HYPOTHESIS TESTING III
One-sample test for mu
The Rare Event Rule
If the probabilityunder a given assumptionof a
particular observed result is small, then the
assumption is probably not correct.
0 0
~ 0 ,
1 1
~ 1 ,
(assumption)
possible values
(truth?)
ANOVA I
Introducing the model & assumptions
Scenario
To investigate the influence of herbivory on plant species
richness, 60 experimental plant communities (initially
containing 15 species) were randomly assigned to one of
three levels of defoliation (to
CONFIDENCE INTERVALS II
t CI for mu (sigma unknown)
If we dont know , why do we know ?
assumes is known
1 100% CI for = 2
Estimate with s:
=
and therefore,
=
2
=
1
2
". " =
Substitute t for z
=
St. Dev. of the
sampling distribution
of means
=
Estimated
RANDOM VARIABLES
Discrete RVs, Binomial distributions
Random variables (RV)
a variable which has a numerical outcome of a random
phenomenon (i.e. procedure)
Example: Let X be the RV equal to the number of students
who have a part time job, out of four. As
DESCRIPTIVE STATISTICS
data types, density histograms, interpretations
The discipline of Statistics
conducting studies to collect, summarize,
analyze, and draw conclusions from data
Descriptive Statistics:
organization,
summarization, and
sample
presentat
CONFIDENCE INTERVALS III
Approximate z CI for p
Approximate z CI for p
1 100% CI for = 2
confidence
level
point
estimate
Assuming,
simple random sample
conditions for B(n,p) are valid
Normal is a good approximation of B(n,p):
a) n 15 and b) n 15
for
CONFIDENCE INTERVALS I
Interpretation, z CI for mu (sigma known)
A Normal example
A researcher reported that children watch an average of 25 h
of TV per week (assume a normal distribution with standard
deviation of 3 h). If an SRS of 20 children is select
HYPOTHESIS TESTS V
Two-sample test for difference in proportions
Scenario
Risk of breast cancer is thought to be influenced by
events between age of menarche and age at first child
birth. An international study was conducted to evaluate
whether the risk o
HYPOTHESIS TESTING
Reasoning for hypothesis testing
Try it!
Data on the general Canadian population suggests that the
prevalence of red-green colour blindness is 4.25%. However,
some researchers claim that the population in Alberta is higher
than this val
HYPOTHESIS TESTS II
Formalization with One-sample for p
Scenario
Data on the general Canadian population suggests that the
prevalence of red-green colour blindness is 5.25%. However,
some researchers claim that the population in Alberta is higher
than thi
HYPOTHESIS TESTING IV
Two-sample tests for means
Comparing hypothesis tests
One-sample tests: comparing a sample value to
a larger population whose parameters are
assumed to be known
=
0
0 0
0
=
Two-sample tests: comparing the parameters of
two differe
Explanatory variable/ independent variable: explain or influence changes in a response variable
Response variable/ dependent variable: measures an outcome of a study
Displaying relationships: scatterplots
The most useful graph for displaying the relations
Chapter 9 Probability
9.1 The idea of Probability
Chance behaviour/ probability is unpredictable in the short run but has a regular and predictable pattern
in the long run. The proportion in a small or moderate number of tosses can be far from the probabi
2244 Test 2 Sample Set 7
Question 1.
At grocery stores, employees move products to the front of the shelf. In refrigerated sections of the
store, the employees not only move products forward, but also make sure the products with the earliest
best before d
2244 Test 2 Sample Set 5 (W2016)
Question 1.
A sales representative for Flora, a natural nutrient and supplements company, is conducting a survey for
market research. The representative asks questions that involve the following four variables. Which of
th
2244 Test 2 Sample Set 1 (W2016)
Question 1.
Midterm grades for the 120 students taking an introductory Physics course are summarized in the following
frequency distribution:
Number of
Grade (%)
Students
20% -30%
7
30% -40%
10
40% - 50%
11
50% - 60%
15
60
2244 Test 2 Sample Set 6 (W2016)
Question 1.
Sidney Crosby, a National Hockey League (NHL) player
with the Pittsburgh Penguins, scored between 0 and 5
points per game during the regular 2014-2015 NHL
season. Sidneys points scored per game for that season
2244 Test 2 Sample Set 2 (W2016)
Question 1.
A population consists of N=661 individuals. Selected R output summarizing the distribution of variable X
for these 661 individuals is included below. What is the mean of the sampling distribution of sample
mean
2244 Test 2 Sample Set 3 (W2016)
Question 1.
The incubation periods (in hours) for 8 people who developed food poisoning after consuming contaminated
salad are listed below.
43
20
18
19
14
21
36
28
What is the IQR of these data? Use the procedures as desc
TYPES OF DATA
Interval the difference between two values is meaningful
Nominal qualitative labels
Ratio all the properties of interval, but a clear 0 point
Ordinal - order matters, but not the difference between values
TYPES OF SAMPLING
Cluster divide peo
CHAPTER 9
EXERCISE 9.2
Part A
1. a) There are 3 places the one girl can occur
F
F
F
I
F G F
I
@AB) = 3 EGH EGH EGH = J or PAA) LIGM EGH EGH = J
F P
F
b) @AO) = EGH = FQ
F
F
F
F
c) @AR) = EGH EGH EGH = J
F
F
F
F
G
G
G
J
P
P
P
QP
a) @AB) = EUH EUH EUH = FGU
CHAPTER 6
EXERCISE 6.2
Part A
1.
P = 22.50a40|.04 + 500(1.04) 40
or P = 500 + (22.50 20)a40|.04 = $549.48
2.
P = 45a30|.05 + 1000(1.05) 30
or P = 1000 + (45 50)a30|.05 = $923.14
3.
P = 65a30|i + 2000(1 + i) 30 where i = (1 +
or P = 2000 + (65 2000i)a30|i
Writing your paper
Table 3.4 Golden rules for reporting numbers.
Rule
Correct expression
Numbers less than 10 are
words.
Numbers 10 or more are
numbers.
Words not numbers begin a
sentence.
Be consistent in lists of
numbers.
Numbers less than 1 begin
with
A
LTEX
Guangyong (GY) Zou, Ph.D.
Department of Epidemiology & Biostatistics
and
Robarts Clinical Trials of Robarts Research Institute
Zou, GY (Western)
Biostatistics 9510A
September 24, 2013
1/9
equation display
Display an equation when it
need to be numb
Biostatistics 9510A: Biostatistical Research Methods
Guangyong (GY) Zou, Ph.D.
Department of Epidemiology & Biostatistics
and
Robarts Clinical Trials of Robarts Research Institute
Zou, GY (Western)
Biostatistics 9510A
December 5, 2013
1 / 262
Chapter 1-2
Statistics: Overview
GY Zou
[email protected]
Department of Epidemiology & Biostatistics
Robarts Research Institute
University of Western Ontario
Sept 11, 2012
The lady tasting tea: P-value
The lady tasting tea: P-value
At a summer tea party in Cambridge,
Topic 11 Linear Correlation
Scatterplot graph of paired sample data (x, y) with the independent variable (X) on the xaxis and the dependent variable (Y) on the y-axis, both variables must be quantitative can
connected to the same subject (known as bivaria
Topic 6 Normal Distribution
Normal Distribution density curve of a continuous probability distribution, used with
p (proportions) or with (means) when is unknown (will talk about this later in
confidence intervals and hypothesis tests)
For a variable to h
Topic 9 Single-sample Hypothesis Tests
Hypothesis Test standard procedure for testing a claim about a population property/
parameter
One-sampled comparing a sample value/statistic to a larger population whose
parameters are assumed to be known
In the hypo