Western University (Ontario)  Also known as University of Western Ontario
Stats for Business and Social Science
STATISTICS 2035

Summer 2017
Independent Samples
Comparing Two Population Means:
Variances Unknown (section 10.2)
There are two ways to calculate confidence
intervals and perform hypothesis tests about
1 2 when
1 and 2 are not known:
(I)
Pooled two sample ttest
(II) Nonpooled two s
Western University (Ontario)  Also known as University of Western Ontario
Stats for Business and Social Science
STATISTICS 2035

Summer 2017
What is Statistics?
Statistics is the science of collecting,
organizing, summarizing and interpreting
numerical facts, which we call data
Statistics start with a question
1.
What percent of students at UWO
smoke?
2. Are there differences in the number of
Western University (Ontario)  Also known as University of Western Ontario
Stats for Business and Social Science
STATISTICS 2035

Summer 2017
Multiple Comparison Tests (section 11.3)
In ANOVA, if H0 is rejected, the test does
not give any information about which means
are different.
Further statistical analysis is needed to
determine which means are different.
One such analysis is called:
Tukey
Western University (Ontario)  Also known as University of Western Ontario
Stats for Business and Social Science
STATISTICS 2035

Summer 2017
Dependent Samples: Inference About the
Difference Between Two Population Means
MatchedPairs tTest (section 10.3)
We start off with a 2sample problem:
x1 = sample data from population 1
x2 = sample data from population 2
However, subjects in our experi
Western University (Ontario)  Also known as University of Western Ontario
Stats for Business and Social Science
STATISTICS 2035

Summer 2017
Counting The Possibilities (section 4.3)
1.
The mn counting rule
For an operation that can be done in mways
and a second operation that can be done in
nways, the operations can then occur, in
order, in mn ways
This rule can be extended to if an
experime
Western University (Ontario)  Also known as University of Western Ontario
Stats for Business and Social Science
STATISTICS 2035

Summer 2017
Comparing Two Population Proportions
(section 10.4)
We have:
population population
proportion
sample
size
count of
sample
successes proportion
1
p1
n1
x1
2
p2
n2
x2
x1
n1
x
p 2 = 2
n2
p 1 =
We are interested in comparing the two
populations
in particular
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 2857

Fall 2013
Stopping Distance, Thinking Distance, Braking Distance and Speed.
1. What is the link between Stopping Distance, Thinking Distance,
and Braking Distance?
2. What affects the thinking distance?
3. List things that affect braking distance.
4. A person in a
Western University (Ontario)  Also known as University of Western Ontario
Biostatistics
STATISTICS 2244

Fall 2014
Question 2 (Two sample t test)
2 variables alpha and group
alpha numeric 8 2 right scale
group string 1 0 left nominal
1.
2.
3.
4.
5.
6.
7.
analyse
compare means
independent sample t test (another name for 2 sample t test)
input alpha (test variable) and
Western University (Ontario)  Also known as University of Western Ontario
Biostatistics
STATISTICS 2244

Fall 2014
Question 1 (One sample t test)
Alternative hypothesis: mean age less than 60
Age key in the value, width=8, decimal=2 , Type of variable=numerical, measure=scale
Analyze
1.
2.
3.
4.
5.
6.
7.
compare means
one sample t test
input the age to test variable
Western University (Ontario)  Also known as University of Western Ontario
Biostatistics
STATISTICS 2244

Fall 2014
Lab 3
Question 3
Length of
stay
Age in
years
15
14
17
35
28
38
25
26
30
25
18
21
a) Using SPSS, calculate the correlation coefficient R and the coefficients a and b in the
regression equation y = a + bx.
b) Plot the data with the regression line.
c) Plot
Western University (Ontario)  Also known as University of Western Ontario
Biostatistics
STATISTICS 2244

Fall 2014
Lab 3
Question 2
City
A
B
C
D
E
5
2
3
3
3
4
3
4
6
1
Density (/m3)
3
2
3
4
2
6
2
2
5
3
4
1
2
1
4
a) Can we conclude that the bird densities are different among the five cities? ( = 0.05)
b) Conduct the Tukeys test.
(i) list the results of the pairwise comp
Western University (Ontario)  Also known as University of Western Ontario
Biostatistics
STATISTICS 2244

Fall 2014
Question 3 (before and after see if theres decline in score)
2 variables
PreGDS numeric 8 2 8 right scale
postGDS numeric
*Must input data as a pair. The order cannot be change.
1.
2.
3.
4.
Analyse
compare means
paired sample t test
input the 2 variables
Western University (Ontario)  Also known as University of Western Ontario
Biostatistics
STATISTICS 2244

Fall 2014
B. Wilcoxon signedrank test (for paired samples)
Question 2
Wilson sign rank test to find out if there is any change
Baseline numeric 8 2 none scale
f=Fivemins numeric 8 2 none scale (for continuous data)
Go to data view type in data analyze nonparametic
Western University (Ontario)  Also known as University of Western Ontario
Biostatistics
STATISTICS 2244

Fall 2014
Lab 4  Question 1
About chisquared test
1 to represent males or females
1 to represent alcohol users and 0 are non alcohol users
Fisher test to draw conclusion between gender and usage
Gender numeric (number to represent diff category) 8 0 0=women 1=men
Western University (Ontario)  Also known as University of Western Ontario
Biostatistics
STATISTICS 2244

Fall 2014
Lab 4  Question 3
C. MannWhitney Utest (Wilcoxon rankSum test)
2 samples one men and one women find out if there is differences
We have 2 independent samples
Waist numeric 8 2 none scale (only one variables include data for a variables)
Gender numeric
Western University (Ontario)  Also known as University of Western Ontario
Biostatistics
STATISTICS 2244

Fall 2014
Lab 3
Question 3
Regression between age in years (independent variable = x) and length of stay in days
(dependent = Y) Find out if there is any correlation
Age numeric 8 2 scale
Length numeric 8 2 scale
Key in data for both variables
Analyse regression li
Western University (Ontario)  Also known as University of Western Ontario
Biostatistics
STATISTICS 2244

Fall 2014
Lab 3
Question 2
Bird_density numeric 8 2 scale
City numeric 8 0 1=A,2=B,3=C,4=D,5=E nominal
Spss prefer use number to identify and distinguish different groups  use column values to
define the meaning of numbers
Analyse compare means one way ANOVA depen
Western University (Ontario)  Also known as University of Western Ontario
Biostatistics
STATISTICS 2244

Fall 2014
Lab 3
Question 1
Cholesterol level of 3 groups of ppl  control and 2 other groups for condition
Only need to define one level for the cholesterol level
Chol numeric 8 2 none none 8 right scale (continuous values for the cholesterol)
Group numeric 8 2 0 1
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 1024

Winter 2014
CHAPTER 20:
Inference about a
Population Mean
SS1024001
2
Conditions for Inference About a
Mean
Conditions for Inference about a Population
Mean sample of size n from the
Random: The data come from a random
population of interest or a randomized experim
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 1024

Winter 2014
Data Ethics
The most complex issues of data ethics
arise when we collect data from people.
This Chapter introduces some basic
standards of data ethics that must be
obeyed by all studies that gather data
from human subjects, both observational
studies an
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 1024

Winter 2014
CHAPTER 19:
From Data Production
to Inference
Part III Review
Basic Practice of
Statistics
7th Edition
Lecture PowerPoint Slides
In Chapter 19, We Cover
Part III summary
Probability
Sampling distributions
General rules of probability*
The sampling distri
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 1024

Winter 2014
Statistical Science 1024
Chapter 21
TwoSample Problems
Unlike the matched pairs designs studied earlier, there is no matching of
the individuals in the two samples, and the two samples can be of different
sizes. Inference procedures for twosample data di
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 1024

Winter 2014
Statistical Science 1024
Chapter 13
General Rules of Probability
Two events are disjoint if they
have no outcomes in common
Events A
and B are
disjoint.
and can never happen together.
Events A and
B are NOT
disjoint.
If you flip a coin once, it may turn o
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 1024

Winter 2014
Statistical Science 1024
Chapter 16
Confidence Intervals: The Basics
A simple ( unrealistic ) setting:
More on the Simple Conditions
assume that the standard deviation
is known
almost never true the more realistic case
of unknown is covered in a later
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 1024

Winter 2014
Statistical Science 1024
Chapter 9
Producing Data: Experiments
Causal relationship
Does aspirin reduce the chance of a
heart attack?
Do a majority of college students prefer
Pepsi to Coke when they taste both
without knowing which they are drinking?
Ca
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 1024

Winter 2014
Statistical Science 1024
Chapter 22
Inference about a Population Proportion
http:/www.cnn.com/2016/01/26/politics/donaldtrumptedcruzpo
Nature of the Population
The population can be divided into two categories
examples
agree or disagree with an issu
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 1024

Winter 2014
Statistical Science 1024
Chapter 8
Producing Data: Sampling
Population, Sample and Sampling Design
The population is the
entire group of individuals
that we want information
about
The sample is part of the
population we examine in
order to gather
inform
Western University (Ontario)  Also known as University of Western Ontario
STATISTICS 1024

Winter 2014
Chapter 1 Picturing Distributions with Graphs
1. Individuals and Variables
Any set of data contains information about some group of individuals. The information is
organized in variables.
 Individuals are the objects described by a set of data.
 A varia