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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

A recent study indicates that simply giving college students a pedometer can result in increased walking (Jackson & Howton, 2008). Students were given pedometers for a 12-week period, and asked to record the average number of steps per day during weeks 1, 6, and 12. The following data are similar to the results obtained in the study.

Number of steps (x1000)
Week
Participant 1 6 12 P  
A 6 8 10 24  
B 4 5 6 15  
C 5 5 5 15 G = 72
D 1 2 3 6 ΣX2= 400
E 0 1 2 3  
F 2 3 4 9  
T = 18 T= 24 T =30  
SS= 28 SS= 32 SS = 40
  1. a. Use a repeated-measures ANOVA with α = .05 to determine whether the mean number of steps changes significantly from one week to another.
  2. b. Compute η2 to measure the size of the treatment effect.
  3. c. Write a sentence demonstrating how a research report would present the results of the hypothesis test and the measure of effect size.

a.

To determine

To use: Repeated measures ANOVA with α=0.05 and determine if mean number of steps charges significantly weekly basis.

Explanation

Given info:

The results regarding number of steps of college students after receiving pedometer is given:

ParticipantWeek

 

N=18G=72X2=400

1 6 12
n=5 T=18 T=24 T=30
SS=28 SS=32 SS=40

Calculation:

Step 1:

The null and alternative hypotheses are:

Null hypothesis:

  H0:μ1=μ2=μ3,

Where μ1μ2μ3 are the mean ratings given to applicants with scar, birthmark and no blemish, respectively.

Alternate hypothesis:

Ha: At least one treatment mean is different.

Step 2:

First stage:

Compute the degrees of freedom (df) for the between treatment effects, within treatment effects and total and corresponding sum of squares (SS).

Now, it is known that, for a given sample size, the degrees of freedom (df) is:

df=(number of units)1.

Thus,

dftotal=N1=17

The number of treatments, k=3. Thus,

dfbetween=k1=2

As within treatments degrees of freedom, dfwithin=dftotaldfbetweentreatment, thus,

dfwithin=df=15

The total sum of squares is:

SStotal=X2G2N.

The within treatment sum of squares is:

SSwithintreatment=SSinsideeachtreatment.

The within treatment sum of squares is:

SSbetween=T2nG2N.

Thus, here,

SStotal=X2G2N=40072218=112

SSwithin=28+32+40=100

SSbetween=T2nG2N=1826+2426+302672218=300288=12

Second stage:

Compute the values of between subject sum of squares and sum of squares due to error.

The between subject sum of squares is:

SSbetweensubject=p2kG2N

b.

To determine

To compute: The value of η2, to measure the size of the treatment effects.

c.

To determine

To write: The results in from of a report.

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