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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

The following data summarize the results from an independent-measures study comparing three treatment conditions.

  M = 2

  n = 10

  T = 20

  s2 = 2.67

M = 3

n = 10

T = 30

s2 = 2.00

M = 4

n= 10

T = 40

s2 = 1.33

a. Use an ANOVA with α = .05 to determine whether there are any significant differences among the three treatment means. Note: Because the samples are all the same size, MSwithin is the average of the three sample variances.

b. Calculate η 2 to measure the effect size for this study.

a.

To determine

To find: Whether there are any significant differences among the three treatment means using ANOVA with α=0.05

Explanation

Given info:

The data with appropriate values are already given in the question.

M=2 M=3 M=4
n=10 n=10 n=10
T=20 T=30 T=40
s2=2.67 s2=2 s2=1.33

Calculations:

Step 1:

Null hypothesis: H0:μ1=μ2=μ3 (all treatments have equal effect)

Alternate hypothesis: Ha: at least one of the treatments is different.

Step 2: Compute degrees of freedom

dfbetween=k1=31=2

Similarly,

dfwithin=Nk=303=27

Critical value:

With α=0.05 and df=2,27, the critical value is CV=3.35.

Step 3: Compute F-ratio

MSwithin=2.67+2+1.333=2

Also,

G=T1+T2+T3=20+30+40=90

He

b.

To determine

To find: The effect size η2 for the given question.

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