Transcript File

Fear Free Stats!
What you need to know to be
successful on the AP Test.
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

Inferential Stats

Organize data so that we can
communicate about that data
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


EXAMPLE
These numbers have little meaning
until they are organized.
91 92 87 99 83 84 82 93 89
91 85 94 91 98 90
Frequency distribution










Frequency distribution- an organized list that
enables us to see clusters or patterns in data.
99
98
97
96
95
94
93
92
91
–
–
–
–
–
–
–
–
–
1
1
0
0
0
1
1
1
3
and so on.
Grouped Frequency
of same scores






95-99
2
90-94
7
85-89
3
80-84
3
N=15
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.
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 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 indicative of 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

The line of the frequency polygon
“tails off” to include these low
frequency ends or SKEWNESS
Line Graphs



Indicate change that occurs during
an experiment.
Shows the change in relationship
between IV and DV
IV always on the
vertical axis and
DV on horizontal
axis
Graphs don’t lie
But
different
representations will
provide a different
visual that can be
deceptive.
Descriptive Statistics


Measures of central tendencythese 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
MEDIAN OF WEEK ONE
MODE OF WEEK ONE
MEAN OF WEEK TWO
MEDIAN OF WEEK TWO
MODE OF WEEK TWO
MEAN OF BOTH WEEKS COMBINED
MEDIAN OF BOTH WEEKS COMBINED
MODE OF BOTH WEEKS COMBINED
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
Information
AGES
 3
 7
 10
 10
 15
 17
 18
 44
 49
 58
 59
 82
 96
NAME AND RELATION
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”?
Answers

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
Negative Correlation
 Indicates
an inverse
relationship between
variables
 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.
Correlation Coefficient




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
Continued





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
not imply
causation!
does
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
Scatter Plot
Scatter Plot
Scatter Plot
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?
Researchers commonly use two
inferential tests to measure
significance
T-test
ANOVA
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.
STATS Activity

Dice and the Bell Curve (Rob McEntarffer)




In this lesson, students use a simple method of
gathering and plotting data. Students will
discover that the data falls along a bell
(normal) curve.
You and a partner or two get a pair of
dice.
Roll the dice, add the results of each die
and record the sum in some organized
manner.
Roll the dice 50 times.