Chapter 11: Analysis of Variance
343
Chapter 11. Analysis of Variance
11-2 OneWay ANOVA
1.
Weights of Poplar Trees
a. H 0 : 1 = 2 = 3= 4
b. H1 : The means are not all the same.
c. The test statistic, F, is identified in the output as F, and is F = 8.448.

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

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

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

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

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?)

Topic 13 One-factor ANOVA
Background
ANOVA ANalysis Of VAriance, used to partition and analyze variation in a continuous variable
in multiple (3 or more) populations, method of performing hypothesis testing on multiple
treatment populations means (paramet

Topic 1 Sampling
Science study of nature/the natural world, use of the observation and the scientific method
Statistics tool for analyzing raw data for objectiveness
Observation ! Hypothesis ! Experiment/Study ! Data/Results !Use statistics to
determine v

2244B Sample Sample Test 2 Questions
Biol/Stats 2244A Test 2 Questions
1. Suppose that two meteorological experts, A and B, independently provide simple weather forecasts of
rain or no rain for the next day. They do this for 100 days, after which it is fo

Biol/Stats 2244B Sample Test 1 Questions
Question1.
A psychological survey asks subjects to rate their level of happiness on a scale from 1 (least happy) to
7 (most happy). Which term best describes the resulting data?
A.
census data
B.
nominal data
C.
ra

Topic 2 Study Design
Subjects individual elements that are being studied, experimental units
Variable (X) characteristic that can take on different values/status,
Treatment group of subjects that have a modified variable(s), typically the group of most
in

Chapter 4
Discrete Probability Distribution
4.2 Random Variables
Random Variable: is a variable (typically represented by x) that has a single numerical value,
determined by chance, for each outcome of a procedure. They can be discrete or continuous
Proba

Topic 4 Probability
Probability the likelihood/chance that a given event will occur
Procedure an experiment/action that will trigger the event
Event outcome (or collection of outcomes) for a particular procedure, a simple event cannot be
broken down furth

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

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 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

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

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

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 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 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

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