Please note that there is some personal opinion in whether an effect size is "practically significant." You may disagree with some of the judgments made in this HW Key.

Problem 1
Calculate effect sized for 2-7 in "First Official Hypothesis Testing" and 3, 5, 6 in "Switching to t-scores".

2) "First Official Hypothesis Testing"

Xbar = 5.3 mhyp = 4.0 s = 1.2 N = 15	d = (Xbar - mhyp)/s = (5.3 - 4.0)/1.2 = 1.08
	* Sample mean is 1.08 SD above the value of interest * Large effect according to Cohen * This may be practically significant in terms of the implications for the social environment of libraries.

3) "First Official Hypothesis Testing"

Xbar = 50 mhyp = 4.8 s = 10 N = 400	d = (Xbar - mhyp)/s = (50 - 48)/10 = .20
	* Sample mean is .20 SD above the value of interest * Small effect according to Cohen

4) "First Official Hypothesis Testing"

Rich East Xbar 1 = 610 s1 = 100

Rich Central Xbar 2 = 595 s2 = 100

d = (Xbar1 - Xbar2)/s = (610 - 595)/100 = .15 * The mean SAT score at Rich East is .15 SD greater than the mean SAT score at Rich Central * Small effect according to Cohen * Doesn't seem very practically significant.

5) "First Official Hypothesis Testing"

XbarD = 4.4 sD = 6.2

d = (XbarD)/sD = 4.4/6.2 = .71 * Clients' ratings were .71 SD greater than those of counselors. * Large effect according to Cohen * This could be practically significant for understanding the counseling relationship.

6) "First Official Hypothesis Testing"

Black XbarB = 6.5 sB= 1.6

White XbarW = 7.7 sW = 1.6

d = (XbarB - XbarW)/s = (6.5 - 7.7)/1.6 = -.75 * The mean rating for the Black applicant was .75 SD below the mean rating for the White applicant * Large effect according to Cohen * Important topic - racial discrimination

7) "First Official Hypothesis Testing"

XbarD = -1.2 sD= 1.0

d = (XbarD)/sD = -1.2/1 = -1.2 * Ratings for Black applicants were, on average, 1.2 SDs less than those for White applicants * Large effect according to Cohen * Practically significant due to social importance of topic.

3) Switching to t-scores

mhyp= 58.7 Xbar = 60.13 s = 1.43	d = (X - mhyp)/s = (60.13 - 58.7)/1.43 = 1.00
	* Our sample mean is 1 SD greater than the value of interest * Large effect according to Cohen * From my perspective, not practically significant, except maybe for the company!

5) Switching to t-scores

mhyp= 27,000 Xbar = 24,000 s = 6226.29	d = (X - mhyp)/s = (24,100 - 27,000)/6,226.29 = -.47
	* Our sample mean is .47 SD less than the value of interest * Medium effect according to Cohen

6) Switching to t-scores

Praise X1 = 1.4 s1 = 1.1 N1 = 9

No Praise X2 = 2.3 s2 = 1.2 N2 = 9

d = N(X 1 - X 2)/ (N1s1 + N2s2) = 18(1.4 - 2.3)/ [9(1.1) + 9(1.2)] = -.78 * The mean number of time forgetting is .78 SD less for the children in the praise condition. * Medium/Large effect according to Cohen * Significance depend upon whether these are your kids!

Problem 2

Effect size for Blueberry Compote

Method A X1 = 2 s1 = .4 N1= 50

Method B X2 = 1.7 s2= .4 N2= 50

d = N(X1 - X2)/ (N1s1 + N2s2) =100(2.0 - 1.7)/ [50(.4) + 50(.4)] = .75 * Method A yields .75 SD more compote than Method B * Large effect according to Cohen * Practically significant, at least for those who want to get their money's worth of blueberry in their yogurt.

Effect size for Stray Matter

Method A X1= .003 s1 = .007 N1= 50

Method B X2 = .001 s2 = .007 N2= 50

d = N(X1 - X2)/ (N1s1 + N2s2) = =100(.003 - .001)/ [50(.007) + 50(.007)] = .75 * Method A yields .29 SD more stray matters than Method B * Small effect according to Cohen * Practically significant because of the potential health risks of having stray matter in yogurt.

As a consumer, I'd be much more concerned about the stray matter than the blueberry compote. You may have a different opinion, though!