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?

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

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?

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

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

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?

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