1. Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Fall 2017 Room 150 Harvill Building 10: :50 Mondays, Wednesdays & Fridays.
Welcome

2. Lecturer’s desk Projection Booth Screen Screen Harvill 150 renumbered
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Harvill 150
renumbered
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Projection Booth
Left handed desk

3. Schedule of readings Before next exam (September 22nd)
Please read chapters in OpenStax textbook
Please read Appendix D online On syllabus this is referred to as online readings 1
Please read Chapters 1, 5, 6 and 13 in Plous
Chapter 1: Selective Perception
Chapter 5: Plasticity
Chapter 6: Effects of Question Wording and Framing
Chapter 13: Anchoring and Adjustment

4. writing assignment forms notebook and clickers to each lecture
Remember bring your
writing assignment forms
notebook and clickers to each lecture

5. Even if you have not yet registered your clicker you can still participate

7. Labs continue this week
Lab sessions
Everyone will want to be enrolled
in one of the lab sessions
Labs continue this week

8. “Serious Gamer” Score “Serious Gamer” Score “Serious Gamer” Score Time
One positive
correlation
One negative
correlation
Comparing
Two means
“Serious Gamer” Score
“Serious Gamer” Score
“Serious Gamer” Score
Time
Studying
Age
Gender

9. You’ve gathered your data…what’s the best way to display it??

10. Frequency distributions
Frequency distributions an organized list of observations and their frequency of occurrence
How many kids are in your family?
What is the most common family size?

11. Another example: How many kids in your family?
Number of kids in family
1 3
1 4
2 4
2 8
2 14 14 4 2 1 4 2 2 3 1 8

12. Describing Data Visually
Lists of numbers too hard to see patterns
Describing Data Visually
Organizing numbers helps
Graphical representation even more clear
This is a dot plot

13. Describing Data Visually
Graphical representation even more clear
This is a dot plot

14. Step 2: List scores in order Step 3: Decide grouped53 58 60 61 64 69 70 72 73 75 76 78 80 82 84 87 88 89 91 93 94 95 99
Scores on an exam
Remember Dot Plots
Step 1: List scores
Step 2: List scores in order
Step 3: Decide grouped
Step 4: Decide 10 for # bins (classes)
5 for bin width (interval size)
Step 5: Generate frequency histogram
Score on exam 6 5 4 3 2 1
Scores on an exam
Score Frequency
80 – 84 5

15. Step 2: List scores in order Step 3: Decide grouped53 58 60 61 64 69 70 72 73 75 76 78 80 82 84 87 88 89 91 93 94 95 99
Scores on an exam
Remember Dot Plots
Step 1: List scores
Step 2: List scores in order
Step 3: Decide grouped
Step 4: Decide 10 for # bins (classes)
5 for bin width (interval size)
Step 5: Generate frequency histogram
Score on exam 6 5 4 3 2 1
Scores on an exam
Score Frequency
80 – 84 5

16. Step 2: List scores in order Step 3: Decide grouped53 58 60 61 64 69 70 72 73 75 76 78 80 82 84 87 88 89 91 93 94 95 99
Scores on an exam
Remember Dot Plots
Step 1: List scores
Step 2: List scores in order
Step 3: Decide grouped
Step 4: Decide 10 for # bins (classes)
5 for bin width (interval size)
Step 5: Generate frequency histogram
Score on exam 6 5 4 3 2 1
Scores on an exam
Score Frequency
80 – 84 5

17. Step 2: List scores in order Step 3: Decide grouped53 58 60 61 64 69 70 72 73 75 76 78 80 82 84 87 88 89 91 93 94 95 99
Scores on an exam
Remember Dot Plots
Step 1: List scores
Step 2: List scores in order
Step 3: Decide grouped
Step 4: Decide 10 for # bins (classes)
5 for bin width (interval size)
Step 5: Generate frequency histogram
Score on exam 6 5 4 3 2 1
Scores on an exam
Score Frequency
80 – 84 5

18. Step 2: List scores in order Step 3: Decide grouped
Scores on an exam
Step 2: List scores in order
Step 3: Decide grouped
Step 4: Decide 10 for # bins (classes)
5 for bin width (interval size)
Step 5: Generate frequency histogram
Scores on an exam
Score Frequency
80 – 84 5
Score on exam 6 5 4 3 2 1

19. Generate frequency polygon
Scores on an exam
Generate frequency polygon
Plot midpoint of histogram intervals
Connect the midpoints
Scores on an exam
Score Frequency
80 – 84 5
Score on exam 6 5 4 3 2 1

20. Generate frequency ogive (“oh-jive”)
Scores on an exam
Generate frequency ogive (“oh-jive”)
Frequency ogive is used for cumulative data
Plot midpoint of histogram intervals
Connect the midpoints
Scores on an exam
Score
95 – 99
80 – 84
Score on exam 30 25 20 15 10 5
Cumulative
Frequency 28 26 23 18 13 9 6 5 2 1

21. Pareto Chart:
Categories are displayed in descending order of frequency

22. Stacked Bar Chart: Bar Height is the sum of several subtotals

23. Simple Line Charts: Often used for time series data (continuous data)
Simple Line Charts: Often used for time series data (continuous data) (the space between data points implies a continuous flow)
Note: For multiple variables lines can be better than bar graph
Note: Fewer grid lines can be more effective
Note: Can use a two-scale chart with caution

24. Pie Charts: General idea of data that must sum to a total (these are problematic and overly used – use with much caution)
Exploded 3-D pie charts look
cool but a simple 2-D chart may be more clear
Exploded 3-D pie charts look
cool but a simple 2-D chart may be more clear
Bar Charts can often be more effective

25. Frequency distributions
Number of kids in family
1 3
1 4
2 4
2 8
2 14
How many kids are in your family?
What is the most common family size?
Frequency distributions
Crucial guidelines for constructing
frequency distributions:
1. Classes should be mutually exclusive: Each observation
should be represented only once (no overlap between classes)
Wrong
0 - 5
5 - 10
Correct
0 - 4
5 - 9
Correct
0 - under 5
5 - under 10
10 - under 15
2. Set of classes should be exhaustive:
Should include all possible data values
(no data points should fall outside range)
Wrong
0 - 4
8 - 11
Correct
0 - 3
4 - 7
No place for our families of 5, 6 or 7

26. Frequency distributions
Number of kids in family
1 3
1 4
2 4
2 8
2 14
How many kids are in your family?
What is the most common family size?
Frequency distributions
Crucial guidelines for constructing
frequency distributions:
3. All classes should have equal intervals
(even if the frequency for that class is zero)
Wrong
0 - 1
2 - 12
Correct
0 - 4
5 - 9
Correct
0 - under 5
5 - under 10
10 - under 15

27. 4. Selecting number of classes is subjective
4. Selecting number of classes is subjective
Generally will often work
How about
6 classes? (“bins”)
How about
16 classes? (“bins”)
How about
8 classes? (“bins”)

28. Lower boundary can be multiple of interval size
5. Class width should be round (easy) numbers
Remember: This is all about helping readers understand quickly and clearly.
Lower boundary can be multiple of interval size
Clear & Easy
8 - 11
Round numbers:
5, 10, 15, 20 etc or
3, 6, 9, 12 etc
6. Try to avoid open ended classes
For example
10 and above
Greater than 100
Less than 50

29. Let’s do one Step 1: List scores Step 2: List scores in order
Scores on an exam
Let’s do one 53 58 60 61 64 69 70 72 73 75 76 78 80 82 84 87 88 89 91 93 94 95 99
Step 1: List scores
Step 2: List scores in order
Step 3: Decide whether grouped or ungrouped
If less than 10 groups, “ungrouped” is fine
If more than 10 groups, “grouped” might be better
How to figure how many values
Largest number - smallest number + 1
= 47
Step 4: Generate number and size of intervals (or size of bins)
If we have 6 bins – we’d have intervals of 8
Sample
size (n)
10 – 16
17 – 32
33 – 64
65 – 128
256 – 511
512 – 1,024
Number of classes 5 6 7 8 9 10 11
Let’s just try it and see which we prefer…
Whaddya think?
Would intervals of 5 be easier to read?

30. Let’s just try it and see which we prefer…
Scores on an exam
Scores on an exam
Score Frequency
80 – 84 5
Scores on an exam
Score Frequency 53 58 60 61 64 69 70 72 73 75 76 78 80 82 84 87 88 89 91 93 94 95 99
Let’s just try it and see which we prefer…
6 bins
Interval of 8
10 bins
Interval of 5
Scores on an exam
Score Frequency
80 – 84 5
Remember: This is all about helping readers understand quickly and clearly.

31. Let’s make a frequency histogram using 10 bins and bin width of 5!!
Scores on an exam
Scores on an exam
Score Frequency
80 – 84 5
Let’s make a
frequency histogram
using 10 bins and
bin width of 5!!

32. Step 6: Complete the Frequency Table
Scores on an exam
Step 6: Complete the Frequency Table
Scores on an exam
Score Frequency
80 – 84 5
Relative Cumulative
Frequency
1.0000
.9285
.8214
.6428
.4642
.3213
.2142
.1785
.0714
.0357
Cumulative
Frequency 28 26 23 18 13 9 6 5 2 1
Relative
Frequency
.0715
.1071
.1786
.1429
.0357
Just adding up the relative frequency data from the smallest to largest numbers
Please note:
Also just dividing cumulative frequency
by total number
1/28 = .0357
2/28 = .0714
5/28 = .1786
Just adding up the frequency data from the smallest to largest numbers
6 bins
Interval of 8
Just dividing each frequency by total number to get a ratio (like a percent)
Please note:
1 /28 = .0357
3/ 28 = .1071
4/28 = .1429

33. “Who is your favorite candidate?”
Simple Frequency Table – Qualitative Data
Who is your favorite candidate
Candidate Frequency
Hillary Clinton 45
Bernie Sanders 23
Joe Biden 17
Jim Webb 1
Other/Undecided 14
Number expected to vote
9,900,000
5,060,000
3,740,000
220,000
3,080,000
We asked 100 Democrats
“Who is your favorite candidate?”
Relative
Frequency
.4500
.2300
.1700
.0100
.1400
Percent
45%
23%
17% 1%
14%
If 22 million Democrats voted today how many would vote for each candidate?
Just divide each frequency by total number
Just multiply each relative frequency by 22 million
Just multiply each relative frequency by 100
Please note:
45 /100 = .4500
23 /100 = .2300
17 /100 = .1700
1 /100 = .0100
Please note:
.4500 x 22m = 9,900k
.2300 x 22m = 35,060k
.1700 x 22m = 23,740k
.0100 x 22m= 220k
Please note:
.4500 x 100 = 45%
.2300 x 100 = 23%
.1700 x 100 = 17%
.0100 x 100 = 1%
Data based on Gallup poll on 8/24/11

37. Describing Data Visually
This is a dot plot

38. Overview Frequency distributions
The normal curve
Challenge yourself as we work through characteristics of distributions to try to categorize each concept as a measure of
1) central tendency
2) dispersion or 3) shape
Mean, Median,
Mode, Trimmed Mean
Standard deviation,
Variance, Range
Mean Absolute Deviation
Skewed right, skewed left
unimodal, bimodal, symmetric

39. Another example: How many kids in your family?
Number of kids in family
1 4
3 2
1 8
4 2
2 14 14 4 2 1 4 2 2 3 1 8

40. Mean: The balance point of a distribution. Found
Measures of Central Tendency (Measures of location) The mean, median and mode
Mean: The balance point of a distribution. Found
by adding up all observations and then dividing
by the number of observations
Mean for a sample:
Σx / n = mean = x
Mean for a population:
ΣX / N = mean = µ (mu)
Measures of “location”
Where on the number line the scores tend to cluster
Note: Σ = add up
x or X = scores
n or N = number of scores

41. Number of kids in family
Measures of Central Tendency (Measures of location) The mean, median and mode
Mean: The balance point of a distribution. Found
by adding up all observations and then dividing
by the number of observations
Mean for a sample:
Σx / n = mean = x
41/ 10 = mean = 4.1
Number of kids in family
1 4
3 2
1 8
4 2
2 14
Note: Σ = add up
x or X = scores
n or N = number of scores

42. How many kids are in your family? What is the most common family size?
Number of kids in family
1 3
1 4
2 4
2 8
2 14
How many kids are in your family?
What is the most common family size?
Median: The middle value when observations are
ordered from least to most (or most to least)

43. Number of kids in family
1 4
3 2
1 8
4 2
2 14
How many kids are in your family?
What is the most common family size?
Median: The middle value when observations are
ordered from least to most (or most to least)
1, 3, 1, 4, 2, 4, 2, 8, 2, 14 1, 1, 2, 2, 2, 3, 4, 4, 8, 14

44. Number of kids in family
1 3
1 4
2 4
2 8
2 14
Number of kids in family
1 4
3 2
1 8
4 2
2 14
How many kids are in your family?
What is the most common family size?
Median: The middle value when observations are
ordered from least to most (or most to least)
1, 3, 1, 4, 2, 4, 2, 8, 2, 14 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 8, 8, 14 14
2.5
µ=2.5
If there appears to be two medians, take the mean of the two
Median always has a percentile rank of 50% regardless of shape of distribution

45. Number of kids in family
Mode: The value of the most frequent observation
Score f .
1 2
2 3
3 1
4 2
5 0
6 0
7 0
8 1
9 0
10 0
11 0
12 0
13 0
14 1
Number of kids in family
1 3
1 4
2 4
2 8
2 14
Please note:
The mode is “2” because it is the most frequently occurring score. It occurs “3” times. “3” is not the mode, it is just the frequency for the value that is the mode
Bimodal distribution:
If there are two most
frequent observations

46. What about central tendency for qualitative data?
Mode is good for nominal or ordinal data
Median can be used with ordinal data
Mean can be used with interval or ratio data

47. Thank you!
See you next time!!