Question

In a cognitive psychology experiment, the researcher is interested in whether encoding condition has an effect on memory for a list of words. She recruits 16 subjects to participate in the experiment. Each subject comes to the lab twice to be tested in two different encoding conditions and their memory performance scores are listed below. 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	Encoding B
1	87	85
2	80	81
3	80	76
4	76	78
5	86	87
6	78	68
7	83	85
8	82	79
9	92	90
10	90	85
11	80	81
12	80	76
13	76	78
14	89	87
15	80	79
16	90	90

a. Identify the dependent variable (this is the outcome measure) and the independent variable (this is what differentiates the two groups of data points being compared). (1 point total: .5 for DV, .5 for IV)

b. What would be the null and alternative hypotheses in both words and symbol notations? (2 points total: 1 for each hypothesis, .5 for written and .5 for notation)

Perform the steps below to get the t statistic for the sample:

c. Calculate the difference scores and enter them into the table below. (1 point, deduct .5 for each error up to 1 point total)

Subject ID	Difference
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16

d. Mean of sample (1 point: .5 if process is correct but answer is wrong)

e. Estimated population standard deviation (1 point: .5 if process is correct but answer is wrong)

f. Standard error (1 point: .5 if process is correct but answer is wrong)

g. Calculated t statistic (1 point: .5 if process is correct but answer is wrong)

With the calculated t statistic, perform the following steps to conclude the hypothesis test.

h. Critical t value (1 point: .5 if process is correct but answer is wrong)

i. Compare the t statistic with the critical t value. Is the calculated t statistic more extreme or less extreme than the critical t value? Then make a decision about the hypothesis test, stating explicitly “reject” or “fail to reject” accordingly. (1 points total: .5 for each answer)

j. Interpret the result in 1-2 sentences to answer the research question (you may use the wording from the hypothesis or explain it in your own words) (1 point)

k. Calculate the standardized effect size of this hypothesis test (1 point: .5 if process is correct but answer is wrong)

Answer 1

a. The dependent varible is 'memory performance' and the independent variable is 'encoding' which consisted of two related groups: "encoding A" and "encoding B".

b. H0: The encoding condition not lead to better memory. i.e., d=0

H1: The encoding condition lead to better memory, i.e., d < 0

c.

Subject ID	Difference
1	2
2	-1
3	4
4	-2
5	-1
6	10
7	-2
8	3
9	2
10	5
11	-1
12	4
13	-2
14	2
15	1
16	0

d. mean of sample

e. estimate of population standard deviation

i. t statistic (=2.11) which is greater than critical value (1.753) i.e., t statistic > critical value. Hence we reject H0.

j. We conclude that the encoding condition lead to better memory, i.e., d < 0 at 5% level of significance.