Introduction to Statistics for the Social Sciences
SBS200 - Lecture Section 001, Spring 2017
Room 150 Harvill Building
9:00 - 9:50 Mondays, Wednesdays & Fridays.
http://www.youtube.com/watch?v=oSQJP40PcGI
Schedule of readings
Before next exam (March 3rd)
Please read chapters 1 - 8 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
By the end of lecture today
2/17/17
Counting ‘standard deviationses’ – z scores
Connecting raw scores, z scores and probability
Connecting probability, proportion and area of curve
Percentiles
No New Homework Assignment
Just review assignments 10 & 11
Finding z scores and areas under the curve.
Both extended to Monday, February 20th
Everyone will want to be enrolled
in one of the lab sessions
Labs continue
With Project 2
Hand out z tables
If we go up one standard deviation
z score = +1.0 and raw score = 105
68%
If we go down one standard deviation
z score = -1.0 and raw score = 95
85 90 95 100 105 110 115
If we go up two standard deviations
z score = +2.0 and raw score = 110
95%
If we go down two standard deviations
z score = -2.0 and raw score = 90
85 90 95 100 105 110 115
If we go up three standard deviations
z score = +3.0 and raw score = 115
99.7%
85 90 95 100 105 110 115
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
Mean = 100
Standard deviation = 5
Normal distribution
Raw scores
z-scores
Have z
Find raw score
Formula
probabilities
Z
Scores
z table
Have z
Find area
Have area
Find z
Have raw score
Find z
Raw
Scores
Area &
Probability
Always draw a picture!
Homework worksheet
Homework worksheet
.6800
1
Homework worksheet
.9500
2
Homework worksheet
.9970
3
Homework worksheet
.5000
4
Homework worksheet
33-30 z = 1.5
z=
2
Go to
table
.4332
5
z=
33-30 z = 1.5
2
Go to
table
.4332
Add area
Lower half
.4332 + .5000 = .9332
6
Homework worksheet
Go to
33-30
z=
.4332
= 1.5
table
2
Subtract
from .5000
.5000 - .4332 = .0668
7
z=
29-30
2
= -.5
Go to
.1915
table
Add to upper
Half of curve .5000 - .1915 = .6915
8
25-30
2
31-30
=
2
=
= -2.5
=.5
Go to table
Go to table
.4938
.1915
.4938 + .1915 = .6853
9
z=
Go to
27-30
= -1.5 table
2
.4332
Subtract
From .5000
.5000 - .4332 = .0668
10
z=
25-30
2
= -2.5
Go to
table
.4938
Add lower
Half of curve .5000 + .4938 = .9938
11
z=
Go to
32-30
= 1.0 table
2
.3413
Subtract
from .5000
.5000 - .3413 = .1587
12
50th percentile = median
30
13
28
32
14
77th percentile
Find area
of interest
.7700 - .5000 = .2700
x = mean + z σ = 30 + (.74)(2) = 31.48
Find nearest z = .74
15
13th percentile
Find area
of interest
.5000 - .1300 = .3700
x = mean + z σ = 30 + (-1.13)(2) = 27.74
Find nearest z = -1.13
16
Please use the following distribution with
a mean of 200 and a standard deviation of 40.
.6800
17
.9500
18
.9970
19
=
230-200
= .75
40
Go to
table
.2734
20
180-200 = -.5 Go to
z=
table
40
.1915
Add to upper
.5000 + .1915 = .6915
Half of curve
22
236-200 = 0.9
z=
40
Go to
table
.3159
Subtract
from .5000
.5000 - .3159 = .1841
23
192 - 200
40
= 222 - 200
40
z=
z
= -.2
=.55
Go to table
Go to table
.0793
.2088
.0793 + .2088 = .2881
24
z=
275-200 = 1.875
40
Go to
table
.4693
or
.4699
Add area
Lower half
.4693 + .5000 = .9693
.4699 + .5000 = .9699
25
295-200 z = 2.375
z=
40
Go to
table
.4911
or
.4913
.5000 - .4911 = .0089
Add area
Lower half .5000 - .4913 = .0087
26
Add to upper
130-200 = -1.75 Go to
.5000 + .4599 = .9599
z=
.4599
table
Half
of
curve
40
27
Subtract
130-200 = -1.75 Go to
z=
.4599
table
from .5000
40
.5000 - .4599 = .0401
28
99th percentile
Find area
of interest
.9900 - .5000 = .4900
x = mean + z σ = 200 + (2.33)(40) = 293.2
Find nearest z = 2.33
29
33rd percentile
Find area
of interest
.5000 - .3300 = .1700
x = mean + z σ = 200 + (-.44)(40) = 182.4
Find nearest z = .44
30
40th percentile
Find area
of interest
.5000 - .4000 = .1000
x = mean + z σ = 200 + (-.25)(40) = 190
Find nearest z = -.25
31
67th percentile
Find area
of interest
.6700 - .5000 = .1700
x = mean + z σ = 200 + (.44)(40) = 217.6
Find nearest z = .44
32