For questions 47-53, refer to the following study and the accompanying SAS output:

Dexterity, as a measure of hand function, is an important component of a thorough hand evaluation. This is especially true in children, for whom the relationship between the commonly measured parameters of range of motion, sensation, and strength may not reflect actual functional ability. Gogola et al. (2013) conducted a study to document normative values from the Functional Dexterity Test (FTD) for typically developing children and to optimize test administration and interpretation. The FDT is a timed pegboard test consisting of 16 thick cylindrical pegs arranged in 4 rows of 4 pegs each. Patients turn over all pegs in a specified order by manipulating each peg in their hand. A total of 174 typically developing children aged 3 to 17 years participated in the study. Children completed the 16-peg FDT with either their dominant (n=105) or nondominant (n=69) hand, and elapsed time was recorded in seconds. Data were analyzed as 16/time, interpreted as FDT speed (pegs per second). Using a 0.05 significance level and the given computer output, you need to test the claim that the mean FDT speeds for dominant (1) and nondominant (0) hands differ significantly after adjusting for age (in years) by answering the questions that follow.

These data were analyzed using two different models. Results from the analysis are provided below labeled SAS Output 1 and SAS Output 2. To answer some of the questions that follow, you need to fill in some critical pieces of information that have been deleted. Letters A, B, C, D, and E indicate missing numbers from the SAS output.

SAS Output 1

Sum of

SourceDFSquaresMean SquareF ValuePr > F

ModelAB1.90029775C<.0001

ErrorDE0.01237307

Corrected Total1735.91638981

R-SquareCoeff VarRoot MSESpeed Mean

0.64238416.699170.1112340.666107

SourceDFType III SSMean SquareF ValuePr > F

Age13.746145603.74614560302.77<.0001

Dominant10.268081510.2680815121.67<.0001

Standard

ParameterEstimateErrort ValuePr > |t|

Intercept0.2309333571 B0.027269908.47<.0001

Age0.03899698620.0022411817.40<.0001

Dominant10.0811365819 B0.017430994.65<.0001

Dominant00.0000000000 B...

Least Squares Means

Adjustment for Multiple Comparisons: Tukey-Kramer

H0:LSMean1=

LSMean2

DominantSpeed LSMEANPr > |t|

10.69828145<.0001

00.61714487

SAS Output 2

Sum of

SourceDFSquaresMean SquareF ValuePr > F

ModelAB 1.26693001 C<.0001

ErrorDE 0.01244470

Corrected Total1735.91638981

R-SquareCoeff VarRoot MSESpeed Mean

0.64241716.74744 0.1115560.666107

SourceDFType III SSMean SquareF ValuePr > F

Age13.226342793.22634279259.25<.0001

Dominant10.034146120.034146122.740.0995

Age*Dominant10.000194540.000194540.020.9006

Standard

ParameterEstimateErrort ValuePr > |t|

Intercept0.2264932870 B0.044822575.05<.0001

Age0.0394158777 B0.004034449.77<.0001

Dominant10.0873575886 B0.052737831.660.0995

Dominant00.0000000000 B...

Age*Dominant 1-.0006074245 B0.00485824-0.130.9006

Age*Dominant 00.0000000000 B...

1.What type of analysis should you perform to test the given hypothesis?

a.Logistic Regression

b.ANCOVA

c.Two-way ANOVA

d.One-way ANOVA

e.Linear regression

2.In SAS Output 2, what number should you insert for the unexplained degrees of freedom (D)?

a.3

b.4

c.169

d.170

e.173

3.Which model is more appropriate for these data: the model in SAS Output 1 or the model in SAS Output 2? Which test statistic and p-value should you use to make this decision?

a.Output 1 because the interaction is not significant (F = 153.58, p-value < 0.0001).

b.Output 1 because the interaction is not significant (F = 0.02, p-value = 0.90).

c.Output 1 because the interaction is not significant (F = 101.80, p-value < 0.0001).

d.Output 2 because the interaction is significant (F = 0.02, p-value = 0.90).

e.Output 2 because the interaction is significant (F = 101.80, p-value < 0.0001).

4.In SAS Output 1, what is the value of the test statistic (C) for the omnibus null hypothesis H₀?

a.302.77

b.153.58

c.21.67

d.17.40

e.4.65

5.Do dominant and nondominant hands differ significantly in their mean FDT speeds? If so, how?

a.Yes, dominant hands were significantly slower than nondominant hands at all ages.

b.Yes, dominant hands were significantly faster than those nondominant hands at all ages.

c.Yes, dominant hands were significantly slower than nondominant hands at younger ages but faster at older ages.

d.Yes, dominant hands were significantly faster than nondominant hands at younger ages but slower at older ages.

e.No, dominant hands and nondominant hands do not differ significantly in their speed.

6.Consider the estimated model from SAS Output 2, which can be written as:

z = age (in years)

x = (1 if dominant hand, 0 otherwise)

What is the mean FDT speed for 12-year-olds using their dominant hands?

a.0.23

b.0.27

c.0.36

d.0.78

e.1.31

7.Which of the following statements is true based on the figure below?

a.The regression lines are coincident.

b.The regression lines are parallel but not coincident.

c.The regression lines are not parallel, and there is a same direction interaction.

d.The regression lines are not parallel, and there is a reverse interaction.

e.As age increases, mean FDT speeds increase at different rates for dominant and nondominant hands.

For questions 54-60, refer to the following study and the accompanying SAS output: A study was conducted on 60 patients to examine the analgesic effects of treatments on elderly patients with neuralgia. Two test treatments and a placebo were compared. The response variable is whether the patient reported pain or not. Letters A, B, C, D, and E indicate missing numbers from the SAS output. Researchers recorded the following variables:

PAIN: patient reported pain (1=yes, 0=no)

TX: treatment (2=test treatment A, 1=test treatment B, 0=placebo)

AGE: age of the patient when the treatment began (in years)

SEX: sex (1=male, 0=female)

DURATION: duration of complaint before the treatment began (in months)

Testing Global Null Hypothesis: BETA=0

TestChi-SquareDFPr > ChiSq

Likelihood Ratio32.76755<.0001

Score25.666650.0001

Wald14.451250.0130

Type 3 Analysis of Effects

Wald

EffectDFChi-SquarePr > ChiSq

tx212.53100.0019

age17.29770.0069

sex15.29460.0214

duration10.03150.8591

Analysis of Maximum Likelihood Estimates

StandardWald

ParameterDFEstimateErrorChi-SquarePr > ChiSq

Intercept1-17.40666.69146.76690.0093

tx11-3.70851.140710.57000.0011

tx21-3.18171.01619.80490.0017

age10.26210.09707.29770.0069

sex111.83220.79635.29460.0214

duration1-0.005860.03300.03150.8591

Odds Ratio Estimates

Point95% Wald

EffectEstimateConfidence Limits

tx1 vs 0A0.0030.229

tx2 vs 0B0.0060.304

ageC 1.0751.572

sex1 vs 0D1.31229.750

durationE0.9321.061

8.What type of analysis is this?

a.ANCOVA

b.Linear regression

c.Logistic regression

d.One-way ANOVA

e.Two-way ANOVA

9.What is the value of the test statistic for the omnibus null hypothesis H₀?

a.14.45

b.25.67

c.32.77

d.Any of the above

e.None of the above

10.Using a 0.05 significance level, what decision and conclusion should you make regarding the omnibus null hypothesis?

a.Because p-value < 0.05, we reject H₀ and conclude that all of the independent variables are significant factors associated with reporting pain.

b.Because p-value < 0.05, we reject H₀ and conclude that none of the independent variables are significant factors associated with reporting pain.

c.Because p-value < 0.05, we reject H₀ and conclude that at least one of the independent variables is a significant factor associated with reporting pain.

d.Because p-value < 0.05, we fail to reject H₀ and conclude that all of the independent variables are significant factors associated with reporting pain.

e.Because p-value < 0.05, we fail to reject H₀ and conclude that none of the independent variables are significant factors associated with reporting pain.

11.Are there any reference cells in this problem? If so, what are they?

a.No, there are no reference cells.

b.Yes, reference cell is younger age.

c.Yes, reference cells are treatment A and male.

d.Yes, reference cells are placebo and female.

e.Both b and c

f.Both b and d

12.How many dummy variables need to be included in the model for TX?

a.3

b.2

c.1

d.0

e.Cannot be determined from the given information

13.What is the estimated odds ratio for reporting pain for a 65-year-old compared to a 60-year-old, controlling for all other variables in the model?

a.0.26

b.1.30

c.1.69

d.3.71

e.7.30

14.Given the estimated odds of reporting pain for a 65-year-old male in treatment group A with a complaint duration of 14 days is 0.165, what is the corresponding risk of reporting pain?

a.0.03

b.0.14

c.0.17

d.1.18

e.1.80