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100 CHAPTER 4 Statistical analysis

nonparametric data that involves two or more independent variables, you can consider
using more recent approaches that extend nonparametric analysis to multifactor analy-
sis (e.g., Kaptein et al., 2010; Wobbrock et al., 2011). For more information on this
topic, please refer to sources that discuss the nonparametric analysis methods in depth,
such as Conover (1999), Newton and Rudestam (1999), and Wasserman (2007).

4.9 SUMMARY
Statistical analysis is a powerful tool that helps us find interesting patterns and dif-
ferences in the data as well as identify relationships between variables. Before run-
ning significance tests, the data needs to be cleaned up, coded, and appropriately
organized to meet the needs of the specific statistical software package. The nature of
the data collected and the design of the study determine the appropriate significance
test that should be used. If the data are normally distributed and intervally scaled,
parametric tests are appropriate. When the normal distribution and interval scale re-
quirements are not met, nonparametric tests should be considered.
A number of statistical methods are available for comparing the means of mul-
tiple groups. A simple t test allows us to compare the means of two groups, with the
independent-samples t test for the between-group design and the paired-samples t
test for the within-group design. A one-way ANOVA test allows us to compare the
means of three or more groups when a between-group design is adopted and there
is only one independent variable involved. When two or more independent variables
are involved in a between-group design, the factorial ANOVA test would be appropri-
ate. If a study adopts a within-group design and involves one independent variable
with more than two conditions, the one level repeated measures ANOVA test would
be appropriate. When two or more independent variables are involved in a within-
group design, the multiple-level repeated measures ANOVA test should be adopted.
For studies that involve both a between-group factor and a within-group factor, the
split-plot ANOVA test should be considered.
Correlation analysis allows us to identify significant relationships between two
variables. When three or more variables are involved and a quantitative model is
needed to describe the relationships between the dependent variables and the inde-
pendent variables, regression analysis can be considered. Different regression pro-
cedures should be used based on the specific goals of the study.
Nonparametric statistical tests should be used when the data does not meet the
required assumptions of parametric tests. The Chi-squared test is widely used to ana-
lyze frequency counts of categorical data. Other commonly used nonparametric tests
include the Mann-Whitney U test, the Wilcoxon signed-rank test, the Kruskal-Wallis
one-way ANOVA by ranks, and the Friedman's two-way ANOVA test. Although non-
parametric tests have less strict requirements for the data, they are not assumption
free and the data still need to be carefully examined before running any nonparamet-
ric tests.