Transcript New copy APSI STATS

A quick introduction, discussion and
conclusion of what you need to know about
Statistics to be successful on the AP
Psychology Exam
This material was originally taken and
modified from a TOPSS unit lesson plan
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Intro to STATS
Statistics (Stats) can be used as a tool to help
demystify research data.
 Examples:

 Election polls
 Market research
 Exercise regimes
 Surveys
 Etc.
Definition of Statistics
A means
of organizing and
analyzing data (numbers)
systematically so that they
have meaning.
Types
Descriptive StatsOrganize data so that
we can
communicate about that data
Inferential StatsAnswers the question, “What can we
infer about the population from data
gathered from the sample?”
Generalizability
Measurement Scales
 Nominal
Scale
 Ordinal
Scale
 Interval
Scale
 Ratio
Scale
Looking at data in a meaningful way
 Frequency
distribution- an
organized list that
enables us to see
clusters or patterns
in data
 Example:
 91
92 87 99 83 84
 82 93 89 91 85 94
 91 98 90
 99
 98
 97
 96
 95
 94
 93
 92
 91
1
1
0
0
0
1
1
1
3
90
89
88
87
86
85
84
83
82
1
1
0
1
0
1
1
1
1
N=15
Grouped Frequency
of same scores
95-99
90-94
85-89
80-84
 N=15
2
7
3
3
The width
of
the intervals in
grouped
frequency
tables must be
equal. There
should be no
overlap.
Moving on to Graphs
These
allow us to quickly
summarize the data collected.
In a glance we can attain some
level of meaning from the
numbers.
Examples:
Pie Charts
A circle within
which all of the
data points or
numbers are
contained in the
form of
percentages
Bar Graphs
 A common method
for representing
nominal data where
the height of the
bars indicates
percentage or
frequency of each
category
Frequency Polygons


A line graph that has the
same vertical and
horizontal labels as the
histogram
Each score’s frequency
of occurrence is marked
with a point on the
graph, when all points
are connected with a
line the polygon takes
shape
The Frequency Polygon
 Useful in showing the
asymmetry in distribution
of ordinal, interval and ratio data.
 This asymmetry is referred to as SKEW.
Positive and Negative SKEW
 If there
is a clustering of data on the high end,
then the skew is NEGATIVE because skewness is
always indicated by the “tail” or low end of the
graph as indicated by low frequency of
occurrence.
 A POSITIVE skew would be indicated by high
frequency of low end data points with a few data
points at the high end
The Tail Tells the Tale
frequency polygon “tails off” to
include these low frequency ends or SKEWNESS
 The line of the
Line Graphs
 Indicate change that
occurs during an
experiment.
 Shows the change in
relationship between
IV and DV
 DV always on the
vertical axis(Y) and IV
on horizontal axis(X)


Mnemonic?? Dry Mix—
DV=Y axis (dry)
IV= X axis (mix)
Graphs don’t lie
 But
different representations will provide
a different visual that can be deceptive.
 Dice
and distribution
Descriptive Statistics
 Measures of central tendency- these
numbers
attempt to describe the “typical” or “average”
score in a distribution.
 What are the
measures of central tendency?
Mode
 The most frequently
occurring score in a set of
scores.
When two different scores occur most frequently
it is referred to as bimodal distribution.
Example?
Median
 The score that
falls in the middle when the scores are ranked
in ascending or descending order.
 This is the best indicator of central tendency when there is a
skew because the median is unaffected by extreme scores.
 If N is odd, then the median will be a whole number, if N is
even, the position will be midway between the two values in
the set.
Mean
 The mathematical average of a set of scores
 The mean is always pulled in the
direction of
extreme scores (pulled toward the skew) of the
distribution.
 Examples?
Examples
SAMPLE TEMPERATURES
Week
One:
 71 74 76 79 98
Week
Two:
70 74 76 77 78
CALCULATE
 MEAN OF WEEK ONE
 MEAN OF WEEK TWO
 MEDIAN OF WEEK ONE
 MEDIAN OF WEEK TWO
 MODE OF WEEK ONE
 MODE OF WEEK TWO
MEASURE OF CENTRAL TENDENCY
CAN BE MISLEADING
 Suppose your mother wants
you to attend a
family reunion on Sunday.
 Everyone in the family protests!
 Your mother attempts to separately convince
each family member that it will not be so bad.
Mom’s story
 Mom tells your younger sister that the
“average”
age of the gathering is 10 years old.
 She tells you the “average” age is 18.
 She tells dad that the “average” age is 36.
 Now each family member feels better about
spending the day at the family reunion.
 Did Mom lie?
The attendees
Years old
3
Name/relation

7

 10

 10

 15

 17

 18

 44

 49

 58

 59

 82

 96

Cousin Susie
Cousin Sammy
Twin Shanda
Twin Wanda
Cousin Marty
Cousin Juan
Cousin Pat
Aunt Harriet
Uncle Stewart
Aunt Rose
Uncle Don
Grandma Faye
Great Aunt Lucille
Answer me this
What is
the median?
What is the mode?
What is the mean?
Did
Mom “lie”?
 What is the
median? 18
 What is the
mode? 10
 What is the
mean? 36
 Did Mom “lie”? Not really. . .
Measures of Variability
 Measures of variability indicate how much
spread or variability there is in a distribution.
 If you collected the ages of all students in the
11th grade, there would be little variability.
 If you collected the shoe sizes of all students in
the 11th grade, there would be greater variability.
Range
 The range is the
difference between the lowest
and highest score in the data set.
 The range of scores can be significantly increased
with a single outlying score.
EXAMPLE
 Class
One: 94, 92, 85, 81, 80, 73, 62
Range=32
 Class
Two: 85, 83, 82, 81, 80, 79, 77
Range= 8
Variance

This is a measure of how different the scores are from
each other.
The difference between the scores is measured by
the distance of each score from the mean of all the
scores.

FORMULA:

 Variance=
Standard Deviation squared
SD2
Standard Deviation
 This measure of variability is also based on how
different scores are from each other.
 There are computer programs and calculators
used for this data.
 FORMULA:
 The Standard
Deviation is the square root
of the variance
Normal Distribution
 The normal curve is a theoretical or hypothetical
frequency curve.
 Most frequency curves are not symmetrical
(remember skew)
 Normal distribution is displayed on a graph with
a “bell” shaped curve.
Bell Curve
%%%%%%%%%%%
Must be memorized
Correlations
 Correlation describes the
relationship between
two variables
 How is studying
related to grades?
 How is playing video games related to grades?
Positive Correlation
 Indicates a
direct relationship between variables
 Variables move in the same direction
 An increase of one variable is accompanied by an
increase in another variable
 A decrease in one variable is accompanied by a
decrease in another variable
 Example
Negative Correlation
 Indicates an inverse relationship
between
variables
 Variables move in opposite directions
 An increase in one variable is accompanied by a
decrease in another variable, or vice versa.
Correlation coefficients
 Correlations are measured with numbers ranging
from -1.0 to +1.0.
 These numbers are called correlation
coefficients.
As the correlation coefficient moves closer to
+1.0, the coefficient shows an increasing positive
correlation.
 As the correlation coefficient moves closer to 1.0, the stronger the negative correlation.
 A zero could indicate no correlation exists
between variables
 .+1.0 and -1.0 indicate a perfect correlation
 Which is a stronger correlation?
 -.85 or +.62
 +.45 or -.23
 -.70 or +.70
 The absolute value of the
number indicates the
strength of the correlation.
BUT. . .
Correlation
does not imply
causation!
Correlational Studies
An often used research
design.
May not have IV and DV,
may be variable one and
two.
Examples?
Scatter plots
A visual representation of
correlations
The x variable is on the
horizontal axis and the y
variable is on the vertical axis
Inferential Statistics
 Inferential
statistics are techniques
that allow us to use representative
samples to make (infer)
generalizations about the
populations from which the samples
were drawn.
Inferential Statistics
 Help us determine if one variable has an effect
on another variable.
 Helps us determine if the difference between
variables is significant enough to infer (for credit
on an AP Exam, you cannot use the term to
define the term) that the difference was due to
the variables, rather than chance.
Statistical Significance
 Are the
results of research strong enough to
indicate a relationship (correlation)? Would you
publish the results? An arbitrary criterion has
been established as .05 (5%).
 Researchers commonly use two inferential
to measure significance


T-test
ANOVA
tests
Are you free of fear?
 Statistics
is an important aspect of research
design in psychology.
 In college you will take an entire course in the
Statistics of psychology.
 If you have a grasp of what was presented today,
you will be successful on the AP Exam.
Concept Map by Alexis
Grosofsky, Ph.D., Beloit College
 It
is a wonderful reference for you and
your students.
 Look for it in the “references” folder
Fun with STATS
 Dice
M
and distribution
and M sampler
 Creating
a Living Frequency Distribution:
Martin Anderson, Ph. D.