1. Hand out z tables

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

3. Lecturer’s desk Projection Booth Screen Screen Harvill 150 renumbered
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Harvill 150
renumbered
table 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Projection Booth
Left handed desk

4. Schedule of readings Before next exam (October 13th)
Please read chapters in OpenStax textbook
Please read Chapters 10, 11, 12 and 14 in Plous
Chapter 10: The Representativeness Heuristic
Chapter 11: The Availability Heuristic
Chapter 12: Probability and Risk
Chapter 14: The Perception of Randomness

5. A note on doodling

6. Lab sessions Labs continue Project 2 Everyone will want to be enrolled
in one of the lab sessions
Labs continue Project 2

14. z score = raw score - mean standard deviation
If we go up one standard deviation
z score = +1.0 and raw score = 105
z = -1
z = +1
68%
If we go down one standard deviation
z score = -1.0 and raw score = 95
If we go up two standard deviations
z score = +2.0 and raw score = 110
z = -2
95%
z = +2
If we go down two standard deviations
z score = -2.0 and raw score = 90
If we go up three standard deviations
z score = +3.0 and raw score = 115
99.7%
z = -3
z = +3
If we go down three standard deviations
z score = -3.0 and raw score = 85
z score: A score that indicates how many standard deviations
an observation is above or below the mean of the distribution
z score = raw score - mean
standard deviation

15. If score is within 2 standard deviations (z < 2)
“not unusual score”
If score is beyond 2 standard deviations (z = 2 or up to 3)
“is unusual score”
If score is beyond 3 standard deviations (z = 3 or up to 4)
“is an outlier”
If score is beyond 4 standard deviations (z = 4 or beyond)
“is an extreme outlier”

16. Scores, standard deviations, and probabilities
What is total percent under curve?
What proportion of curve is above the mean?
.50
100%
The normal curve always has the same shape.
They differ only by having different means and standard deviation

17. Scores, standard deviations, and probabilities
What percent of curve is below a score of 100?
What score is associated with 50th percentile?
50%
median
Mean = 100
Standard deviation = 5

18. Raw scores, z scores & probabilities
Distance from the mean
(z scores)
convert
convert
Raw Scores
(actual data)
Proportion of curve
(area from mean)
68%
z = -1
z = 1
We care about this!
What is the actual number on this scale? “height” vs “weight”
“pounds” vs “test score”
We care about this!
“percentiles”
“percent of people”
“proportion of curve” “relative position”
68%
Raw Scores
(actual data)
Proportion of curve
(area from mean)
z = -1
z = 1
Distance from the mean
(z scores)
convert
convert

19. z table Formula Normal distribution Raw scores z-scores probabilities
Have z
Find raw score Z
Scores
Have z
Find area
z table
Formula
Have area
Find z
Area &
Probability
Have raw score
Find z
Raw Scores

20. Find z score for raw score of 60
z score: A score that indicates how many standard deviations
an observation is above or below the mean of the distribution
z score = raw score - mean
standard deviation 60 50 10
z = 1
Mean = 50
Standard deviation = 10

21. Find the area under the curve that falls between 50 and 60
34.13%
1) Draw the picture
2) Find z score
3) Go to z table - find area under correct column
4) Report the area 60 50 10
z = 1

22. Find the area under the curve that falls between 40 and 60
Mean = 50 Standard deviation = 10
68.26%
Find the area under the curve that falls between 40 and 60
34.13%
34.13%
z score = raw score - mean
standard deviation
Hint always draw a picture!
z score = 10
z score = 10
z score = = 1.0 10
z score = = -1.0 10
z table
z table
z score of 1 = area of .3413
z score of 1 = area of .3413
= .6826

23. Find the area under the curve that falls between 30 and 50
Mean = 50 Standard deviation = 10
1) Draw the picture
2) Find z score
3) Go to z table - find area under correct column
4) Report the area
Find the area under the curve that falls between 30 and 50
z score = raw score - mean
standard deviation
z score = 10
z score = = 10
Hint always draw a picture!

24. Find the area under the curve that falls between 30 and 50
Mean = 50 Standard deviation = 10
1) Draw the picture
2) Find z score
3) Go to z table - find area under correct column
4) Report the area
47.72%
Find the area under the curve that falls between 30 and 50
z score = raw score - mean
standard deviation
z score = 10
z score = = 10
z table
z score of - 2 = area of .4772
Hint always draw a picture!
Hint always draw a picture!

25. Find the area under the curve that falls between 70 and 50
Mean = 50 Standard deviation = 10
47.72%
Find the area under the curve that falls between 70 and 50
z score = raw score - mean
standard deviation
z score = 10
z score = = +2.0 10
z table
z score of 2 = area of .4772
Hint always draw a picture!

26. Find the area under the curve that falls between 30 and 70
Mean = 50 Standard deviation = 10
.4772
.4772
95.44%
z score of 2 = area of .4772
Find the area under the curve that falls between 30 and 70
= .9544
Hint always draw a picture!

27. Scores, standard deviations, and probabilities
Actually 68.26
Actually 95.44
To be exactly 95% we will use z = 1.96

28. Writing Assignment Let’s do some problems
Mean = 50 Standard deviation = 10
Writing Assignment Let’s do some problems

29. Find the percentile rank for score of 60
Mean = 50 Standard deviation = 10 ?
Let’s do some problems 60
Find the area under the curve that falls below 60
means the same thing as
Find the percentile rank for score of 60
Problem 1

30. Find the percentile rank for score of 60
Mean = 50 Standard deviation = 10 ?
Let’s do some problems
Find the percentile rank for score of 60 60
.5000
.3413
1) Find z score
z score = 10
= 1
2) Go to z table
- find area under correct column (.3413)
3) Look at your picture - add to = .8413
4) Percentile rank or score of 60 = 84.13%
Problem 1
Hint always draw a picture!

31. Find the percentile rank for score of 75
Mean = 50 Standard deviation = 10 ?
Find the percentile rank for score of 75 75
.4938
1) Find z score
z score = 10
z score = 10
= 2.5
2) Go to z table
Problem 2
Hint always draw a picture!

32. Find the percentile rank for score of 75
Mean = 50 Standard deviation = 10 ?
.9938
Find the percentile rank for score of 75 75
.4938
.5000
1) Find z score
z score = 10
z score = 10
= 2.5
2) Go to z table
3) Look at your picture - add to = .9938
4) Percentile rank or score of 75 = 99.38%
Problem 2
Hint always draw a picture!

33. Find the percentile rank for score of 45
Mean = 50 Standard deviation = 10 ?
Find the percentile rank for score of 45 45
1) Find z score
z score = 10
z score = 10
= -0.5
2) Go to z table
Problem 3

34. Find the percentile rank for score of 45
Mean = 50 Standard deviation = 10 ?
Find the percentile rank for score of 45
.1915 45 ?
1) Find z score
z score = 10
z score = 10
= -0.5
2) Go to z table
Problem 3

35. Find the percentile rank for score of 45
Mean = 50 Standard deviation = 10 ?
Find the percentile rank for score of 45
.1915 45
.3085
1) Find z score
z score = 10
z score = 10
= -0.5
2) Go to z table
3) Look at your picture - subtract = .3085
Problem 3
4) Percentile rank or score of 45 = 30.85%

36. Find the percentile rank for score of 55
Mean = 50 Standard deviation = 10 ?
Find the percentile rank for score of 55 55
1) Find z score
z score = 10
z score = 10
= 0.5
2) Go to z table
Problem 4

37. Find the percentile rank for score of 55
Mean = 50 Standard deviation = 10 ?
Find the percentile rank for score of 55 55
.1915
1) Find z score
z score = 10
z score = 10
= 0.5
2) Go to z table
Problem 4

38. Find the percentile rank for score of 55
Mean = 50 Standard deviation = 10 ?
Find the percentile rank for score of 55 55
.1915 .5
1) Find z score
z score = 10
z score = 10
= 0.5
2) Go to z table
3) Look at your picture - add = .6915
4) Percentile rank or score of 55 = 69.15%
Problem 4

39. Find the score that is associated
Mean = 50 Standard deviation = 10 ?
Find the score for z = -2 30
Hint always draw a picture!
Find the score that is associated
with a z score of -2
raw score = mean + (z score)(standard deviation)
Raw score = 50 + (-2)(10)
Raw score = (-20) = 30
Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion

40. percentile rank of 77%ile
Mean = 50 Standard deviation = 10 ?
Find the score for
percentile rank of 77%ile
.7700 ?
Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion
Problem 5

41. percentile rank of 77%ile
Mean = 50 Standard deviation = 10
.27 ?
Find the score for
percentile rank of 77%ile .5
= .77 .5
.27
.7700 ?
1) Go to z table - find z score for
for area ( ) = .27
Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion
area = .2704
(closest I could find to .2700)
z = 0.74
Problem 5

42. percentile rank of 77%ile
Mean = 50 Standard deviation = 10
.27 ?
Find the score for
percentile rank of 77%ile .5
x = 57.4 .5
.27
.7700 ?
To Be Continued
2) x = mean + (z)(standard deviation)
x = 50 + (0.74)(10)
x = 57.4
x = 57.4
Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion

43. Thank you!
See you next time!!