Need Help with 2 chapters, ten questions each.

Chapter 18 questions to be graded:

Follow your instructor ’ s directions to submit your answers to the following questions for grading.

Your instructor may ask you to write your answers below and submit them as a hard copy for

grading. Alternatively, your instructor may ask you to use the space below for notes and submit your

answers online at http://evolve.elsevier.com/Grove/Statistics/ under “Questions to Be Graded.”

1. Mayland et al. (2014) do not provide the degrees of freedom ( df ) in their study. Use the degrees

of freedom formulas provided at the beginning of this exercise to calculate the group df and the

error df .

2. What is the F value and p value for spiritual need—patient? What do these results mean?

3. What is the post hoc result for facilities for the hospital with LCP vs. the hospital without LCP

(see Table 2 )? Is this result statistically signifi cant? In your opinion, is this an expected fi nding?

4. What are the assumptions for use of ANOVA?

5. What variable on Table 3 has the result F = 10.6, p < 0.0001? What does the result mean?

6. ANOVA was used for analysis by Mayland et al. (2014) . Would t -tests have also been appropriate?

Provide a rationale for your answer.

7. What type of post hoc analysis was performed? Is the post hoc analysis performed more or less

conservative than the Scheffé test?

8. State the null hypothesis for care for the three study groups (see Table 2 ). Should the null

hypothesis be accepted or rejected? Provide a rationale for your answer.

9. What are the post hoc results for care? Which results are statistically signifi cant? What do the

results mean?

10. In your opinion, do the study fi ndings presented in Tables 2 and 3 have implications for end of

life care? Provide a rationale for your answer.

STATISTICAL TECHNIQUE IN REVIEW

Analysis of variance (ANOVA) statistical technique is conducted to examine differences

between two or more groups. There are different types of ANOVAs, 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 ANOVAs can be found in

your research textbook and statistical texts ( Grove, Burns, & Gray, 2013 ; Plichta & Kelvin,

2013 ). 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 differences among

the groups studied is true; the probability of obtaining an F -ratio as large as the obtained

value in a given sample is determined by the calculated p value. If the p value is greater

than the level of signifi cance, or alpha ( α ), = 0.05 set for the study, then the study results

are nonsignifi cant and the F -ratio will be less than the critical values for F in the statistical

table (see Appendix C Critical Values of F for α = 0.05 and α = 0.01 at the back of this

text). With nonsignifi cant results, researchers will accept the null hypothesis of no signifi

cant differences between the groups. In a study, if p = 0.01, this value is less than α =

0.05, which indicates the groups are signifi cantly different 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 α . When α = 0.05, there are 5

chances in 100 the results are a Type I error, or saying something is signifi cant when it is

not.

ANOVA is similar to the t -test because the null hypothesis (no differences between

groups) is rejected when the analysis yields a smaller p value, such as p ≤ 0.05, than the α

set for the study. Assumptions for the ANOVA statistical technique include the

following:

1. The populations from which the samples were drawn or the random samples are normally

distributed.

2. The groups should be mutually exclusive.

3. The groups should have equal variance, also known as homogeneity of variance.

4. The observations are independent.

5. The dependent variable is measured at the interval or ratio level ( Plichta & Kelvin, 2013 ;

Zar, 2010 ).

EXERCISE

180 EXERCISE 18 • Understanding Analysis of Variance (ANOVA) and Post Hoc Analyses

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 as follows:

F (2,120) 4.79, p 0.01

where:

• F is the statistic.

• 2 is the group degrees of freedom ( df ) calculated by k − 1, where k = number of groups

in the study. In this example, k − 1 = 3 − 1 = 2.

• 120 is the error degrees of freedom ( df ) that is calculated based upon the number of

participants, or N − k . In this example, 123 subjects − 3 groups = 120 error df .

• 4.79 is the F -ratio or value.

• p indicates the signifi cance of the F -ratio in this study or p = 0.01.

The simplest ANOVA is the one-way ANOVA, but many of the studies in the literature

include more complex ANOVA statistical 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 or intervention variable(s).

Post Hoc Analyses Following ANOVA

When a signifi cant F value is obtained from the conduct of ANOVA, additional analyses

are needed to determine the specifi c location of the differences in a study with more than

two groups. Post hoc analyses were developed to determine where the differences lie,

because some of the groups might be different and others might be similar. For example,

a study might include three groups, an experimental group (receiving an intervention),

placebo group (receiving a pseudo or false treatment such as a sugar pill in a drug study),

and a comparison group (receiving standard care). The ANOVA resulted in a signifi cant

F -ratio or value, but post hoc analyses are needed to determine the exact location of the

differences. With post hoc analyses, researchers might fi nd that the experimental group

is signifi cantly different from both the placebo and comparison groups but that the

placebo and comparison groups were not signifi cantly different from each other. One

could conduct three t -tests to determine differences among the three groups, but that

would infl ate the Type I error. A Type I error occurs when the results indicate that two

groups are signifi cantly different when, in actuality, the groups are not different. Thus

post hoc analyses were developed to detect the differences following ANOVA in studies

with more than two groups to prevent an infl ation of a Type I error. The frequently used

post hoc analyses include the Newman-Keuls test, the Tukey Honestly Signifi cant Difference

(HSD) test, the Scheffé test, and the Dunnett test ( Plichta & Kelvin, 2013 ).

With post hoc analyses, the α level is reduced in proportion to the number of additional

tests required to locate the statistically signifi cant differences. As the α level is decreased,

reaching the level of signifi cance becomes increasingly more diffi cult. The Newman-Keuls

test compares all possible pairs of means and is the most liberal of the post hoc tests

discussed here. “Liberal” indicates that the α is not as severely decreased. The Tukey HSD

test computes one value with which all means within the data set are compared. It is

considered more stringent than the Newman-Keuls test and requires approximately equal

sample sizes in each group. The most conservative test is the Scheffé, but with the decrease

in Type I error there is an increase in Type II error, which is saying something is not

Understanding Analysis of Variance (ANOVA) and Post Hoc Analyses • EXERCISE 18 181

signifi cant when it is. The Dunnett test requires a control group, and the experimental

groups are compared with the control group without a decrease in α . Exercise 33 provides

the step-by-step process for calculating ANOVA and post hoc analyses.

RESEARCH ARTICLE

Source

Mayland, C. R., Williams, E. M., Addington-Hall, J., Cox, T. F., & Ellershaw, J. E. (2014).

Assessing the quality of care for dying patients from the bereaved relatives ’ perspective:

Further validation of “Evaluating Care and Health Outcomes—for the Dying.” Journal of

Pain and Symptom Management, 47 (4), 687–696.

Introduction

The Liverpool Care Pathway (LCP) for the Dying Patient was created to address the need

for better end of life care for both patients and families, which had been identifi ed as an

issue in the United Kingdom at the national level. “LCP is an integrated care pathway

used in the last days and hours of life that aims to transfer the hospice principles of best

practice into the acute hospital and other settings” ( Mayland et al., 2014 , p. 688). “Evaluating

Care and Health Outcomes—for the Dying (ECHO-D) is a post-bereavement questionnaire

that assesses quality of care for the dying and is linked with the Liverpool Care

Pathway for the Dying Patient (LCP)” ( Mayland et al., 2014 , p. 687).

The purpose of this comparative descriptive study was to assess the internal consistency

reliability, test-retest reliability, and construct validity of the key composite subscales of

the ECHO-D scale. The study ’ s convenience sample consisted of 255 next-of-kin or close

family members of the patients with an anticipated death from cancer at either the

selected hospice or hospital in Liverpool, United Kingdom. The sample consisted of three

groups of family members based on where the patients received end of life care; the

hospice, which used LCP; the hospital group that also used LCP; and another group from

the same hospital that did not use LCP. The ECHO-D questionnaire was completed by

all 255 study participants and a subset of self-selected participants completed a second

ECHO-D 1 month after the completion of the fi rst ECHO-D. Mayland and colleagues

(2014) concluded their study provided additional evidence of reliability and validity for

ECHO-D in the assessment of end of life care.

Relevant Study Results

“Overall, hospice participants had the highest scores for all composite scales, and ‘hospital

without LCP’ participants had the lowest scores ( Tables 2 and 3 ). The scores for the ‘hospital

with LCP’ participants were between these two levels” ( Mayland et al., 2014 , p. 693).

The level of signifi cance was set at 0.05 for the study. One-way analysis of variance was

calculated to assess differences among the hospice, hospital with LCP, and hospital

without LCP groups. Post hoc testing was conducted with the Tukey HSD test. ANOVA

and post hoc results are displayed in Tables 2 and 3 .

182 EXERCISE 18 • Understanding Analysis of Variance (ANOVA) and Post Hoc Analyses

TABLE 2 COMPARISON OF HOSPICE AND HOSPITAL PARTICIPANTS ’ SCORES FOR COMPOSITE

SCALES WITHIN THE ECHO-D QUESTIONNAIRE

Composite

Scale

Mean ( SD ) Range

ANOVA

( p ) a

Post Hoc Comparisons Using

Tukey HSD Test b

All

Participants

( n = 255)

Hospice

( n = 109)

Hospital

with LCP

( n = 78)

Hospital

without

LCP

( n = 68)

Hospice

vs.

Hospital

with

LCP

Hospice

vs.

Hospital

without

LCP

Hospital

with

LCP vs.

Hospital

without

LCP

Ward

environment

7.3 (2.7)

0–10

9.1 (1.2)

5–10

6.4 (2.6)

0–10

5.4 (2.7)

0–10

60.4

( < 0.0001)

< 0.0001 < 0.0001 0.01

Facilities 7.3 (4.8)

0–18

10.5 (4.0)

2–18

4.5 (3.8)

0–18

4.1 (2.7)

0–18

76.7

( < 0.0001)

< 0.0001 < 0.0001 0.85

Care 18.4 (6.4)

0–25

22.0 (3.75)

7–25

16.8 (0.66)

3–25

14.6 (7.33)

0–25

35.9

( < 0.0001)

< 0.0001 < 0.0001 0.05

Communication 9.8 (3.7)

0–14

11.2 (3.2)

0–14

9.4 (3.5)

0–14

8.2 (3.8)

0–14

16.6

( < 0.0001)

0.002 < 0.0001 0.86

ECHO-D = Evaluating Care and Health Outcomes for the Dying; ANOVA = analysis of variance; HSD = honestly signifi cant

difference; LCP = Liverpool Care Pathway for the Dying Patient.

a One-way ANOVA (between-groups ANOVA with planned comparisons).

b Post hoc comparisons allow further exploration of the differences between individual groups using the Tukey HSD test, which

assumes equal variances for the groups.

Mayland, C. R., Williams, E. M., Addington-Hall, J., Cox, T. F., & Ellershaw, J. E. (2014). Assessing the quality of care for dying

patients from the bereaved relatives ’ perspective: Further validation of “Evaluating Care and Health Outcomes-for the Dying.” Journal

of Pain and Symptom Management, 47 (4), p. 691.

Understanding Analysis of Variance (ANOVA) and Post Hoc Analyses • EXERCISE 18 183

TABLE 3 COMPARISON OF HOSPICE AND HOSPITAL PARTICIPANTS ’ SCORES FOR COMPOSITE VARIABLES WITHIN THE ECHO-D

QUESTIONNAIRE

Composite Variable

Mean (Range)

ANOVA ( p )

Post Hoc Comparisons Using Tukey

HSD Test

All

Participants

( n = 255)

Hospice ( n

= 109)

Hospital

with LCP

( n = 78)

Hospital

without LCP

( n = 68)

Hospice vs.

Hospital

with LCP

Hospice vs.

Hospital

without

LCP

Hospital

with LCP

vs. Hospital

without LCP

Symptom Control

Degree of affl iction from symptoms

commonly associated with dying

patients: pain, restlessness, respiratory

tract secretions, nausea and/or

vomiting, and breathlessness.

Scores range from 0 (all fi ve symptoms

present all of the time) to 10 (no

symptoms present).

6.8 (0–10) 7.0 (0–10) 7.0 (2–10) 6.1 (1–10) 4.4 (0.01) 0.99 0.02 0.03

Symptom Management

Refl ecting whether more should have been

done by staff to control symptoms.

Scores range from 0 (not enough done by

staff to control symptoms) to 6 (staff

did all they could to control symptoms).

4.8 (0–6) 5.2 (2–6) 4.8 (0–6) 4.2 (0–6) 10.6 ( < 0.0001) 0.17 < 0.0001 0.02

Spiritual Need—Patient

Refl ecting whether patients ’ spiritual and

religious needs were met.

Scores range from 0 (where need was not

met at all) to 6 (where needs were

extremely well met).

3.0 (1.9) 3.9 (0–6) 2.9 (0–6) 1.6 (0–6) 38.1 ( < 0.0001) 0.0001 0.0001 0.0001

Spiritual Need—Next-of-Kin

Refl ecting whether relatives ’ religious and

spiritual needs were met.

Scores range from 0 (where need was not

met at all) to 7 (where needs were

extremely well met).

2.7 (0–7) 3.5 (0–7) 2.6 (0–7) 1.5 (0–7) 22.6 ( < 0.0001) 0.006 0.0001 0.002

Exercise 33 Questions to be graded: Please use SPSS

Follow your instructor ’ s directions to submit your answers to the following questions for grading.

Your instructor may ask you to write your answers below and submit them as a hard copy for

grading. Alternatively, your instructor may ask you to use the space below for notes and submit your

answers online at http://evolve.elsevier.com/Grove/statistics/ under “Questions to Be Graded.”

1. Do the data meet criteria for homogeneity of variance? Provide a rationale for your answer.

2. If calculating by hand, draw the frequency distribution of the dependent variable, hours worked

at a job. What is the shape of the distribution? If using SPSS, what is the result of the Shapiro-

Wilk test of normality for the dependent variable?

3. What are the means for three groups ’ hours worked on a job?

4. What are the F value and the group and error df for this set of data?

5. Is the F significant at α = 0.05? Specify how you arrived at your answer.

6. If using SPSS, what is the exact likelihood of obtaining an F value at least as extreme as or as

close to the one that was actually observed, assuming that the null hypothesis is true?

7. Which group worked the most weekly job hours post-treatment? Provide a rationale for your

answer.

8. Write your interpretation of the results as you would in an APA-formatted journal.

9. Is there a difference in your final interpretation when comparing the results of the LSD post hoc

test versus Tukey HSD test? Provide a rationale for your answer.

10. If the researcher decided to combine the two Treatment as Usual groups to represent an overall

“Control” group, then there would be two groups to compare: Supported Employment versus

Control. What would be the appropriate statistic to address the difference in hours worked

between the two groups? Provide a rationale for your answer.

Exercise 33 Data Set:

ID	Group	Hours


		15
		17
		24
		15
		18

		18
10		16
11		25
12		28
13		35
14		30
15		15

Analysis of variance (ANOVA) is a statistical procedure that compares data between

two or more groups or conditions to investigate the presence of differences between those

groups on some continuous dependent variable (see Exercise 18 ). In this exercise, we will

focus on the one-way ANOVA , which involves testing one independent variable and one

dependent variable (as opposed to other types of ANOVAs, such as factorial ANOVAs that

incorporate multiple independent variables).

Why ANOVA and not a t -test? Remember that a t -test is formulated to compare two

sets of data or two groups at one time (see Exercise 23 for guidance on selecting appropriate

statistics). Thus, data generated from a clinical trial that involves four experimental

groups, Treatment 1, Treatment 2, Treatments 1 and 2 combined, and a Control, would

require 6 t -tests. Consequently, the chance of making a Type I error (alpha error) increases

substantially (or is infl ated) because so many computations are being performed. Specifi -

cally, the chance of making a Type I error is the number of comparisons multiplied by

the alpha level. Thus, ANOVA is the recommended statistical technique for examining

differences between more than two groups ( Zar, 2010 ).

ANOVA is a procedure that culminates in a statistic called the F statistic. It is this value

that is compared against an F distribution (see Appendix C ) in order to determine whether

the groups signifi cantly differ from one another on the dependent variable. The formulas

for ANOVA actually compute two estimates of variance: One estimate represents differences

between the groups/conditions, and the other estimate represents differences

among (within) the data.

RESEARCH DESIGNS APPROPRIATE FOR THE ONE-WAY ANOVA

Research designs that may utilize the one-way ANOVA include the randomized experimental,

quasi-experimental, and comparative designs ( Gliner, Morgan, & Leech, 2009 ).

The independent variable (the “grouping” variable for the ANOVA) may be active or attributional.

An active independent variable refers to an intervention, treatment, or program.

An attributional independent variable refers to a characteristic of the participant, such as

gender, diagnosis, or ethnicity. The ANOVA can compare two groups or more. In the case

of a two-group design, the researcher can either select an independent samples t -test or a

one-way ANOVA to answer the research question. The results will always yield the same

conclusion, regardless of which test is computed; however, when examining differences

between more than two groups, the one-way ANOVA is the preferred statistical test.

Example 1: A researcher conducts a randomized experimental study wherein she randomizes

participants to receive a high-dosage weight loss pill, a low-dosage weight loss

pill, or a placebo. She assesses the number of pounds lost from baseline to post-treatment

EXERCISE

378 EXERCISE 33 • Calculating Analysis of Variance (ANOVA) and Post Hoc Analyses Following ANOVA

for the three groups. Her research question is: “Is there a difference between the

three groups in weight lost?” The independent variables are the treatment conditions

(high-dose weight loss pill, low-dose weight loss pill, and placebo) and the dependent

variable is number of pounds lost over the treatment span.

Null hypothesis: There is no difference in weight lost among the high-dose weight loss

pill, low-dose weight loss pill, and placebo groups in a population of overweight adults.

Example 2: A nurse researcher working in dermatology conducts a retrospective comparative

study wherein she conducts a chart review of patients and divides them into three

groups: psoriasis, psoriatric symptoms, or control. The dependent variable is health status

and the independent variable is disease group (psoriasis, psoriatic symptoms, and control).

Her research question is: “Is there a difference between the three groups in levels of health

status?”

Null hypothesis: There is no difference between the three groups in health status.

STATISTICAL FORMULA AND ASSUMPTIONS

Use of the ANOVA involves the following assumptions ( Zar, 2010 ):

1. Sample means from the population are normally distributed.

2. The groups are mutually exclusive.

3. The dependent variable is measured at the interval/ratio level.

4. The groups should have equal variance, termed “homogeneity of variance.”

5. All observations within each sample are independent.

The dependent variable in an ANOVA must be scaled as interval or ratio. If the

dependent variable is measured with a Likert scale and the frequency distribution is

approximately normally distributed, these data are usually considered interval-level measurements

and are appropriate for an ANOVA ( de Winter & Dodou, 2010 ; Rasmussen,

1989 ).

The basic formula for the F without numerical symbols is:

F Mean Square Between Groups

Mean Square Within Groups

The term “mean square” ( MS ) is used interchangeably with the word “variance.” The

formulas for ANOVA compute two estimates of variance: the between groups variance

and the within groups variance. The between groups variance represents differences

between the groups/conditions being compared, and the within groups variance represents

differences among (within) each group ’ s data. Therefore, the formula is F = MS

between/MS within.

HAND CALCULATIONS

Using an example from a study of students enrolled in an RN to BSN program, a subset

of graduates from the program were examined ( Mancini, Ashwill, & Cipher, 2014 ). The

data are presented in Table 33-1 . A simulated subset was selected for this example so that

Calculating Analysis of Variance (ANOVA) and Post Hoc Analyses Following ANOVA • EXERCISE 33 379

the computations would be small and manageable. In actuality, studies involving one-way

ANOVAs need to be adequately powered ( Aberson, 2010 ; Cohen, 1988 ). See Exercises 24

and 25 for more information regarding statistical power.

The independent variable in this example is highest degree obtained prior to enrollment

(Associate ’ s, Bachelor ’ s, or Master ’ s degree), and the dependent variable was

number of months it took for the student to complete the RN to BSN program. The null

hypothesis is “There is no difference between the groups (highest degree of Associate ’ s,

Bachelor ’ s, or Master ’ s) in the months these nursing students require to complete an RN

to BSN program.”

The computations for the ANOVA are as follows:

Step 1: Compute correction term, C .

Square the grand sum ( G ), and divide by total N :

C460

7 837 04

, .

Step 2: Compute Total Sum of Squares.

Square every value in dataset, sum, and subtract C :

17 19 24 18 24 16 16 12 7 837 04

8 234 7 837 0

2 2 2 2 2 2 2 2 −

−