Question

In an experiment, participants were shown three of the famous Rorschach “inkblot” images, each accompanied by an actual response from a patient undergoing psychiatric evaluation. They were asked: “Based on this response to the inkblot, how unstable do you think the patient is, on a scale from 1 (very stable) to 10 (very unstable)?"

They were divided into two experimental groups: Group 1 had patients with common names (Sara, Mary, John) and Group 2 had patients with uncommon names (Desdemona, Edmund, Roderick).

The hypothesis was that there is a bias against patients with uncommon names, such that their responses will seem more unstable. Use these results to answer the questions

Group 1 (common): M₁ = 5.04, n₁ = 32, s²₁ = 2.68

Group 2 (uncommon): M₂ = 5.30, n₂ = 32, s²₂ = 2.13

A. What is the pooled variance, s²_p?

B. What is the estimated standard error, s_(M1–M2) ?

C.

What is the t-stat (Remember: this is an independent samples t-test)?

D. What is the r² effect size measure?

E. Write a proper sentence reporting the results of the t-test and the effect size measure. You may chose your own alpha-criterion and whether to do one- or two-tailed, but be sure to include that information in your sentence.

Answer 1

NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

Group 1 (common): M₁ = 5.04, n₁ = 32, s²₁ = 2.68

Group 2 (uncommon): M₂ = 5.30, n₂ = 32, s²₂ = 2.13

A] POOLED VARIANCE= s1^2(n1-1)+s2^(n2-1)/n1+n2-2

= 2.404

B] Standard error = 0.3876

C] test statistic t= difference of means/Standard error of mean

= -0.26/0.3876

= -0.6707

The p-value is .252673.The result is not significant because p > .05.

D] r^2= t^2/t^2+df

= (-0.671)^2/(-0.671)^2+62

= 0.00721 VERY SMALL EFFECT SIZE

E] CONCLUSION: We donot have suuficient evidence to conclude that  there is a bias against patients with uncommon names at 0.05 level of significance .