Question

In a cognitive psychology experiment, the researcher is interested in whether encoding condition has a significant effect on memory for a list of words. She recruits 32 subjects to participate in the experiment. Each recruited subject is randomly assigned to either encoding condition A or encoding condition B. The researcher would like to leave the hypothesis non-directional without predicting which encoding condition would lead to better memory, and she sets the significance level at α = .05 for a two-tailed test.

Hint: You may remember a similar scenario in the previous assignment, but with a crucial difference. In the previous assignment, each subject attends BOTH condition A and condition B, while each subject here attends only ONE condition (either A or B).

Q1) Independent-Samples t Test (20 points total)

In a cognitive psychology experiment, the researcher is interested in whether encoding condition has a significant effect on memory for a list of words. She recruits 32 subjects to participate in the experiment. Each recruited subject is randomly assigned to either encoding condition A or encoding condition B. The researcher would like to leave the hypothesis non-directional without predicting which encoding condition would lead to better memory, and she sets the significance level at α = .05 for a two-tailed test.

Subject ID	Encoding A		Subject ID	Encoding B
1	87		11	85
2	80		12	80
3	78		13	76
4	76		14	77
5	86		15	86
6	77		16	68
7	83		17	85
8	82		18	79
9	91		19	89
10	90		20	85

Hint: You may remember a similar scenario in the previous assignment, but with a crucial difference. In the previous assignment, each subject attends BOTH condition A and condition B, while each subject here attends only ONE condition (either A or B).

h. Calculate standard deviation (S_diffmean)of the comparison distribution (1 point total: .5 if the process is correct but the answer is wrong)

Hint: This comparison distribution consists of differences between all possible sample means drawn from the two sampling distributions. Its standard deviation is the denominator of the t statistic formula.

i. Calculate the t statistic (1 point total: .5 if the process is correct but the answer is wrong)

j. For the two-tailed test, find the critical t values for this hypothesis test based on the total degree of freedom (from question d above), and the preset alpha level. (1 point total)

k. Compare the calculated t statistic with the critical t value by stating which is more “extreme”, and then draw a conclusion about the hypothesis test by stating clearly “reject” or “fail to reject” the null hypothesis. (2 points total: 1 for comparison, 1 for decision)

l. Calculate the pooled standard deviation for the populations (use the pooled variance calculated in question f); and then calculate the standardized effect size of this test. (2 points total: 1 for pooled standard deviation, 1 for effect size. Deduct .5 if a result is wrong but the process is correct.)

m. Draw a conclusion based on the hypothesis test result and the effect size. In other words, did encoding condition have a significant effect on memory score? Was the effect small, medium, or large? (1 point total: .5 for each element).

Answer 1

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R Console Untitled- R Editor x1- Encoding A , x2-Encoding B xl-c (87,80,78,76,86,77,83,82,91, 90) x2-c (85, 80,76, 77,86, 68,85,79,89,B5) xl-c (87,80,78,76, 86, 77,83, 82,91,9 >x2-c (85,80,76,77,86, 68,85,79,89,8 > xlbar-mean (xl) >x2bar-mean (x2) > nl-length (xl) > n2-length (x2) >s1-var x1) >s2-var (x2) xlbar-mean (xl) x2bar-mean (x2) nllength (xl) n2=length (x2) spsq (nl-1)s1) +( (n2-1)s2) ) / (rs1-var (xl) >sp-sqrt (spsq) s2-var (x2) spsq (( (nl-1) sl) sp sqrt (spsq) (n2-1)s2)) / (nl+n2-2) >sp [] 5.821416 sp d-x1-x2 d-x1-x2 sd (d) sd (d) [1] 3.197221 t(xlbar-x2bar)/(sp sqrt( (1/nl)+t= (xlbar-x2bar)/(spsqrt((1/nl)+ (1/n2) ) ) steffect (xlbar-x2bar) /sp [ 0.7692213 steffect=(xibar-x2bar)/sp steffect qt (0.975, (nl+n2-2)) steffect [ 0.343559 qt (0.975, (nl+n2-2) } 2.100922