Slides to accompany Chapter 1

1. BEHAVIORAL STATISTICS
Statistics are all around us!

2. Why Study Behavioral Statistics?
A. Because you have to
B. Because you need it
C. Because it’s FUN
A. Yes, to get your degree
B. Yes, to understand science
C. Ok, maybe not, but it’s
IMPORTANT!

3. Course Moodle Site
• Please make sure you log on EVERY DAY and do all of
the required work
https://moodle.purchase.edu/moodle2/course/view.php?id=32663
• The secret to succeeding in a course like this:
• Keep up with the work – missing one day makes the remaining
days all that much harder to complete
• Test yourself often!

4. Course Objectives
• What will you learn?
• How to interpret and draw inferences findings from scientific
research
• How to employ statistical models to answer questions
• How to recognize the limitations of statistical modeling
• How will you learn?
• Moodle
• Textbook Readings
• Aplia
• Problem Sets
• Lab Exercises

5. BASIC MATH REVIEW
Appendix A

6. Symbols and Notation
Symbol Meaning Example
+ Addition 5 + 7 = 12
- Subtraction 8 – 3 = 5
×, ( ) Multiplication 3 × 9 = 27, 3(9) = 27
÷, / Division 15 ÷ 3 = 5, 15/3 = 5
> Greater than 20 > 10
< Less than 7 < 11
≠ Not equal to 5 ≠ 6

7. Some basics
Given the following
distribution of numbers:
How would you solve
for:
x1 3
x2 1
x3 0
x4 4
x5 2
?2
 X
  ?
2
X

8. Reading equations
• First you must understand what the problems are
numberssquaredtheofallofsumthe2
 X
  squarednumbers,allofsumThe
2
 X
 2
X  2
Xvs.

9. Order of Operations (PEMA)
Remember:
1. Solve all equations in Parentheses
2. Solve Exponents
3. Solve Multiplication/Division
4. Complete Adding/Subtracting

10. Solving equations
• Therefore, for the distribution:
• The solution for is:
x1 3
x2 1
x3 0
x4 4
x5 2
numberssquaredtheofallofsumthe2
 X
222222
24013  X
4160192
 X
302
 X
 2
X

11. Solving equations
• Therefore, for the distribution:
• And the solution for is:
x1 3
x2 1
x3 0
x4 4
x5 2
 2
X
  squarednumbers,allofsumThe
2
 X
  22
)2401(3  X
  22
10 X
  100
2
 X

12. What else should you know?
• Most (if not all) of you are not here by choice
• No one picked this because it seemed like a fun course to take
• Most (if not all) of you have some anxiety about math
• Lucky for you, statistics is not so much about math as it is about
solving puzzles. So if you’re good with puzzles, you’ll be good at
this.
• How can you make this easier on yourselves?
• Keep up.
• All new material builds on old material. So if you get lost and don’t
speak up, you will not be able to follow along.
• Test yourself.
• Do the homeworks.
• Try to do the example problems at the end of each chapter.

13. STATISTICS
A set of mathematical procedures for organizing,
summarizing, and interpreting information

14. Why Statistics?
• Important for behavioral science
• Hypothesis testing: description and analysis of data
• Allows a technical ‘language’ to communicate results

15. Where do we see statistics?

16. Statistics is used for the study of groups
Population
• Set of all the individuals
(N) of interest in a
particular study
• Typically this concerns a
large group
Sample
• Set of individuals (n)
selected from a population
• Intended to be
representative of the
population
• Varies in size

17. Is it a Population or is it a Sample?
• Often, defining a population or a sample depends on the
research question
• Given all the students in this course:
• Population: We are interested in the performance of students in this
particular class
• Sample: We are interested in the performance of undergraduates
taking statistics courses
Yankees fans
A population of everyone who likes
the Yankees
vs.
A sample of baseball fans

18. The
relationship
between the
population and
the sample

19. Describing Groups
Population Parameter
• Typically numerical value
that describes some
aspect of a population
• Average age of college
students
• Average GPA of high school
students
• Most commonly reported
favorite color of young
children
Sample Statistic
• Typically numerical value
that describes some
aspect of a sample
• Average age of college
Psych majors
• Average GPA of students in
the cafeteria
• Most commonly reported
favorite color by your
younger siblings

20. Descriptive Statistics
• Used to summarize, organize and
simplify data
• Makes the data more manageable and
easier to describe
• Graphs, charts, reporting
averages

21. Inferential Statistics
• Techniques that allow us to study samples and then make
generalizations about the populations from which they
were selected
• Based on sample statistics, can we draw conclusions about the
populations from which they were sampled?

22. Sampling Error
The amount of error that
exists between a sample
statistic and the
corresponding
population parameter

23. Statistics in the
Context of
Research
The goal of statistics is
to help researchers
organize and interpret
the data
Measurements
obtained in a
research study
are called data

24. VARIABLES &
MEASUREMENT

25. What is a Variable?
• A variable is a characteristic or condition that changes or
has different values for different individuals
Height
Hair color
GPA
Climate

26. What is a Construct?
• Constructs are internal attributes or characteristics that
cannot be directly observed
Fear?
Shyness?
Surprise?
Anticipation?

27. The Operational Definition of a Construct
• Identifies a measurement procedure
(a set of operations) for measuring an
external behavior and uses the
resulting measurements as a
definition and a measurement of a
hypothetical construct
• Two components:
• Describes a set of operations for
measuring a construct
• Defines the construct in terms of the
resulting measurements

28. Types of Variables
Discrete Variables
• Indivisible categories
Continuous Variables
• Infinitely divisible
Homer
Marge
Lisa
Bart
Maggie
Santa’s Little Helper
Foreman
Doctor
Student
Executive
Intern
Time
Liquid measurement
Distance

29. Real Limits for Continuous Variables
• Real Limits: Boundaries located exactly between adjacent
categories
• Measurement of a continuous variable will almost never
result in identical scores
• We decide the measurement categories (the interval)

30. Scales of Measurement (NOIR)
• Nominal scale (colors, political party, major)
• Label and categorize observations with no quantitative distinctions
• Ordinal scale (year in school, finish in a race)
• Categories organized in an ordered sequence in terms of size or
magnitude
• Interval scale
• Ordered categories that are all intervals of exactly the same size
• Arbitrary zero (0)
• Farenheit temperature (0 is not an absence of temperature, and
negative numbers are possible)
• Ratio scale
• Interval scale with an absolute zero (0; the absence of the variable)
• Meaningful ratios
• Height, weight, time

31. Scales of Measurement (NOIR)
Scale Description Example
Nominal Label and categorize observations with
no quantitative distinctions
Colors, political party,
major
Ordinal Categories organized in an ordered
sequence in terms of size or magnitude
Year in school, placing in
a race
Interval Ordered categories that are all intervals
of exactly the same size, arbitrary zero
(0)
Fahrenheit temperature
(0 is not an absence of
temperature, and can
lower)
Ratio Interval scale with an absolute zero
point (absence of variable), and
meaningful ratios
Height, weight, time

32. Why are these scales important?
• Different statistical tests require data meet certain
levels of measurement
• The average of scores measuring height makes sense
• The average of blue (1), green (2), and red (3) does not

33. DATA STRUCTURES,
RESEARCH METHODS, &
STATISTICS

34. Types of Research Methods
• Descriptive
• To be discussed in later chapters
College students sleep an average of X hours per day
• Correlational
• Two variables are observed for one group to examine if a
relationship exists between the variables
Is there a relationship between sleep habits and academic
performance in college students?
• Experimental and non-Experimental
• Two or more groups are compared on one variable
Does less sleep result in lower scores on tests?

35. The Correlational Method
• Determines whether there is a relationship between two
variables
• Describes that relationship
• Does not allow a determination of cause-and-effect

36. The Experimental Method
• Demonstrates a cause-and-effect relationship between
two variables
• Variables:
• Independent variable (notation: X)
Manipulated by the researcher
• Dependent variable (notation: Y)
Outcome observed to assess the
effect of manipulations of X
• Two important characteristics of the experimental method
• Manipulation (experimental condition vs. control condition)
• Control of extraneous variables (usually participant or
environmental variables)

37. The Non-
Experimental
Method
Non-equivalent
groupsdesign
If there is no
manipulation of an IV
and no control of
extraneous variables,
then it is NOT an
experimental design
Pre-postdesign

38. STATISTICAL NOTATION

39. Summation Notation
• The Greek letter sigma (Σ) stands for “the sum of”
• Thus, ΣX means “the sum of (Σ) scores (X)”
• Remember your order of operations!
1. Parentheses
2. Exponents
3. Multiplication/Division
• (from left to right)
4. Summation (Σ)
5. Remaining addition/subtraction

40. Example 1.3
• ΣX = ?
• ΣX = 3 + 1 + 7 + 4 = 15
• ΣX2 = ?
• ΣX2 = 9 + 1 + 49 + 16 = 75
• (ΣX)2 = ?
• (ΣX)2 = (15)2 = 225
Person X X2
A 3 9
B 1 1
C 7 49
D 4 16