A psychologist would like to evaluate the relationship between verbal skills as

Question

A psychologist would like to evaluate the relationship between verbal skills as measured by the Scholastic Achievement Test (SAT) and performance on an anagram task. (Anagrams arc words with the letters scrambled. The task is to unscramble the letters and identify the word.) Each subject is given a set of 10 anagrams, and the psychologist records how much time is needed to solve all 10. The anagram times and each subject's SAT score are as follow s. Use a Spearman correlation to measure and describe the relationship between SAT and anagram performance.

Explanation / Answer

a)

X Values
∑ = 1234
Mean = 123.4
∑(X - Mx)2 = SSx = 48772.4

Y Values
∑ = 5060
Mean = 506
∑(Y - My)2 = SSy = 73240

X and Y Combined
N = 10
∑(X - Mx)(Y - My) = -57134

R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -57134 / √((48772.4)(73240)) = -0.96 = Peason Correlation Coefficient

b) let SAT score = y, time = x

Hence regression equation is:

y = 650.556-1.171x

No.of Inputs 10 Slope(B) -1.171 X Mean 123.4 Y Mean 506 Intercept(A) 650.556

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