EXERCISE 36 ANALYSIS OF VARIANCE (ANOVA) I
STATISTICAL TECHNIQUE IN REVIEW
An analysis of variance (ANOVA)
statistical technique is conducted to examine differences between two or more
groups. There are different types of ANOVA, with the most basic being the one-way
ANOVA, which is used to analyze data in studies with one independent and
one dependent variable. More details on the types of ANOVA can be found in your
research textbook and statistical texts (Burns & Grove, 2005; Munro, 2001).
The outcome of ANOVA is a numerical value for the F statistic. The
calculated F-ratio from ANOVA indicates the extent to which group means
differ, taking into account the variability within the groups. Assuming the
null hypothesis of no difference among groups is true; the probability of
obtaining an F-ratio as large or larger than that obtained in the given
sample is indicated by the calculated p value. For example, if p
= 0.0002, this indicates that the probability of obtaining a result like this
in future studies is rare, and one may conclude that group differences exist
and the null hypothesis is rejected. However, there is always a possibility
that this decision is in error, and the probability of committing this Type I
error is determined by the alpha (a) set for the study, which is usually 0.05
that is smaller in health care studies and occasionally 0.01.
ANOVA is similar to the t-test
since the null hypothesis (no differences between groups) is rejected when the
analysis yields a smaller p value, such as p = 0.05, than the
alpha set for the study. Assumptions for the ANOVA statistical technique
distribution of the populations from which the samples were drawn or random
should be mutually exclusive;
should have equal variance or homogeneity of variance;
variable is measured at least at the interval level (Burns & Grove, 2005;
Researchers who perform ANOVA on
their data record their results in an ANOVA summary table or in the text of a
research article. An example of how an ANOVA result is commonly expressed is:
343) = 15.46,p
F is the statistic
1 is the group degrees of freedom (df)
calculated by K – 1, where K = number of groups in the study. In
this example, K – 1 = 2 – 1 = 1.
343 is the error degrees of freedom (df)
that is calculated based upon the number of participants or N – K.
In this example, 345 subjects – 2 groups = 343 error df.
15.46 is the F ratio or value
p indicates the significance of the F ratio in this
study or p
There are different types of ANOVA,
but the focus of these analysis techniques is on examining differences between
two or more groups. The simplest is the one-way ANOVA, but many of the studies
in the literature include more complex ANOVA techniques. A commonly used ANOVA
technique is the repeated-measures analysis of variance, which is used
to analyze data from studies where the same variable(s) is (are) repeatedly
measured over time on a group or groups of subjects. The intent is to determine
the change that occurs over time in the dependent variable(s) with exposure to
the independent treatment variable(s).
Source: Baird, C. L., & Sands, L. (2004). A pilot study of
the effectiveness of guided imagery with progressive muscle relaxation to
reduce chronic pain and mobility difficulties of osteoarthritis. Pain
Management Nursing, 5 (3), 97–104.