Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2012
Chapter 3 Probability
3.1 Overview:
Rare Event Rule if under a given assumption the probability of a particular even
is extremely small we conclude that the assumption is probably not correct
3.2 Fundamentals
In considering probability we deal with proc
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2014
10Confidence intervals of p
sampling distribution of proportions
confidence intervals of p
point estimate and margin of error
requirements
using normal approximation of binomial
distribution
estimating n required to achieve a particular
margin of e
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2014
8Confidence intervals for
confidence intervals for , if known
definition
confidence level and complement
point estimate and margin of error
assumptions
interpretation
sample size to estimate within E
Textbook:
Ch. 14, pp. 335344 (up to but not i
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2014
11Hypothesis tests for p
vocabulary for hypothesis tests
null and alternative hypotheses
test statistic
significance level and Pvalue
Type I and Type II error s
power
procedure for hypothesis test for p
Textbook
Chapter 19, pp. 463 469, 471479
(
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2014
12One sample hypothesis test for
onesample hypothesis test for
hypotheses
assumptions
test statistic (t)
Pvalues for onetailed versus twotailed tests
righttailed vs lefttailed
Textbook:
Chapter 14, pp. 344357
Chapter 15, pp. 371385
Chapte
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2014
9  CI of , unknown
confidence intervals for , if is unknown
estimating with s
comparing T to Z
using the t distribution table
increasing the precision of our estimate
Textbook:
Ch. 14, pp. 335344 (up to but not including Rasoning of tests of signif
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2014
14twosample hypothesis test for p
hypothesis test for difference in proportions
pooled estimate,
test statistic, requirements
confidence interval
Textbook:
Chapter 18, pp. 437455
Chapter 20, pp. 483488, 491494, 500503
(see exceptions posted on
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2014
17Inference for Regression
Residuals
Checking the linear model assumptions
hypothesis test for the slope ()
hypotheses
test statistic, degrees of freedom
SPSS output
confidence interval for the slope ()
predictions & extrapolation
Textbook:
Chapt
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2014
16Regression model & assumptions
Purposes of regression analysis
The linear regression model
model assumptions
parameters and interpretation
estimating the population regression
least squares regression line
coefficient of determination, r2
Textbo
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2016
OneWay ANOVA and posthoc tests
The weakness of doing multiple ttests is that we get multiple Pvalues, one for each test
performed
o Doesnt tell us how likely it is that the sample means are spread apart as far as these are
o The problem gets worse as
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
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Fall 2016
Binomial Distribution
The distribution of a count depends on how the data are produced
The binomial setting is as follows:
o There are a fixed number n of observation
o The n observations are all independent which means that knowing the result of one
obse
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2016
Normal Distribution
Normal curves are density curves that are symmetric, singlepeaked, and bell shaped
o Describes normal distributions
o All normal distributions have the same overall shape
o The exact density curve for a particular normal distribution
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2016
Confidence Intervals for p
Our discussion of statistical inference up to this point has concerned making inferences about
population means
o Now we turn to questions about the proportion of some outcome in a population when
studying a categorical variable
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2014
7Sampling Distributions
Sampling distributions
comparison with distributions
mean and standard error
shape of sampling distributions
Central Limit Theorem
zscores and probabilities for sampling
distributions
Textbook:
Chapter 3 (all sections)
Stat
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2014
Introduction & Sampling Strategies
Course administration
some quick highlights
read the syllabus! Do the quiz!
Sampling Designs
vocabulary
sampling concerns and issues
sampling designs
Textbook sections
Chapter 7, p. 158164 (Sampling & Sampling De
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
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Fall 2014
6Normal Distribution
continuous random variables and density
curves
normal distributions
characteristics
assessing normality with QQ plots
standard normal
zscores & distribution table
finding probability given z scores
finding z scores given pr
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2012
Chapter 2 Describing, Exploring and Comparing Data
21 Overview:
Important characteristics of Data:
o Center a representative or average value that indicated where the
middle of the data set is located
o Variation a measure of the amount that the data va
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2012
Chapter 4 Discrete Probability Distributions
4.2 Random Variables
Random Variables a variable (typically expressed by x) that has a single
numerical value, determined by chance , for each outcome of a procedure
Probability Distribution a graph, table, or
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2012
Chapter 11 Analysis of Variation
11.1 Overview
Want a procedure for testing the hypothesis that three or more population means
are equal the null hypothesis H0: 1 = 2 = 3 = 4
Analysis of Variance (ANOVA) method of testing the equality of three or more
po
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
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Fall 2012
Chapter 10 Multinomial Experiments and Contingency Tables
10.1 Overview
Categorical data (qualitative or attributes) can be separated into different
categories, known as cells that are based on some nonnumerical characteristic
Main goal is to test claim
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2012
Chapter 8 Inferences From Two Samples
Two sample tests are very useful in drug testing (Placebo vs. Drug)
8.2 Inferences About Two Proportions
When testing a hypothesis made about two population proportions, or when
constructing a confidence interval to
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2012
Chapter 5 Normal Probability Distributions
5.1 Overview
A random variable is a variable having a single numerical value, determined by
chance
A probability distribution for a discrete random variable describes the probability
for each value of the random
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
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Fall 2012
Chapter 6 Estimates and Sample Sizes with One Sample
6.1 Overview
Use sample data to make inferences about population parameters
Two major applications of inferential statistics involve the use of sample data to:
1. Estimate the value of a population pa
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2012
Chapter 9 Correlation and Regression
9.1 Overview
Making inferences based on sample data that comes in pairs
o Determining whether there is an association between two variables and
if the association exists, describe it with an equation
9.2 Correlation
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2012
Chapter 7 Hypothesis Testing with One Sample
7.1 Overview
Two major activities of inferential statistics are the estimation of population
parameters and hypothesis testing
o Hypothesis test is a standard procedure for testing some claim
Hypothesis is a c
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2012
Chapter 1 Introduction
1.1  Overview:
Data observations that have been collected
Statistics collection of methods for planning experiments, obtaining data and
then organizing, summarizing, analyzing, interpreting, presenting and drawing
conclusions bas
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
STATS 2244A

Fall 2014
Probability
Probability
vocabulary/notation (see Ch. 9, p. 212)
classical vs relative frequency approaches
law of large numbers
Mutually exclusive vs independent events
Additional and Multiplication rules
Conditional probability
Complementary even
Western University (Ontario)  Also known as University of Western Ontario
Statistics for Sci
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Fall 2014
Random variables & binomial distribution
Random variables in general (see p. 158161)
discrete vs. continuous RV
probability distributions & histograms
Binomial distribution (BD)
distinguishing features
formula for probability (incl. combinations)