measured more than two times (Hayes, 1994; Plichta & Kelvin, 2013). The broad
question being answered is whether group means significantly differ from one
another. Using ANOVA allows researchers to compare a combination of pairs
of means while reducing the odds for a type I error. For example, suppose that
a researcher is testing three different styles of education with adolescents who
have asthma: peer, text messaging, and Web-based. There would be three dif-
ferent pairs of means to compare: peer to text messaging, peer to Web-based,
and text messaging to Web-based. If t tests were conducted for each pair,
the same null hypothesis would be tested three times, increasing the risk of
a type I error. By using an ANOVA, researchers can compare the variations
among the groups using one statistical test, thereby reducing the chances of
making a type I error.
ANOVA and t tests are very closely related. When testing only two groups,
the same mathematical answer would result whether an ANOVA or a t test
were used. Using ANOVA, researchers calculate the F statistic, which is based
on the F distribution using degrees of freedom. The greater the F statistic, the
greater the variation between the means of the groups. Tables of the F distribu-
tions and degrees of freedom are also used. F = 4.65, df = 2, 50, p < .05 is an
example of the notation that would be used to report an ANOVA. However,
the F statistic indicates only that the null hypothesis can be rejected because
there is a difference between the group means, but the F test alone does not tell
which specific group differed. Instead, researchers have to conduct post hoc
tests to determine where the significant difference occurred.
Two variations of ANOVA, analysis of covariance (ANCOVA) and multivariate
analysis of variance (MANOVA), are also used in nursing research. ANCOVA
is used to statistically control for known extraneous variables. For example,
if a researcher believes that level of education affects the amount learned by
the adolescents with asthma, the researcher may use ANCOVA to control for
grade in school. When researchers have more than one dependent variable,
they used MANOVA instead of ANOVA to analyze data.
Other Tests of Significance
Table 13-12 shows that a number of other inferential statistics can be used
to determine whether there are statistically significant differences between
groups. These include Kolmogorov-Smirnov test, sign test, Wilcoxin matched
pairs test, signed rank test, median test, and Mann-Whitney U test (Hayes,
1994; Plichta & Kelvin, 2013). These tests are used when ordinal level data are
involved; thus, they are categorized as nonparametric tests. Tests are selected
based on considerations such as the number of groups being compared, the
distribution pattern of the data (normal or skewed), and other nuances that
can be found in the data.
13.8 Using Statistical Tests to Make Inferences About Populations 367