected in the Boxplots display
  

• Click on Continue
  

• In the Display box, ensure that Both is activated
  

• Click on the Options...command pushbutton to open the Explore: Options sub-dialogue box
  

• In the Missing Values box, click on the Exclude cases pairwise (if not selected by default)
  

• Click on Continue and then OK.
  

20    25  30   35  40   45  50   60  65   70    75  80

                            Scores

Figure 2.1 Scores of a Test on Scientific     

                     Literacy