1. Reasoning in Psychology Using Statistics
2015

2. Please complete the survey mentioned in President Dietz’s email.
While at it, feel free to think about statistics:
What scales of measurement?
How would I graph these results?
Etc.

3. Rolling the dice Let’s collect set of data
I’ll pass out some pairs of dice
Collect n=36 data points
12 people roll a pair of dice three times
Write down the 36 numbers on the board
Type numbers here:
Rolling the dice

4. Distributions Distribution Type numbers here:
The distribution of a variable is a summary of all the different values of a variable
The set of all of the outcomes of rolling the dice
Both type (each value) and token (each instance)
Un-organized, the overall pattern and properties of the distribution are difficult to see
A “picture” of the distribution is usually helpful
Type numbers here:
Distributions

5. Distributions Descriptive statistics
Statistical tools/procedures to help organize, summarize, and simplify large sets of data (distributions)
Important descriptive properties of distribution
Center
Where most of the data in the distribution are
Spread (variability)
How similar/dissimilar are the scores in the distribution?
Shape
Symmetric vs. asymmetric (skew)
Unimodal vs. multimodal
Distributions

6. Distributions A “picture” of the distribution is usually helpful
Gives a good sense of the properties of the distribution
Many different ways to display distribution
Table
Frequency distribution table
Stem and leaf plot
Graphs
Distributions

7. Frequency distribution table
The values of the variable
The number of tokens of each variable
The proportion of tokens at each value
The percentage of tokens at each value
Cumulative percentage
p = f/N
N=total
Set-up for values of pair of dice
Frequency distribution table

8. Cumulative percent Quiz: “What % got this score or worse?” 10
10% got a 1 or worse
Simpler case oo a short quiz
Cumulative percent

9. Cumulative percent Quiz: “What % got this score or worse?”
15% got a 2 &
10% got a 1 25 10
25% got a 2 or worse
Cumulative percent

10. Cumulative percent Quiz: “What % got this score or worse?”
10% got a 3 &
15% got a 2 &
10% got a 1 35 25 10
35% got a 3 or worse
Cumulative percent

11. Cumulative percent Quiz: “What % got this score or worse?”
35% got a 4 &
10% got a 3 &
15% got a 2 &
10% got a 1 70 35 25 10
70% got a 4 or worse
Cumulative percent

12. Cumulative percent Quiz: “What % got this score or worse?”
20% got a 5 &
35% got a 4 &
10% got a 3 &
15% got a 2 &
10% got a 1 90 70 35 25 10
90% got a 5 or worse
Cumulative percent

13. Cumulative percent Quiz: “What % got this score or worse?”
10% got a 6 &
20% got a 5 &
35% got a 4 &
10% got a 3 &
15% got a 2 &
10% got a 1
100 90 70 35 25 10
100% got a 6 or worse
Cumulative percent

14. Frequency distribution: sum of 2 dice
Fill in numbers from
our class:
Sample distribution
n = 36
Frequency distribution: sum of 2 dice

15. Theoretical Frequency distribution: sum of 2 dice
p = probability when
predicting
p = proportion when
describing what you
observed
Think of this as defining our population distribution of the outcome of tossing two dice
Theoretical Frequency distribution: sum of 2 dice

16. Theoretical Frequency distribution: sum of 2 dice
Value
D1+D2 D1 D2
frequency D1 D2 D1 D2 12 1 4 3 2 7 6 5 3 6 11 2 11 10 9 8 3 2 1 4 5 5 4
Total outcomes = 62 = 36
= = 36
Theoretical Frequency distribution: sum of 2 dice

17. Theoretical Frequency distribution: sum of 2 dice

18. Theoretical frequency distribution & class sample (Actual fs are from a previous term.)

19. Distributions Important properties of distribution Center
Where most of the data in the distribution are
Spread (variability)
How similar/dissimilar are the scores in the distribution?
Shape
Symmetric vs. asymmetric (skew)
Unimodal vs. multimodal
Distributions

20. Describing the distribution
What is the most frequent score? 7
Describing the distribution

21. Describing the distribution
What is the most frequent score?
Where do most of the scores lie?
Two-thirds of the data are here
Describing the distribution

22. Describing the distribution
What is the most frequent score?
Maximum score: 12
Where do most of the scores lie?
What was the range of scores?
Minimum score: 2
Describing the distribution

23. Distributions A “picture” of the distribution is usually helpful
Gives a good sense of the properties of the distribution
Many different ways to display distribution
Table
Frequency distribution table
Stem and leaf plot
Graphs
Distributions

24. Stem and Leaf Plots Distribution of exam scores (section 01): 5 7 6 4
67, 90, 92, 58, 76, 75, 84, 92, 78, 93, 89, 74, 62, 98, 75, 73, 75, 89, 89, 76, 65, 49 5 7 6 4 9 10 8 2 2 3 8 4 9 9 9 6 5 8 4 5 3 5 6 7 2 5 8 9
Stem and Leaf Plots

25. Stem and Leaf Plots Distribution of exam scores (section 01): 1 5 3 4
67, 90, 92, 58, 76, 75, 84, 92, 78, 93, 89, 74, 62, 98, 75, 73, 75, 89, 89, 76, 65, 49 1 5 3 4 2 8 9 6 5 7 6 4 9 10 8 5 7 6 4 9 8 3 2
Distribution of exam scores (section 03):
72, 90, 83, 58, 66, 65, 84, 95, 72, 93, 89, 70, 42, 100, 71, 73, 75, 62, 62, 74, 65
Stem and Leaf Plots

26. Distributions A “picture” of the distribution is usually helpful
Gives a good sense of the properties of the distribution
Many different ways to display distribution
Table
Frequency distribution table
Stem and leaf plot
Graphs
Graphs types
Continuous variable:
histogram, line graph (frequency polygons)
Categorical (discrete) variable:
pie chart, bar chart
Distributions

27. Graphs for continuous variables
Histogram
Line graph
Graphs for continuous variables

28. Graphs for categorical variables
Bar chart
Pie chart
Graphs for categorical variables

29. Distributions Important properties of distribution Center
Where most of the data in the distribution are
Spread (variability)
How similar/dissimilar are the scores in the distribution?
Shape
Symmetric vs. asymmetric (skew)
Unimodal vs. multimodal
Distributions

30. Symmetric
Asymmetric
Positive Skew
Negative Skew
tail
tail
Shape

31. Shape Unimodal (one mode) Multimodal Major mode Minor mode
Bimodal examples
Shape

32. Descriptive statistics
Coming up in future lectures:
In addition to pictures of the distribution, numerical summaries are also presented.
Numeric Descriptive Statistics
Shape
Skew (symmetry) & Kurtosis (shape)
Number of modes
Measures of Center
Measures of Variability (Spread)
In lab, create basic tables and graphs both by hand and using SPSS
If time in lecture there are some SPSS show and tell slides
Descriptive statistics

33. Drag & drop
Drag & drop
SPSS: Bar graph

34. Frequency distribution of different categories
SPSS: Bar graph

35. SPSS: Cluster bar graph
Drag & drop
Drag & drop
SPSS: Cluster bar graph

36. SPSS: Cluster bar graph
Legend
Frequency distribution of categories broken down into another category
SPSS: Cluster bar graph

37. Drag & drop
Drag & drop
SPSS: Histogram

38. Frequency distribution
SPSS Graphing