Statistic Practice
Directions: Please read each of the following questions carefully. These practice exercises are a mixture of conceptual, applied, and computational questions; in all cases you must thoroughly explain your answers (in addition to showing all your work) for all calculations, as well as completely answer the question.
1. Five sophomores were given an English achievement test before and after receiving instruction on basic grammar. The scores of these students are shown below.
|
Student
|
Before Instruction
|
After Instruction
|
|
Alfred
|
20
|
20
|
|
Ben
|
14
|
22
|
|
Chris
|
13
|
18
|
|
Donna
|
14
|
17
|
|
Ellen
|
12
|
16
|
a) Conduct an appropriate t-test using these data. Based on your results, it is reasonable to conclude that future students would show higher scores after instruction? Why or why not?
b) Calculate the effect size as well as a confidence interval for the results you got in part (a). What do these mean?
c) Write up the results of this t-test in APA style and indicate (in plain English) what your conclusion isin terms of the effectiveness of the basic grammar instruction.
2. Suppose you are a data analyst for the major pharmaceutical corporation Drugs 'n Stuff. The research & development department has recently begun conducting clinical in order to evaluate the effectiveness of their new drug Pessimism S. (or PS for short) in relieving negative affect. You are given the data below.
|
Mood
|
Drug Dosage (mg.)
|
Neuroticism Score
|
|
5
|
3.8
|
3
|
|
3
|
6.5
|
1
|
|
7
|
2.6
|
8
|
|
4
|
3.1
|
3
|
|
8
|
1.4
|
6
|
|
2
|
6.9
|
5
|
|
4
|
3.5
|
6
|
|
7
|
2.7
|
7
|
The researchers conducted the study as follows:
The eight participants in this study were, upon agreeing to participate, given a self-report questionnaire measuring their level of neuroticism (emotional instability; Neuroticism Score), which was scored on a scale from 1 - 10 (1 = low neuroticism and 10 = high neuroticism). The participants were then given a randomly determined dosage of PS (in mg.; Drug Dosage). After one hour (the amount of time it takes for the drug to have an effect), the researchers asked each participant to indicate their level of mood (Mood), scored on a scale of 1 - 10 (1 = positive mood and 10 = negative mood).
You are tasked with analyzing these data and informing the CEO of Drugs 'n Stuff if the drug is effective.
a) Which of these variables are linearly related? Conduct three Pearson r's and test each one for statistical significance.
b) Build a simple regression equation predicting Mood from Drug Dosage. Don't forget to test the significance of the b as well as the entire equation!
c) Write up the results of part (a) in APA style.
d) Write up the results of part (a) in APA style.
e) Write up what you would tell the CEO about the effectiveness of PS (in non-technical language; don't worry about APA style here).
3. A social psychologist conducted an experiment in which he gave participants (randomly divided into different groups) either water, soda, beer, or non-alcoholic beer to drink (without telling the participants what they were drinking of course). He then observed how the participants interacted with each other, recording each person's level of sociability on a 20-point scale, with higher scores indicating higher levels of sociability. The psychologist wants to know if the actual alcohol content or perceived alcohol content makes a difference in people's willingness to interact socially with others. The data for this study are below.
|
Water
|
Soda
|
Non-Alcoholic Beer
|
Regular Beer
|
|
9
|
12
|
16
|
17
|
|
6
|
13
|
19
|
18
|
|
7
|
14
|
18
|
16
|
|
9
|
13
|
19
|
19
|
|
10
|
15
|
17
|
20
|
|
12
|
15
|
20
|
19
|
|
13
|
9
|
17
|
17
|
|
6
|
12
|
16
|
16
|
|
8
|
13
|
20
|
17
|
|
7
|
15
|
18
|
18
|
a) Conduct an appropriate ANOVA on these data. If you get a significant F-statistic, conduct a Tukey'sHSD post-hoc test, as well as produce a bar graph of the means.
b) Write up the results you got in part (a) in APA style AND explain, in plain English, what those results say.