1. A quick introduction, discussion and conclusion of what you need to know about
Statistics to be successful on the AP Psychology Exam
Fear Free Stats!

2. Intro to STATS Election polls Market research Exercise regimes Surveys
Statistics (Stats) can be used as a tool to help demystify research data.
Examples:
Election polls
Market research
Exercise regimes
Surveys
Etc.

3. Definition of Statistics
A means of organizing and analyzing data (numbers) systematically so that they have meaning.

4. 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 (G Theory)
Statistical framework for conceptualizing, investigating, and designing reliable observations
Used to determine reliability (reproducibility of measurements under specific conditions

5. Measurement Scales Nominal Scale
A discrete classification of data, in which data are neither measured nor ordered but subjects are merely allocated to distinct categories
Ordinal Scale
Data is shown in order of magnitude since there is no standard of measurement of differences
Interval Scale
Numeric scales in which not only the order is known, but also the exact differences between the values
Ratio Scale
An interval scale in which distances are stated with respect to a rational zero rather than with respect to, for example, the mean

6. Looking at data in a meaningful way
Frequency distribution- an organized list that enables us to see clusters or patterns in data ,
Example:

7.
N=15

8. Grouped Frequency of same scores
N=15
The width of the intervals in grouped frequency tables must be equal. There should be no overlap.

9. 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:

10. Pie Charts
A circle within which all of the data points or numbers are contained in the form of percentages

11. Bar Graphs
A common method for representing nominal data where the height of the bars indicates percentage or frequency of each category

12. 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

13. The Frequency Polygon
Useful in showing the asymmetry in distribution of ordinal, interval and ratio data.
This asymmetry is referred to as SKEW.

14. 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

15. The Tail Tells the Tale
The line of the frequency polygon “tails off” to include these low frequency ends or SKEWNESS

16. 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—Dependent is Responding and on the Y axis (dry)
Manipulated is Independent and on the X axis. (mix)

17. Graphs don’t lie
But different representations will provide a different visual that can be deceptive.
Dice and distribution

18. 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?

19. 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?

20. 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.

21. 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?

22. Examples Week One: 71 74 76 79 98 Week Two: 70 74 76 77 78
SAMPLE TEMPERATURES
CALCULATE
Week One:
Week Two:
MEAN OF WEEK ONE
MEAN OF WEEK TWO
MEDIAN OF WEEK ONE
MEDIAN OF WEEK TWO
MODE OF WEEK ONE
MODE OF WEEK TWO

23. 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.

24. 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?

25. The attendees Years old Name/relation3 7 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

26. Answer me this What is the median? What is the mode? What is the mean?
Did Mom “lie”?

27. What is the median? 18
What is the mode? 10
What is the mean? 36
Did Mom “lie”? Not really. . .

28. 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.

29. 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.

30. EXAMPLE Range=32 Range= 8 Class One: 94, 92, 85, 81, 80, 73, 62
Class Two: 85, 83, 82, 81, 80, 79, 77
Range= 8

31. Variance SD2 Variance= Standard Deviation squared
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

32. Standard Deviation FORMULA:
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

33. 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.

34. Bell Curve

35. %%%%%%%%%%% Must be memorized

36. Correlations
Correlation describes the relationship between two variables
How is studying related to grades?
How is playing video games related to grades?

37. 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

38. 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.

39. Correlation coefficients
Correlations are measured with numbers ranging from -1.0 to +1.0.
These numbers are called correlation coefficients.

40. As the correlation coefficient moves closer to +1
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

41. Which is a stronger correlation?
The absolute value of the number indicates the strength of the correlation.

42. Correlation does not imply causation!
BUT. . .
Correlation does not imply causation!

43. Correlational Studies
An often used research design.
May not have IV and DV, may be variable one and two.
Examples?

44. Scatter plots A visual representation of correlations
The x variable is on the horizontal axis and the y variable is on the vertical axis

48. 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.

49. 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.

50. 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

51. 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.

52. 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

53. Fun with STATS Dice and distribution M and M sampler
Creating a Living Frequency Distribution: Martin Anderson, Ph. D.