Survey research and design in psychology/Tutorials/ANOVA/Descriptive statistics

Descriptive statistics

View the accompanying screencast: [1]

For ANOVA results, report descriptive statistics (M, SD, Skewness, Kurtosis) and n for each cell and for the marginal and overall cells. Usually, this is best done in a table.
1. e.g., for a 2 x 2 design, there are four cells (2 x 2 table). The marginal means are also of interest, so a 3 x 3 table is needed.
Obtain the descriptive statistics using SPSS:
1. If you have a within-subjects factor, then compute a total score via Transform - Compute e.g., totalscore = mean(factor1,factor2, etc.)
2. Analyze - Means - Compare Means - Put factor1, factor2, and totalscore (if you have one) into the first box, and your between-subjects variable in the between-subjects variable box. In Options, request M, SD, Skewness, Kurtosis, and N. This provides a better output than via Analyze - Explore.
To obtain histograms for each cell, use Analyze - Frequencies - switch off statistics and switch on histograms via Charts with normal distribution curve. When there is a between-subjects variable, first split the file, then run Frequencies. Remember to switch the split file off afterwards.
Examining the normality assumption:
1. Examine the histograms for each cell:
  1. If there is a between-subjects IV, then split the file so that output is sorted by groups
  2. Analyze - Frequencies - Put the DV or all within-subjects variables into the r.h. box, then Charts - Histograms - Normal Curve - and run
2. Examine the skewness and kurtosis for each cell - are they between -1 and +1? If so and you have at least 20 per cell, ANOVA should be quite robust to these relatively minor departures from normality. This is quite a conservative guideline. Some texts suggest robustness for skewness of between -2 and +2. If the sample data is outside these guidelines, consider whether ANOVA is appropriate.
3. Shapiro-Wilk tests of normality can also be used to help examine whether a variable is normally distributed. If the test is significant, it would seem to be unlikely that the data is drawn from a population which has a perfectly normal distribution. However, ANOVA is robust to violation of normality assumptions with large cell sample sizes. Shapiro-Wilk statistics are often significant even when the data is appropriate for ANOVA. So, be aware that Shapiro-Wilks is a particularly sensitive test, especially with large sample sizes. If using this test, accompany the interpretation with your own examination of the skewness and kurtosis for each of the cells. Remember also that the ANOVA assumption is about normality for the data within each cell, thus it would be important to obtain Shapiro-Wilk tests of normality for each cell separately, such as by using split file.