1. Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2017 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays.
Welcome

2. A note on doodling

3. Schedule of readings Before next exam (February 10)
Please read chapters in OpenStax textbook
Please read Appendix D, E & F online On syllabus this is referred to as online readings 1, 2 & 3
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. Homework Assignment 6 Please complete the homework modules
on the D2L website
HW6 – Part 1 - Measures of Central Tendency
HW6 - Part 2 - Descriptive Statistics Deviation Scores
Due: Monday, January 30th

5. Homework Assignment 6 Please complete the homework modules
on the D2L website
HW6 – Part 1 - Measures of Central Tendency
HW6 - Part 2 - Descriptive Statistics Deviation Scores
Due: Monday, January 30th

6. By the end of lecture today 1/27/17
Use this as your
study guide
By the end of lecture today 1/27/17
Frequency distributions and Frequency tables
Cumulative Frequency
Relative Frequency and percentages
Predicting frequency of larger sample based on relative frequency
Pie Charts
Relative Cumulative Frequency
Measures of Central Tendency
Mean, Median, Mode

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

8. Project 1 - Likert Scale - Correlations - Comparing two means (bar graph)
Questions?

10. Review of Homework Worksheet
Notice Gillian asked 1300 people
.10 x 1,000,000 = 100,000
130/1300 = .10
.10 10
100,000
.08 8
80,000
.10x100=10
.25 25
250,000
.35 35
350,000
.22 22
220,000
=1300

11. Review of Homework Worksheet
.10 10
100,000
.08 8
80,000
.25 25
250,000
.35 35
350,000
.22 22
220,000

12. Review of Homework Worksheet

13. Review of Homework Worksheet
Strong
Negative
Review of Homework Worksheet
Down
-.9 9 8 7 6
Dollars Spent 5 4 3 2 1 10 20 30 40 50
Age

14. Review of Homework Worksheet
Strong
Negative
Review of Homework Worksheet
Down
=correl(A2:A11,B2:B11) =

15. Review of Homework Worksheet
Strong
Negative
Review of Homework Worksheet
Down
This shows a strong negative relationship (r = ) between the amount spent on snacks and the age of the moviegoer
Description includes:
Both variables
Strength (weak,moderate,strong)
Direction (positive, negative)
Correlation r (actual number)
=correl(A2:A11,B2:B11) =

16. Review of Homework Worksheet
Strong
Negative
Review of Homework Worksheet
Down
Must be complete and must be stapled
Hand in your homework
=correl(A2:A11,B2:B11) =

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

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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

24. 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

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

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

27. 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

28. 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

29. 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

30. 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

31. 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

32. 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

33. 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)

34. 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

35. 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

36. 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

37. 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

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
Skewed right, skewed left
unimodal, bimodal, symmetric

39. 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
Skewed right, skewed left
unimodal, bimodal, symmetric

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

41. A little more about frequency distributions
An example of a normal distribution

42. A little more about frequency distributions
An example of a normal distribution

43. A little more about frequency distributions
An example of a normal distribution

44. A little more about frequency distributions
An example of a normal distribution

45. A little more about frequency distributions
An example of a normal distribution

46. Measure of central tendency: describes how scores tend to
Measure of central tendency: describes how scores tend to cluster toward the center of the distribution
Normal distribution
In all distributions:
mode = tallest point
median = middle score
mean = balance point
In a normal distribution:
mode = mean = median

47. Measure of central tendency: describes how scores tend to
Measure of central tendency: describes how scores tend to cluster toward the center of the distribution
Positively skewed distribution
In all distributions:
mode = tallest point
median = middle score
mean = balance point
In a positively skewed distribution:
mode < median < mean
Note: mean is most affected by outliers or skewed distributions

48. Measure of central tendency: describes how scores tend to
Measure of central tendency: describes how scores tend to cluster toward the center of the distribution
Negatively skewed distribution
In all distributions:
mode = tallest point
median = middle score
mean = balance point
In a negatively skewed distribution:
mean < median < mode
Note: mean is most affected by outliers or skewed distributions

49. Mode: The value of the most frequent observation
Bimodal distribution: Distribution with two most
frequent observations (2 peaks)
Example: Ian coaches two boys baseball teams. One team is made up of 10-year-olds and the other is made up of 16-year-olds. When he measured the height of all of his players he found a bimodal distribution

50. Thank you!
See you next time!!