Can ANOVA be used to test proposed relationships or predicted correlations between variables in a single group?
TATISTICAL 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
include:
1.normal
distribution of the populations from which the samples were drawn or random
samples;
2.groups
should be mutually exclusive;
3.groups
should have equal variance or homogeneity of variance;
4.independence
of observations;
5.dependent
variable is measured at least at the interval level (Burns & Grove, 2005;
Munro, 2001).
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:
F(1,
343) = 15.46,p
Where:
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).
RESEARCH ARTICLE
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.
Introduction
“Osteoarthritis (OA) is a common,
chronic condition that affects most older adults. Adults with OA must deal with
pain that leads to limited mobility and may lead to disability and difficulty
maintaining independence” (Baird & Sands, 2004, p. 97). Baird and Sands
(2004) conducted a longitudinal, randomized clinical trial pilot study “to
determine whether Guided Imagery (GI) with Progressive Muscle Relaxation (PMR)
would reduce pain and mobility difficulties of women with OA” (Baird &
Sands, 2004, p. 97). The sample included 28 women over 65: 18 women were
randomly assigned to the intervention group, and 10 were randomly assigned to
the control group. “The treatment consisted of listening twice a day to a
10-to-15 minute audiotaped script that guided the women in GI with PMR.
Repeated measures ANOVA revealed a significant difference between the two
groups in the amount of change in pain and mobility difficulties they
experienced over 12 weeks. The treatment group reported a significant reduction
in pain and mobility difficulties at week 12 compared to the control group.
Members of the control group reported no differences in pain and nonsignificant
increases in mobility difficulties. The results of this pilot study justify
further investigation of the effectiveness of GI with PMR as a self-management
intervention to reduce pain and mobility difficulties associated with OA”
(Baird & Sands, 2004, p. 97).
Relevant Study Results
“Repeated-measures ANOVA revealed a
significant difference between the two groups in how much change in pain they
experienced for 12 weeks (F[1, 26] = 4.406, p =
0.046). The 17 participants in the intervention group reported a significant
reduction in pain (p Figure 1)” (Baird & Sands, 2004, p. 100).
FIGURE 1 Change in pain over 12 weeks. Pain was significantly less in
the guided imagery intervention group (p = .046).
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), p. 101. Copyright © 2004, with permission from
the American Society for Pain Management Nursing.
“Repeated-measures ANOVA revealed a
significant difference between the two groups in how much change in mobility
the women experienced over the 12 weeks (F(1, 22)= 9.619, p
= 0.005). The participants in the intervention group reported a significant
reduction in mobility difficulty at week 12 (p Figure 2)” (Baird & Sands, 2004, p. 101).
FIGURE 2 Change in mobility difficulties over 12 weeks. Mobility
difficulties were significantly less in the guided imagery intervention group (p
= .005).
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), p. 101. Copyright © 2004, with permission from
the American Society for Pain Management Nursing.
STUDY
QUESTIONS
1.What
type of analysis was conducted in this study? Was this analysis technique
appropriate? Provide a rationale for your answer.
2.According
toFigure 1, at which time was the
average pain score for the guided imagery group most similar to the control
group? Discuss the importance of this finding.
3.Discuss
what each aspect of this result means: F(1, 26) = 4.406, p
= 0.046.
4.Is
the change in the pain scores after 12 weeks of guided imagery statistically
significant for the intervention group? If yes, at what probability?
5.State
the null hypothesis for the effect of guided imagery on pain scores for the
subjects in the treatment group at 12 weeks. Should this null hypothesis be
accepted or rejected? Provide a rationale for your answer.
6.How
many means are being compared for the pain scores at 12 weeks?
7.What
did the researcher set the level of significance or alpha (a) at for this
study? When will study results be considered significant?
8.The
researchers do not report the standard deviations associated with the means.
Would you be interested in knowing the standard deviations? Provide a rationale
for your answer.
ANSWERS
TO STUDY QUESTIONS
1.A
repeated-measures ANOVA was conducted to examine differences between the
intervention group, receiving the treatment of GI and the control group over 12
weeks. The groups were examined for differences for the dependent variables of
pain and mobility over the 12-week time period. The repeated-measures ANOVA was
appropriate since the focus was on examining group differences over time. In
addition, the groups were independent due to random group assignment, and the
dependent variables (pain and mobility) were measured at least at the interval
level of measurement.
2.According
toFigure 1, the average pain scores for
the guided imagery intervention group and the control group were most similar
at baseline. This is what the researchers would hope for, since they had a
sample of 28 subjects who were randomly assigned to the treatment and control
groups to promote similarity of the groups at the start of the study. Thus if a
change occurred between the two groups during the study, it is assumed it is
due to the treatment and not because the groups were different at the start of
the study.
3.F(1,
26) = 4.406, p = 0.046, where F is the statistic for
ANOVA and the group df = 1 and the error df = 26. The F
ratio or value = 4.406, which is significant at p = 0.046
4.Yes,
F(1, 26) = 4.406, p = 0.046 is statistically
significant at p = 0.046. The level of significance for this study was
set at a = 0.05, and since p is
5.The
null hypothesis is: Women with OA receiving guided imagery have no greater
improvement in their pain scores than those in the control group at 12 weeks.
The study results indicated a significant improvement in the pain scores of
women with OA who received the treatment of guided imagery (F(1,
26) = 4.406, p = 0.046). Thus, the null hypothesis was
rejected.
6.Two
means are being compared at 12 weeks. The mean of the control group and the
mean of the guided imagery group for pain are being compared at 12 weeks.
7.The
researchers set the level of significance or alpha (a) = 0.05, which means that
any results with a p (probability) of = 0.05 will be considered
significant.
8.Answers
may vary, but it would be helpful to include the standard deviations with the
means since the standard deviations indicate the spread of the scores for the
two groups. The standard deviations for the treatment and control groups also
are needed to calculate the effect size or the effect of the treatment in a
study. The effect size is needed to conduct a power analysis to predict the
sample size needed for future studies. In addition, if the results from this
study were to be combined with the results from other studies, the means and
standard deviations for the treatment and control groups are needed to conduct
a meta-analysis to combine study results to determine current knowledge in an
area. In summary, it is helpful to report all means and standard deviations for
study variables whether the results are significant or nonsignificant, because
they are valuable to consider in conducting future research and meta-analyses.
Name:____________________________________________
Class: ____________________
Date:
_________________________________________________________________________________
? EXERCISE 36 Questions to be Graded
1.The
researchers found a significant difference between the two groups (control and
treatment) for change in mobility of the women with osteoarthritis (OA) over 12
weeks with the results of F(1, 22) = 9.619, p = 0.005.
Discuss each aspect of these results.
2.State
the null hypothesis for the Baird and Sands (2004) study that focuses on the
effect of the GI with PMR treatment on patients’ mobility level. Should the
null hypothesis be rejected for the difference between the two groups in change
in mobility scores over 12 weeks? Provide a rationale for your answer.
3.The
researchers stated that the participants in the intervention group reported a
reduction in mobility difficulty at week 12. Was this result statistically
significant, and if so at what probability?
4.If
the researchers had set the level of significance or a = 0.01, would the
results of p = 0.001 still be statistically significant? Provide a
rationale for your answer.
5.If
F(3, 60) = 4.13, p = 0.04, and a = 0.01, is the result
statistically significant? Provide a rationale for your answer. Would the null
hypothesis be accepted or rejected?
6.Can
ANOVA be used to test proposed relationships or predicted correlations between
variables in a single group? Provide a rationale for your answer.
7.If
a study had a result of F(2, 147) = 4.56, p = 0.003,
how many groups were in the study, and what was the sample size?
8.The
researchers state that the sample for their study was 28 women with a diagnosis
of OA, and that 18 were randomly assigned to the intervention group and 10 were
randomly assigned to the control group. Discuss the study strengths and/or
weaknesses in this statement.
9.In
your opinion, have the researchers established that guided imagery (GI) with
progressive muscle relaxation (PMR) reduces pain and decreases mobility
difficulties in women with OA?
10.The
researchers stated that this was a 12-week longitudinal, randomized clinical
trial pilot study with 28 women over 65 years of age with the diagnosis of OA.
What are some of the possible problems or limitations that might occur with
this type of study?
(Grove 267)
Grove, Susan K.. Statistics for Health Care
Research: A Practical Workbook. W.B. Saunders Company, 022007.