Can anyone help with 2 assignments, ten questions each.

Chapter 19 Questions to be graded:

1. According to the relevant study results section of the Darling-Fisher et al. (2014) study, what

categories are reported to be statistically significant?

2. What level of measurement is appropriate for calculating the χ 2 statistic? Give two examples

from Table 2 of demographic variables measured at the level appropriate for χ 2 .

3. What is the χ2 for U.S. practice region? Is the χ 2 value statistically signifi cant? Provide a rationale

for your answer.

4. What is the df for provider type? Provide a rationale for why the df for provider type presented

in Table 2 is correct.

5. Is there a statistically significant difference for practice setting between the Rapid Assessment

for Adolescent Preventive Services (RAAPS) users and nonusers? Provide a rationale for your

answer.

6. State the null hypothesis for provider age in years for RAAPS users and RAAPS nonusers.

7. Should the null hypothesis for provider age in years developed for Question 6 be accepted or

rejected? Provide a rationale for your answer.

8. Describe at least one clinical advantage and one clinical challenge of using RAAPS as described

by Darling-Fisher et al. (2014) .

9. How many null hypotheses are rejected in the Darling-Fisher et al. (2014) study for the results

presented in Table 2 ? Provide a rationale for your answer.

10. A statistically significant difference is present between RAAPS users and RAAPS nonusers for

U.S. practice region, χ 2 = 29.68. Does the χ 2 result provide the location of the difference? Provide

a rationale for your answer.

Chapter 19 content:

Understanding Pearson

Chi-Square

STATISTICAL TECHNIQUE IN REVIEW

The Pearson Chi-square ( χ2 ) is an inferential statistical test calculated to examine differences

among groups with variables measured at the nominal level. There are different

types of χ 2 tests and the Pearson chi-square is commonly reported in nursing studies. The

Pearson χ 2 test compares the frequencies that are observed with the frequencies that were

expected. The assumptions for the χ 2 test are as follows:

1. The data are nominal-level or frequency data.

2. The sample size is adequate.

3. The measures are independent of each other or that a subject ’ s data only fi t into one

category ( Plichta & Kelvin, 2013 ).

The χ2 values calculated are compared with the critical values in the χ 2 table (see Appendix

D Critical Values of the χ 2 Distribution at the back of this text). If the result is greater

than or equal to the value in the table, signifi cant differences exist. If the values are statistically

signifi cant, the null hypothesis is rejected ( Grove, Burns, & Gray, 2013 ). These

results indicate that the differences are probably an actual refl ection of reality and not

just due to random sampling error or chance.

In addition to the χ2 value, researchers often report the degrees of freedom ( df ).

This mathematically complex statistical concept is important for calculating and determining

levels of signifi cance. The standard formula for df is sample size ( N ) minus 1, or

df = N − 1; however, this formula is adjusted based on the analysis technique performed

( Plichta & Kelvin, 2013) . The d f formula for the χ 2 test varies based on the number of

categories examined in the analysis. The formula for df for the two-way χ2 test is df =

(R − 1) (C − 1), where R is number of rows and C is the number of columns in a χ 2 table.

For example, in a 2 × 2 χ 2 table, d f = (2 − 1) (2 − 1) = 1. Therefore, the d f is equal to 1.

Table 19-1 includes a 2 × 2 chi-square contingency table based on the fi ndings of An

et al. (2014) study. In Table 19-1 , the rows represent the two nominal categories of alcohol

EXERCISE

TABLE 19-1 CONTINGENCY TABLE BASED ON THE RESULTS OF AN ET AL. (2014) STUDY

Nonsmokers n = 742 Smokers n = 57 *

No alcohol use 551 14

Alcohol use † 191 43

* Smokers defi ned as “smoking at least 1 cigarette daily during the past month.”

† Alcohol use “defi ned as at least 1 alcoholic beverage per month during the past year.”

An, F. R., Xiang, Y. T., Yu., L., Ding, Y. M., Ungvari, G. S., Chan, S. W. C., et al. (2014). Prevalence of nurses ’ smoking habits in

psychiatric and general hospitals in China. Archives of Psychiatric Nursing, 28 (2), 120.

192 EXERCISE 19 • Understanding Pearson Chi-Square

use and alcohol nonuse and the two columns represent the two nominal categories of

smokers and nonsmokers. The df = (2 − 1) (2 − 1) = (1) (1) = 1, and the study results were

as follows: χ2 (1, N = 799) = 63.1; p < 0.0001. It is important to note that the df can also

be reported without the sample size, as in χ 2 (1) = 63.1, p < 0.0001.

If more than two groups are being examined, χ2 does not determine where the differences

lie; it only determines that a statistically signifi cant difference exists. A post hoc

analysis will determine the location of the difference. χ 2 is one of the weaker statistical

tests used, and results are usually only reported if statistically signifi cant values are

found. The step-by-step process for calculating the Pearson chi-square test is presented

in Exercise 35.

RESEARCH ARTICLE

Source

Darling-Fisher, C. S., Salerno, J., Dahlem, C. H. Y., & Martyn, K. K. (2014). The Rapid

Assessment for Adolescent Preventive Services (RAAPS): Providers ’ assessment of its usefulness

in their clinical practice settings. Journal of Pediatric Health Care, 28 (3), 217–226.

Introduction

Darling-Fisher and colleagues (2014 , p. 219) conducted a mixed-methods descriptive

study to evaluate the clinical usefulness of the Rapid Assessment for Adolescent Preventative

Services (RAAPS) screening tool “by surveying healthcare providers from a wide

variety of clinical settings and geographic locations.” The study participants were recruited

from the RAAPS website to complete an online survey. The RAAPS risk-screening tool

“was developed to identify the risk behaviors contributing most to adolescent morbidity,

mortality, and social problems, and to provide a more streamlined assessment to help

providers address key adolescent risk behaviors in a time-effi cient and user-friendly

format” ( Darling-Fisher et al., 2014 , p. 218). The RAAPS is an established 21-item questionnaire

with evidence of reliability and validity that can be completed by adolescents in

5–7 minutes.

“Quantitative and qualitative analyses indicated the RAAPS facilitated identifi cation

of risk behaviors and risk discussions and provided effi cient and consistent assessments;

86% of providers believed that the RAAPS positively infl uenced their practice” ( Darling-

Fisher et al., 2014 , p. 217). The researchers concluded the use of RAAPS by healthcare

providers could improve the assessment and identifi cation of adolescents at risk and lead

to the delivery of more effective adolescent preventive services.

Relevant Study Results

In the Darling-Fisher et al. (2014 , p. 220) mixed-methods study, the participants ( N = 201)

were “providers from 26 U.S. states and three foreign countries (Canada, Korea, and

Ireland).” More than half of the participants ( n = 111; 55%) reported they were using the

RAAPS in their clinical practices. “When asked if they would recommend the RAAPS to

other providers, 86 responded, and 98% ( n = 84) stated they would recommend RAAPS.

The two most common reasons cited for their recommendation were for screening

( n = 76, 92%) and identifi cation of risk behaviors ( n = 75, 90%). Improved communication

( n = 52, 63%) and improved documentation ( n = 46, 55%) and increased patient understanding

of their risk behaviors ( n = 48, 58%) were also cited by respondents as reasons

to recommend the RAAPS” ( Darling-Fisher et al., 2014 , p. 222).

Understanding Pearson Chi-Square • EXERCISE 19 193

TABLE 2 DEMOGRAPHIC COMPARISONS BETWEEN RAPID ASSESSMENT FOR ADOLESCENT

PREVENTIVE SERVICE USERS AND NONUSERS

Current user Yes (%) No (%) χ 2 p

Provider type ( n = 161) 12 .7652, d f = 2 < .00

Health care provider 64 (75.3) 55 (72.4)

Mental health provider 13 (15.3) 2 (2.6)

Other 8 (9.4) 19 (25.0)

Practice setting ( n = 152) 12 .7652, d f = 1 < .00

Outpatient health clinic 20 (24.1) 36 (52.2)

School-based health clinic 63 (75.9) 33 (47.8)

% Adolescent patients ( n = 154) 7.3780, df = 1 .01

≤ 50% 26 (30.6) 36 (52.2)

> 50% 59 (69.4) 33 (47.8)

Years in practice ( n = 157) 6.2597, df = 1 .01

≤ 5 years 44 (51.8) 23 (31.9)

> 5 years 41 (48.2) 49 (68.1)

U.S. practice region ( n = 151) 29.68, d f = 3 < .00

Northeastern United States 13 (15.3) 15 (22.7)

Southern United States 11 (12.9) 22 (33.3)

Midwestern United States 57 (67.1) 16 (24.2)

Western United States 4 (4.7) 13 (19.7)

Race ( n = 201) 1.2865, df = 2 .53

Black/African American 11 (9.9) 5 (5.6)

White/Caucasian 66 (59.5) 56 (62.2)

Other 34 (30.6) 29 (32.2)

Provider age in years ( n = 145) 4.00, df = 2 .14

20–39 years 21 (25.6) 8 (12.7)

40–49 years 24 (29.3) 19 (30.2)

50 + years 37 (45.1) 36 (57.1)

χ 2 , Chi-square statistic.

df , degrees of freedom.

Darling-Fisher, C. S., Salerno, J., Dahlem, C. H. Y., & Martyn, K. K. (2014). The Rapid Assessment for Adolescent Preventive Services

(RAAPS): Providers ’ assessment of its usefulness in their clinical practice settings. Journal of Pediatric Health Care, 28 (3), p. 221.

Chapter 14 Questions to be graded:

1. According to the study narrative and Figure 1 in the Flannigan et al. (2014) study, does the APLS

UK formula under- or overestimate the weight of children younger than 1 year of age? Provide

a rationale for your answer.

2. Using the values a = 3.161 and b = 0.502 with the novel formula in Figure 1 , what is the predicted

weight in kilograms (kg) for a child at 9 months of age? Show your calculations.

3. Using the values a = 3.161 and b = 0.502 with the novel formula in Figure 1 , what is the predicted

weight in kilograms for a child at 2 months of age? Show your calculations.

4. In Figure 2 , the formula for calculating y (weight in kg) is Weight in kg = (0.176 × Age in months)

+ 7.241. Identify the y intercept and the slope in this formula.

5. Using the values a = 7.241 and b = 0.176 with the novel formula in Figure 2 , what is the predicted

weight in kilograms for a child 3 years of age? Show your calculations.

6. Using the values a = 7.241 and b = 0.176 with the novel formula in Figure 2 , what is the predicted

weight in kilograms for a child 5 years of age? Show your calculations.

7. In Figure 3 , some of the actual mean weights represented by blue line with squares are above

the dotted straight line for the novel formula, but others are below the straight line. Is this an

expected fi nding? Provide a rationale for your answer.

8. In Figure 3 , the novel formula is (weight in kilograms = (0.331 × Age in months) − 6.868. What

is the predicted weight in kilograms for a child 10 years old? Show your calculations.

9. Was the sample size of this study adequate for conducting simple linear regression? Provide a

rationale for your answer.

10. Describe one potential clinical advantage and one potential clinical problem with using the three

novel formulas presented in Figures 1, 2, and 3 in a PICU setting.

Chapter 14 content:

STATISTICAL TECHNIQUE IN REVIEW

In nursing practice, the ability to predict future events or outcomes is crucial, and researchers

calculate and report linear regression results as a basis for making these predictions.

Linear regression provides a means to estimate or predict the value of a dependent variable

based on the value of one or more independent variables. The regression equation is

a mathematical expression of a causal proposition emerging from a theoretical framework.

The linkage between the theoretical statement and the equation is made prior to

data collection and analysis. Linear regression is a statistical method of estimating the

expected value of one variable, y , given the value of another variable, x . The focus of this

exercise is simple linear regression , which involves the use of one independent variable,

x , to predict one dependent variable, y .

The regression line developed from simple linear regression is usually plotted on a

graph, with the horizontal axis representing x (the independent or predictor variable) and

the vertical axis representing the y (the dependent or predicted variable; see Figure 14-1 ).

The value represented by the letter a is referred to as the y intercept, or the point where

the regression line crosses or intercepts the y -axis. At this point on the regression line,

x = 0. The value represented by the letter b is referred to as the slope, or the coeffi cient of

x . The slope determines the direction and angle of the regression line within the graph.

The slope expresses the extent to which y changes for every one-unit change in x . The

score on variable y (dependent variable) is predicted from the subject ’ s known score on

variable x (independent variable). The predicted score or estimate is referred to as Ŷ

(expressed as y -hat) ( Cohen, 1988 ; Grove, Burns, & Gray, 2013 ; Zar, 2010 ).

EXERCISE

FIGURE 14-1 ■ GRAPH OF A SIMPLE LINEAR REGRESSION LINE

y-axis

a (y intercept)

b (slope)

x-axis

140 EXERCISE 14 • Understanding Simple Linear Regression

Simple linear regression is an effort to explain the dynamics within a scatterplot (see

Exercise 11 ) by drawing a straight line through the plotted scores. No single regression

line can be used to predict, with complete accuracy, every y value from every x value.

However, the purpose of the regression equation is to develop the line to allow the highest

degree of prediction possible, the line of best fi t . The procedure for developing the line

of best fi t is the method of least squares . If the data were perfectly correlated, all data

points would fall along the straight line or line of best fi t. However, not all data points

fall on the line of best fi t in studies, but the line of best fi t provides the best equation for

the values of y to be predicted by locating the intersection of points on the line for any

given value of x .

The algebraic equation for the regression line of best fi t is y = bx + a , where:

y dependent variable (outcome)

x independent variable (predictor)

b slope of the line (beta, or what the increase in value is along the x-axis for every unit of increase

in the y value), also called the regression coefficient.

a y −intercept (the point where the regression line intersects the y-axis also called the regression

constant Zar 2 1

( , 0 0).

In Figure 14-2 , the x -axis represents Gestational Age in weeks and the y -axis represents

Birth Weight in grams. As gestational age increases from 20 weeks to 34 weeks, birth

weight also increases. In other words, the slope of the line is positive. This line of best fi t

can be used to predict the birth weight (dependent variable) for an infant based on his or

her gestational age in weeks (independent variable). Figure 14-2 is an example of a line of

best fi t that was not developed from research data. In addition, the x -axis was started at

22 weeks rather than 0, which is the usual start in a regression fi gure. Using the formula

y = bx + a , the birth weight of a baby born at 28 weeks of gestation is calculated below.

Formula: y bx a

In this example, a 500, b 20, and x 28 weeks

y 20(28) 500 560 500 1,060 grams

FIGURE 14-2 ■ EXAMPLE LINE OF BEST FIT FOR GESTATIONAL AGE

AND BIRTH WEIGHT

Birth weight1200

1400

1000

800

600

1600

400

22 24 26 28 30 32 34

Gestational age

Understanding Simple Linear Regression • EXERCISE 14 141

The regression line represents y for any given value of x . As you can see, some data

points fall above the line, and some fall below the line. If we substitute any x value in the

regression equation and solve for y , we will obtain a ŷ that will be somewhat different

from the actual values. The distance between the ŷ and the actual value of y is called

residual , and this represents the degree of error in the regression line. The regression line

or the line of best fi t for the data points is the unique line that will minimize error and

yield the smallest residual ( Zar, 2010 ). The step-by-step process for calculating simple

linear regression in a study is presented in Exercise 29 .

RESEARCH ARTICLE

Source

Flannigan, C., Bourke, T. W., Sproule, A., Stevenson, M., & Terris, M. (2014). Are APLS

formulae for estimating weight appropriate for use in children admitted to PICU? Resuscitation,

85 (7), 927–931.

Introduction

Medications and other therapies often necessitate knowing a patient ’ s weight. However,

a child may be admitted to a pediatric intensive care unit (PICU) without a known weight,

and instability and on-going resuscitation may prevent obtaining this needed weight.

Clinicians would benefi t from a tool that could accurately estimate a patient ’ s weight

when such information is unavailable. Thus Flannigan et al. (2014) conducted a retrospective

observational study for the purpose of determining “if the revised APLS UK

[Advanced Paediatric Life Support United Kingdom] formulae for estimating weight are

appropriate for use in the paediatric care population in the United Kingdom” ( Flannigan

et al., 2014 , p. 927). The sample included 10,081 children (5,622 males and 4,459 females),

who ranged from term-corrected age to 15 years of age, admitted to the PICU during a

5-year period. Because this was a retrospective study, no geographic location, race, and

ethnicity data were collected for the sample. A paired samples t- test was used to compare

mean sample weights with the APLS UK formula weight. The “APLS UK formula ‘weight

= (0.05 × age in months) + 4’ signifi cantly overestimates the mean weight of children

under 1 year admitted to PICU by between 10% [and] 25.4%” ( Flannigan et al., 2014 , p.

928). Therefore, the researchers concluded that the APLS UK formulas were not appropriate

for estimating the weight of children admitted to the PICU.

Relevant Study Results

“Simple linear regression was used to produce novel formulae for the prediction of the

mean weight specifi cally for the PICU population” ( Flannigan et al. , 2014, p. 927). The

three novel formulas are presented in Figures 1, 2, and 3 , respectively. The new formulas

calculations are more complex than the APLS UK formulas. “Although a good estimate

of mean weight can be obtained by our newly derived formula, reliance on mean weight

alone will still result in signifi cant error as the weights of children admitted to PICU in

each age and sex [gender] group have a large standard deviation . . . Therefore as soon as

possible after admission a weight should be obtained, e.g., using a weight bed” ( Flannigan

et al., 2014 , p. 929).

142 EXERCISE 14 • Understanding Simple Linear Regression

FIGURE 2 ■ COMPARISON OF ACTUAL WEIGHT WITH WEIGHT

CALCULATED USING APLS FORMULA “WEIGHT IN KG = (2 × AGE IN

YEARS) + 8” AND NOVEL FORMULA “WEIGHT IN KG = (0.176 × AGE IN

MONTHS) + 7.241”

F lannigan, C., Bourke, T. W., Sproule, A., Stevenson, M., & Terris, M. (2014). Are APLS

formulae for estimating weight appropriate for use in children admitted to PICU? Resuscitation,

85 (7), p. 928.

Actual weight

Weight = (2 x age in years) + 8

Weight = (0.176 x age in months) + 7.241

1 2 3 4 5

Weight (kg)

Age (years)

FIGURE 1 ■ COMPARISON OF ACTUAL WEIGHT WITH WEIGHT

CALCULATED USING APLS FORMULA “WEIGHT IN KG = (0.5 × AGE IN

MONTHS) + 4” AND NOVEL FORMULA “WEIGHT IN KG = (0.502 × AGE IN

MONTHS) + 3.161”

F lannigan, C., Bourke, T. W., Sproule, A., Stevenson, M., & Terris, M. (2014). Are APLS

formulae for estimating weight appropriate for use in children admitted to PICU? Resuscitation,

85 (7), p. 928.

Actual weight

Weight = (0.5 x age in months) + 4

Weight = (0.502 x age in months) + 3.161

0 1 2 3 4 11

Weight (kg)

Age (months)

Understanding Simple Linear Regression • EXERCISE 14 143

FIGURE 3 ■ COMPARISON OF ACTUAL WEIGHT WITH WEIGHT

CALCULATED USING APLS FORMULA “WEIGHT IN KG = (3 × AGE IN

YEARS) + 7” AND NOVEL FORMULA “WEIGHT IN KG = (0.331 × AGE IN

MONTHS) − 6.868”

Flannigan, C., Bourke, T. W., Sproule, A., Stevenson, M., & Terris, M. (2014). Are APLS

formulae for estimating weight appropriate for use in children admitted to PICU?