Download Measure of Variability

Chapter Nine:
Variability , the normal curve,
correlation
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education
Practice
•
A researcher examines whether scores on a
final exam are influenced by whether
background music is soft, loud, or absent.
•
•
•
•
•
What is the independent variable?
Is the independent variable manipulated or not
manipulated?
How many levels are there for the independent
variable?
What is the dependent variable?
What is the scale of measurement for the
dependent variable?
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education
Practice
•
A researcher compares freshmen, sophomores,
juniors, and seniors with respect to how much fun
they have while attending college (1 = no fun at all,
7 = maximum amount of fun).
•
•
•
•
•
What is the independent variable?
Is the independent variable manipulated or not
manipulated?
How many levels are there for the independent variable?
What is the dependent variable?
What is the scale of measurement for the dependent
variable?
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education
• Suppose we conduct a study on whether hand stamps at
bars affect behavior. As patrons enter a bar, they are
randomly assigned to receive one of the following hand
stamps:
• “AIDS Kills”
• “Practice Safe Sex”
• Smiley face
• No stamp
• At the exit of the bar, there is a table where people can
buy condoms at a greatly reduced price. We are interested
in seeing if the type of hand stamp affects how many
condoms patrons buy. It was hypothesized that a fear
message (“AIDS Kills”) would be more effective in
persuading people to buy condoms than a non-fear
messages.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education
Number of condoms purchased
AIDS kills Safe
(n=5)
Sex(n=5)
Smiley
face(n=5)
None(n=5)
5
4
0
0
6
2
0
0
0
3
1
1
5
1
2
1
3
3
3
2
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education
Practice
• What kind of study is this (e.g., survey, case study,
observational study, correlational study, experiment)?
• Identify the independent variable in this study.
• How many levels does this independent variable have?
• What is the dependent variable in this study?
• What is the level of measurement for the dependent variable?
• What is the mean number of condoms bought by participants in
each condition?
•
•
•
•
“AIDS Kills”:
________
“Practice Safe Sex”: ________
Smiley face:
________
No stamp:
________
• Create an APA style bar graph depicting these means.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education
Objectives:
• Review measures of variability
• Evaluate scores in relation to a
distribution
• Evaluate relationships between scores
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education
Measure of Variability
• Variability
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education
Measures of Variability
• Variability
• Range
• A measure of variability that is computed by subtracting the
smallest score from the largest score.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education
Measures of Variability
• Variability
• Range
• Variance
• A single number that represents the total amount of variation in a
distribution.
• The mean of the squared deviations from the mean
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education
Measures of Variability
•
•
•
•
Variability
Range
Variance
Standard Deviation
• The standard deviation is the square root of the variance. It has
important relations to the normal curve.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education
Measures of Variability
• Normal distribution
• A symmetrical, bell-shaped distribution having half the scores
above the mean and half the scores below the mean.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education
Normal Distribution and standard
deviation
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education
Computing z-scores
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education
Practice problem
• Data: 20, 6, 15, 22, 13, 9, 2, 20, 10
• Make a frequency distribution
• Describe shape (skew)
• Find mode, median mean
• Find range, variance and standard
deviation
• What is the z score for 6? 13? 22?
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education
Answers
Mean = 13
20
7
49
6
-7
49
15
2
4
22
9
81
13
0
0
9
-4
16
2
-11
121
20
7
49
10
-3
9
Var = 42
SD = 6.5
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education
Correlation
• Correlation Coefficient
• A single number representing the degree of relation between two
variables.
• The value of a correlation coefficient can range from –1 to +1.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education
Relations between two variables
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education
Computing the Correlation
Coefficient (Pearson R)
.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education
Example: Computing Pearson R
X
Y
Zx
Zy
12.00
7.00
.17700
.52350
15.00
3.00
.81419
-1.27135
8.00
7.00
-.67259
.52350
4.00
4.00
-1.52218
-.82264
11.00
5.00
-.03540
-.37393
17.00
9.00
1.23899
1.42092
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education
Z scores and cross-products
Zx
Zy
ZxZy
0.177
0.524
0.09
0.814
-1.271
-1.03
-0.673
0.5235
0.351
-1.522
-0.822
0.250
-0.035
-0.374
0.01
1.239
1.420
1.76
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education
Computing the Correlation
Coefficient (Pearson R)
• r = 1.73/6
• r = .29
.
1.73
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education