# Chapter Nine: Variability , the normal curve, correlation

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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 (n=5) Safe Sex(n=5) Smiley face(n=5) None(n=5) 5 4 6 2 3 1 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
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

Measures of 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
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
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 20 7 49 6 -7 15 2 4 22 9 81 13 -4 16 -11 121 10 -3 Mean = 13 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
Y Zx Zy 12.00 7.00 .17700 .52350 15.00 3.00 .81419 8.00 4.00 11.00 5.00 17.00 9.00 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)
1.73                 . The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education