null hypothesis

 

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.

 

F (1, 22) = 9.619, p = 0.005, where F is the statistic for ANOVA and the group df = 1 and the error df = 22.The F ratio or value = 9.619, that is significant at p = 0.005 to reject null hypothesis. This suggests that there is a variation in the control and treatment groups.

 

 

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.

 

The null hypothesis is: Women with OA receiving GI have no greater improvement in their pain scores than those in the control group at 12 weeks. The study results shows a momentous improvement in the mobility scores of women with OA who received the treatment (F(1, 22)   – 9.619, p = 0.005). Therefore, the null hypothesis should be rejected.

 

 

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?

 

The result was statistically significant with a probability score of p is less than 0.001.

 

4. If the researchers had set the level of significance or = 0.01, would the results of p 0.001 still be

statisticallysignificant? Provide a rationale for your answer.

 

Yes, because 0.001 is less than 0.01 therefore it is significant.

 

 

5. If F(3, 60) 4.13, p 0.04, and = 0.01, is the result statistically significant? Provide a rationale for your

answer. Would the null hypothesis be accepted or rejected?

 

The   0.04 > 0.01 would indicate that statistically are significant therefore it null hypothesis is accepted.

 

6. Can ANOVA be used to test proposed relationships or predicted correlations between variables in a single

group? Provide a rationale for your answer.

 

ANOVA can not be used to test proposed relationships or predicted correlations between variables in a single group.  This is because ANOVA is used to test relationships within various groups and among the groups.

 

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?

 

The study had 3 groups and a sample size of 148.

 

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.

The study strength is that the assignment of the treatments to the subjects was random. The weakness is that the treatments were not equally assigned to the subjects.

 

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?

 

In my opinion the research has established that GI with progressive muscle relaxation (PMR) reduces pain and decreases mobility difficulties in women with OA. This is because repeated measures of ANOVA demonstrated a significant difference between the two groups in the amount of change in pain and mobility difficulties they experienced over 12 weeks.

 

 

1. 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?

 

The possible problems or limitations of this kind of study were that the subjects were aged and could have more old-age complications compared to those being studied.

References

 

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.

Ott, L.R. & Mendenhall, W. (1994) Understanding statistics, USA: Duxbury Press.

Armstrong RA, Slade SV, &  Eperjesi F. (2000). An introduction to analysis of variance   (ANOVA)       with special reference to data from clinical experiments in optometry.   Aston University,        Birmingham, UK.

Appendix

 

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 () 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 0.001

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

pindicates the significance of the F ratio in this study or p 0.001.

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 0.001) at week 12 compared to the

control group, whose members reported no change in their pain at week 12 (see 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).

 

 

E XERCEIS 36

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 < 0.001). In contrast, those in the control group actually had increases in

mobility difficulty at week 12, although these increases did not reach statistical significance

(see 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.

 

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