Fear Free Stats!

A quick introduction, discussion and conclusion of what you need to know about Statistics to be successful on the AP Psychology ExamThis material was originally taken and modified from a TOPSS unit lesson planJoin TOPSS today!

Intro to STATS

Statistics (Stats) can be used as a tool to help demystify research data.

Examples:

Election pollsMarket researchExercise regimesSurveysEtc.

Definition of Statistics A means of organizing and

analyzing data (numbers) systematically so that they have meaning.

TypesDescriptive Stats-Organize data so that we can

communicate about that dataInferential Stats-Answers the question, “What can we

infer about the population from data gathered from the sample?”

Generalizability

Measurement ScalesNominal Scale

Ordinal Scale

Interval Scale

Ratio Scale

Looking at data in a meaningful wayFrequency 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 1 90 1 98 1 89 1 97 0 88 0 96 0 87 1 95 0 86 0 N=15 94 1 85 1 93 1 84 1 92 1 83 1 91 3 82 1

Grouped Frequency of same scores95-99 290-94 785-89 380-84 3 N=15

The width of the intervals in grouped frequency tables must be equal. There should be no overlap.

The Challenger Disaster

Intro 30 sec

7 mins

Misuse of Stats The decision to launch the Challenger was in part

based on the correlational analysis of failure rates and temperature. You can look at the actual data available to the experts who decided to launch the shuttle and decide if you would have actually launched the shuttle.

Temp # of failures

53 2 57 1 58 1 63 1 70 2 75 2

The Data:Table A

Temp / # of failures 53 2 57 1 63 1 66 0 67 0 68 0 69 0 70 2 72 0 73 0 75 0 76 0 79 0 81 0

The DataTable B

What other factors impacted the decision of the company to allow for the launch of the Challenger?

Just a moment for DiscussionTo the teacher: a brief research of the issue can be done to expand this topic.Application of critical thinking skills is an important marker for success on the AP Exam.

Moving on to GraphsThese allow us to quickly

summarize the data collected.In a glance we can attain some

level of meaning from the numbers.

Examples:

Pie ChartsA 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

DV always on the vertical axis(Y) and IV on horizontal axis(X) ******

Graphs don’t lieBut 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?

ExamplesSAMPLE 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 attendeesYears old Name/relation 3 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 thisWhat 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 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 StudiesAn often used research

design.May not have IV and DV,

may be variable one and two.

Examples?

Scatter plotsA visual representation of

correlationsThe x variable is on the

horizontal axis and the y variable is on the vertical axis

Back to the Challenger Disaster Plot the data from Table A and from Table B to

establish a visual representation of the scatterplot.

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 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.

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 and distribution

M and M sampler