1. Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2019 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays.
February 15

2. Even if you have not yet registered your clicker you can still participate
The
Green
Sheets

3. Before next exam (March 1st)
Schedule of readings
Before next exam (March 1st)
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

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

7. 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

8. Hand out z tables

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

10. Find the percentile rank for score of 550
Mean = 500 Standard deviation = 100 ?
Find the percentile rank for score of 550
550
.1915 .5
1) Find z score
z score =
100
z score =
100
= 0.5
2) Go to z table
3) Look at your picture - add = .6915
4) Percentile rank or score of 550 = 69.15%
Review

11. Find the score that is associated
New Mean &
Standard Deviation
Mean = 50 Standard deviation = 10 ? 30
Hint always draw a picture!
Find the score for z = -2
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
Review

12. 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 1

13. 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 1

14. 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 ?
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
Problem 1

15. percentile rank of 55%ile
Mean = 50 Standard deviation = 10 ?
Find the score for
percentile rank of 55%ile
.5500 ?
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 2

16. percentile rank of 55%ile
Mean = 50 Standard deviation = 10
.05 ?
Find the score for
percentile rank of 55%ile .5
= .55 .5
.05
.5500 ?
1) Go to z table - find z score for
for area ( ) = .05
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 = .0517
(closest I could find to .0500)
z = 0.13
Problem 2

17. percentile rank of 55%ile
Mean = 50 Standard deviation = 10
.05 ?
Find the score for
percentile rank of 55%ile .5 .5
.05
.5500 ?
1) Go to z table - find z score for
for area ( ) = .05
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 = .0517
(closest I could find to .0500)
z = 0.13
Problem 2

18. percentile rank of 55%ile
Mean = 50 Standard deviation = 10
.05 ?
Find the score for
percentile rank of 55%ile .5
x = 51.3 .5
.05
.5500 ?
1) Go to z table - find z score for
for area ( ) = .0500
area = .0517
(closest I could find to .0500)
z = 0.13
2) x = mean + (z)(standard deviation)
x = 50 + (0.13)(10)
x = 51.3
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
x = 51.3
Problem 2

19. ? .7500 .25 .5000 . Find score associated with the 75th percentile
Go to
table
nearest z = .67
.2500
x = mean + z σ = 30 + (.67)(2) = 31.34
.7500
.25
.5000 24 26 28 30 ? 34 36
31.34
Problem 3
z = .67

20. ? .2500 .25 .25 . Find the score associated with the 25th percentile
Go to
table
nearest z = -.67
.2500
x = mean + z σ = 30 + (-.67)(2) = 28.66
.2500
.25
.25 24 26
28.66 28 ? 30 34 36
Problem 4
z = -.67

21. A word on “add-in”
Using Excel ?

22. t-tests
Using Excel

23. t-tests
Using Excel

29. Homework Assignment Worksheet
Distributed in Class
Interpreting t-tests

30. Whether or not feed had corn oil
No, feed had no corn oil
Yes, the feed had corn oil
Weight of eggs
60 grams if no corn oil
63 grams if corn oil
weight of eggs based on corn oil in food
weight of eggs based on corn oil in food
true experiment
between
nominal
ratio
200
100
100
198 99 99

31. -3.35
1.97
Yes
Yes
Yes
Yes
0.05
The weights of eggs for chickens who received the corn oil was 63
grams, while the weights of the eggs for chickens who did not receive
the corn oil was 60 grams. A t-test found this to be a significant
difference t(198) = -3.35; p < 0.05

32. Thank you!
See you next time!!