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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

calculated

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

sample is indicated by the calculated

= 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.