Lecture 1: TwoSample
t
Test
Slide 9.3 / 9.126
Week 9 Announcement
The due date for the statistics assignment is Friday 15th (Week
9) November before 2pm. The link to submit your assignments
on Moodle will be open soon.
You can ask questions on the dedicated Moodle forum
which is
located in the assessment tab
.
Week 9 online tutorial is due Sunday before 6pm.
Chapter 9
:
Statistical Inference for Two Parameters
MATH1041:
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Lecture 1: TwoSample
t
Test
Slide 9.4 / 9.126
The Agenda Slide
Overarching aim of the course:
introducing Statistics, the study
of collecting, analysing and interpreting data (fundamental to any
quantitative research)
First class of Week 9
Last time:
Confidence intervals for a proportion
Hypothesis tests for a proportion
Today:
Twosample
t
test
Paired
t
test
For next time:
Read appropriate pages in the textbook
Chapter 9
:
Statistical Inference for Two Parameters
MATH1041:
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Lecture 1: TwoSample
t
Test
Slide 9.5 / 9.126
Lecture 1 Learning Outcomes
[
Ch9L1O1
]
Understand formulas for twosample
t
test
[
Ch9L1O2
]
Know the formula for confidence intervals for the difference of
means for independent samples
By the end of this lecture you should be able to:
Perform a twosample
t
test
Build a confidence interval for a difference in means
Chapter 9
:
Statistical Inference for Two Parameters
MATH1041:
Page 992 / 1115
Lecture 1: TwoSample
t
Test
Slide 9.6 / 9.126
Data analysis for one or two variables
one variable
two variables
variable
type:
categorical
quantitative
both
categorical
one categorical,
one quantitative
both
quantitative
useful
for
inference:
CI
for
p
(for
binary var)
CI
for
μ
CI
for
μ
1

μ
2
CI
for
β
1
useful test:
1samp for
p
(for
binary
var)
1sample
t

test
for
μ
(or
Z
test if
σ
known)
χ
2
test for
indepen
dence
2sample
t
(for
independence
binary+quant)
test regression
slope (
β
1
)
Chapter 9
:
Statistical Inference for Two Parameters
MATH1041:
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Lecture 1: TwoSample
t
Test
Slide 9.7 / 9.126
Example – Do Ravens Fly to Gunshots?
Example 9.73
Do ravens intentionally fly towards gunshot sounds (to scavenge on
the carcass they expect to find)?
(
Ecology
2005, 86:1057–1060)
Crow White addressed this question by counting raven numbers at a
location, firing a gun, then counting raven numbers 10 minutes later.
He did this in 12 locations. Results:
location
1
2
3
4
5
6
7
8
9
10
11
12
before
1
0
1
0
0
0
0
5
1
1
2
0
after
2
3
2
2
1
1
2
2
4
2
0
3
Is there evidence that ravens fly towards the location of gunshots?
Chapter 9
:
Statistical Inference for Two Parameters
MATH1041:
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Lecture 1: TwoSample
t
Test
Slide 9.8 / 9.126
Example – Pregnancy and Smoking
Example 9.74
What is the effect of a mother’s smoking during pregnancy on the
resulting offspring?
(
Journal of General Psychology
1993, 120(1): 49–63)
A randomised controlled experiment investigated this by injecting
pregnant guinea pigs with 0.5 mg/kg nicotine hydrogen tartrate in
saline solution. The control group was injected with a saline solution
without nicotine.
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