The table below displays hypothetical data showing the results from a study used

Question

The table below displays hypothetical data showing the results from a study used between-subjects (independent-groups) design and a study that used a within-subjects (repeated-measures) design The two sets of data use identical numerical scores and they both show the same 5-point mean difference between treatments. Analysis of the data from the study that used a between-subjects design. Calculate the variance for each of the two samples and then compute the pooled variance. Conduct a two-tailed independent-samples t test with alpha = .05. Find the critical value of t. Do these data indicate a significant difference between the two treatments? Analysis of the data from the study that used a within-subjects (repeated measures) design. Conduct a two-tailed paired-samples t test with alpha = .05. Find the critical value of t. Do these data indicate a significant difference between the two treatments?

Explanation / Answer

a)            H0: 1 - 2 = 0 i.e. (1 = 2)

               H1: 1 - 2 0 i.e. (1 2)

S2p= (n1-1)S21+(n2-1) S22/(n1-1) +(n2-1)

      = (3-1)*(114)^2+(3-1)*(86)^2/(3-1)+(3-1)

      = 2*12996+2*7396/4

      =10196

t=(X1-X2)-(µ1- µ2)/ S2p(1/n1+1/n2)

t=(26-21)-0/10196(1/3+1/3)

t=5/82.45

t=0.06

tCRICT is 2.7764 and hence cannot reject null hypothesis.

b)

tSTAT=D- /S.D/sqrt(n)

Where tSTAT has n - 1 d.f

tSTAT=-5-0/8/sqrt(3)

      =-1.08

t critical value=-4.3026

Hence cannot reject H0

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