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Descriptive statistics

Uses of descriptive statistics

The first phase of data analysis involves the use of descriptive statistics, which can be used to:

  • describe the characteristics of your sample using tables and graphs.
  • check your variables for any violation of assumptions that underlie statistical techniques.
  • address specific research questions.

Descriptive statistics for categorical variables

Frequencies will tell you how many people gave each response.

  1. Click on Analyze\Descriptive Statistics\Frequencies.
  2. Choose the variables you are interested in and move them into the Variable box.
  3. Click OK.

Descriptive statistics for continuous variables

For continuous variables use Descriptives, as this will provide you a summary of statistics such as mean, median and standard deviation.

  1. Click on Analyze\Descriptive Statistics\Descriptive.
  2. Move the variables you would like to analyse into the Variables box.
  3. Click on the options button to make sure mean, standard deviation, minimum, maximum, skewness and kurtosis are selected.
  4. Click OK.

Assessing normality

Many statistical techniques assume that the distribution of scores of the dependent variable is normal (i.e. has the greatest frequency of scores in the middle section). The Explore option of the Descriptive Statistics menu will allow you to assess the normality of the distribution of scores.

  1. Click on Analyze\Descriptive Statistics\Explore.
  2. Move the variables you are interested in into the Dependent List box.
  3. In the Label cases by, put your ID variable.
  4. In the Display section, make sure that Both is selected.
  5. Click on the Statistics button and click on Descriptives and Outliers. Click on Continue.
  6. Click on the Plots button. Under Descriptive, click on Histogram. Click on Steam-and-leaf to unselect it. Click on Normality plots with tests. Click on Continue.
  7. Click on the Options button. In the Missing Values section, click on Exclude cases pairwise. Click on Continue and OK.
  8. You can also do this separately for different groups in your sample by specifying an additional categorical variable in the Factor List option.

Interpreting results of normality assessment

The Kolmogorov-Smirnov test assesses the normality of the distribution of scores. A non-significant result (Sig value of more than .05) indicates normality.

For the Normal Q-Q Plot, check whether data points follow a straight line.

Kolmogorov-Smirnov test example

Reprint Courtesy of International Business Machines Corporation, © International Business Machines Corporation. SPSS Inc. was acquired by IBM in October, 2009.

 

The Boxplot will show values that are considered as outliers (i.e. extreme values).

Boxplot example

Reprint Courtesy of International Business Machines Corporation, © International Business Machines Corporation. SPSS Inc. was acquired by IBM in October, 2009.

 

Visually inspect the Histogram.

Normal distribution  Positive kurtosis  Negatively skewed distribution

Reprint Courtesy of International Business Machines Corporation, © International Business Machines Corporation. SPSS Inc. was acquired by IBM in October, 2009.

 

A normal distribution will be bell-shaped and symmetrical (left image above).

Skewness measures the symmetry of the distribution. Distributions with positive skewness have a longer tail to the right, those with negative skewness have a longer tail to the left. The right image above has negative skewness. 

Kurtosis refers to the peak of the distribution. More peaked distributions have positive kurtosis. Flatter distributions have negative kurtosis. The centre image above has positive kurtosis. 

Normal distributions have skewness and kurtosis values close to zero.