1. Fear Free 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
Join TOPSS today!

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

5. Measurement Scales Nominal Scale Ordinal Scale Interval Scale
Ratio Scale

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. The Challenger Disaster
Intro 30 sec
7 mins

10. 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.

11. Temp # of failures
The Data:
Table A

12. The Data Table B Temp / # of failures 53 2 57 1 63 1 66 0 67 0 68 0
The Data
Table B

13. Just a moment for Discussion
What other factors impacted the decision of the company to allow for the launch of the Challenger?
Just a moment for Discussion
To 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.

14. 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:

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

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

17. 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

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

19. 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

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

21. 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) ******

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

23. 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?

24. 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?

25. 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.

26. 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?

27. 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

28. 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.

29. 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?

30. 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

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

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

33. 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.

34. 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.

35. 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

36. 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

37. 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

38. 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.

39. Bell Curve

40. %%%%%%%%%%% Must be memorized

41. Figure 1.10 The normal curve Myers: Psychology, Ninth Edition Copyright © 2010 by Worth Publishers

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

43. 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

44. Negative Correlation
Indicates an inverse relationship between variables
An increase in one variable is accompanied by a decrease in another variable, or vice versa.

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

46. 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

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

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

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

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

54. Back to the Challenger Disaster
Plot the data from Table A and from Table B to establish a visual representation of the scatterplot.

55. 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.

56. When is an Observed Difference Reliable?
Making Inferences
When is an Observed Difference Reliable?
Representative samples are better than biased samples.
Less variable observations are more reliable than more variable ones.
More cases are better than fewer cases.
OBJECTIVE 19| Identify three principles for making generalizations from samples.

57. When is a Difference Significant?
Making Inferences
When is a Difference Significant?
When sample averages are reliable and the difference between them is relatively large, we say the difference has statistical significance.
For psychologists this difference is measured through alpha level set at 5 percent.
OBJECTIVE 20| Explain how psychologists decide whether differences are meaningful.

58. 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

59. Type I and Type II Errors
Statistical tests make use of data from samples. These results are then generalized to the general population. How can we know that it reflects the correct conclusion?
Ironically, the possibility of a research error is what makes the research scientific in the first place. If a hypothesis cannot be falsified (e.g. the hypothesis has circular logic), it is not testable, and thus not scientific, by definition

60. Prediction and Type I and Type II Errors
Variable has an effect
Variable does not have an effect
Deciding that a variable has an effect
Correct
Positive
Deciding that a variable does not have an effect
Unit VIII. Motivation and Emotion

61. Prediction and Type I and Type II Errors
Variable has an effect
Variable does not have an effect
Deciding that a variable has an effect
Correct
Positive
Deciding that a variable does not have an effect
Negative
Unit VIII. Motivation and Emotion

62. Type I and Type II Errors
Type I Error (false positive)
Deciding that one variable has an effect on (or relationship to another variable) when it doesn’t
Incorrectly rejecting the null hypothesis and accepting the hypothesis
p-level gives us the odds of making this kind of error

63. Prediction and Type I and Type II Errors
Variable has an effect
Variable does not have an effect
Deciding that a variable has an effect
Correct
Positive
False
Type I Error
Deciding that a variable does not have an effect
Negative
Type II Error
Unit VIII. Motivation and Emotion

64. Type II Error (false negative)
Deciding that one variable does not have an effect on (or a relationship to) another variable when it does
Incorrectly accepting the null hypothesis and rejecting the hypothesis
There is no easy way to estimate the odds of this kind of error

65. Prediction and Type I and Type II Errors
Variable has an effect
Variable does not have an effect
Deciding that a variable has an effect
Correct
Positive
False
Type I Error
Deciding that a variable does not have an effect
Negative
Type II Error
Unit VIII. Motivation and Emotion

66. Replication This is one of the reasons experiments must be replicated.
This is how science regulates, and minimizes, the potential for Type I and Type II errors
Replication is often not possible in medical diagnosis so Type I and II errors are a factor
In the legal system fingerprinting and DNA have a possibility of false positives leading to false convictions.

67. 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.

68. Fun with STATS
Dice and distribution
M and M sampler