Researchers are interested in testing whether cognitive behavioral therapy (CBT)

Question

Researchers are interested in testing whether cognitive behavioral therapy (CBT) can reduce the social anxiety of highly anxious people. They recruited 18 sets of identical twins, both of whom suffered from similar levels of social anxiety prior to the study and neither of whom had ever underwent any kind of therapy. For each set of twins, the researchers randomly assigned one twin to receive CBT and the other twin continued to receive no therapy. After two months have passed, the researchers measured the twins' self-reported social anxiety. The social anxiety scores are shown to the right. Assume that social anxiety scores are known to be normally distributed in the population and that lower scores denote lower levels of social anxiety. At the = 0.05 level of significance, is there evidence to suggest that CBT is effective at reducing social anxiety?

b) Suppose the researchers were able to recruit 4,000 sets of identical twins. As before, both of the twins suffered from similar levels of social anxiety prior to the study and neither had ever underwent any kind of therapy. Again, as before, for each set of twins, the researchers randomly assigned one twin to receive CBT and the other twin continued to receive no therapy. Under this new study, the researchers found that twins who had undergone CBT had significantly lower self-reported social anxiety scores than twins who had received no therapy at the = 0.001 level of significance. The researchers contend that their study design provides causal evidence that CBT is effective at lowering social anxiety for the participants in their study. Given the design of the study, do you agree with their conclusion? Why or why not?  

Twin Pair No Therapy CBT 1 40 32 2 38 34 3 36 30 4 42 31 5 32 29 6 26 27 7 42 43 8 28 25 9 46 48 10 34 33 11 42 43 12 29 26 13 33 34 14 23 24 15 29 27 16 37 35 17 44 43 18 36 40

Explanation / Answer

a)

Two-Sample T-Test and CI: No Therapy, CBT

Two-sample T for No Therapy vs CBT

             N   Mean StDev SE Mean
No Therapy 18 35.39   6.63      1.6
CBT         18 33.56   7.16      1.7

Difference = (No Therapy) - (CBT)
Estimate for difference: 1.83
95% CI for difference: (-2.84, 6.50)
T-Test of difference = 0 (vs ): T-Value = 0.80 P-Value = 0.431 DF = 34
Both use Pooled StDev = 6.8957

p-value = 0.431 > 0.05

hence we fail to reject the null and conclude that At the = 0.05 level of significance, there is no evidence to suggest that CBT is effective at reducing social anxiety

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