jpeg("exp.jpg")
dat = rexp(1000,2)
hist(dat, freq=F)
x = seq(0,4,.01)
f = dexp(x,2)
lines(x,f, col=2)
dev.off()
Consider a population consisting of n objects. If we take a sample of size m
from this population (without replacement), then there are nCm (re
Points
~ 3
®
4 oglfm le'
1. ln a certain study, families consisting of exactly 5 members are considered. Suppose it is known
that exactly two people in each family are employed. Two members of each family are randomly
called, and asked whether they are em
é
m Cw [m]: Cw[é2+M,?] = saVIz,z)+c.w1u,a}:,/§=g
q 61 W ?
2 O
/\(=E\r[(]=EY[%?tU3=%_EY[?3+EF[LAJ :ME
A O
d=%/A_}q/Az =7 929 = E Yf? :iz
01$: CWHK): Cw[x, ghoc] : ._§,.r awful + CWNM]
o = Cw[vw)+ emu] thul
W M
D
O
'. OZY=é CSVDCL'Z') : .3: C641 [2*4 '
x = y = as.vector( c(1:4)
one = rep(1,4)
fxy = matrix(c(1,1,1,1, 1,0,0,0, 1,0,0,0, 1,1,1,1), nrow=4, ncol=4, byrow=T)
fxy = fxy/sum(fxy)
fx = fxy %*% one
# one marginal
fy = t(one) %*% fxy
# the other marginal
fx = as.vector(fx)
# R thinks fx is matrix. F
Stat 509/Econ 580: Econometrics 1
Midterm Practice Problems and Solutions
Solution:
To get a pattern of hhh, all that matters is the outcome of the last couple of tosses. For example, getting
a sequence of ththtthh is no dierent than a sequence of hhthh a
Statistical Concepts and Methods for the Social Sciences
STATS 221

Fall 2012
CHAPTER 5:
Fact 1. The distinction between explanatory and response variables is essential in regression. Leastsquares
regression makes the distances of the data points from the line small only in the y direction.
Fact 2. There is a close connection betw
Statistical Concepts and Methods for the Social Sciences
STATS 221

Fall 2012
Statistics 221 Summary of Material
James McQueen, Autumn 2012
This guide is meant to be a brief summary of important results including formulas and the occasional denition. It is not meant
to cover every topic in the book.
This notation will be used throu
Statistical Concepts and Methods for the Social Sciences
STATS 221

Fall 2012
Describing Distributions
withhapter 2
Numbers
C
What we learned last time
Any study begins with a research question.
Depending on the question of interest, a
researcher collects data through a survey,
experiment, census or otherwise. The first
stage of da
Statistical Concepts and Methods for the Social Sciences
STATS 221

Fall 2012
Chapters 10, 12
Probability
Outline
Probability space
Probability rules
Disjoint (mutually exclusive) events
Conditional probability
Independent events
Idea of Probability
Chance behavior is unpredictable in the short run
but has a regular and predictable
Statistical Concepts and Methods for the Social Sciences
STATS 221

Fall 2012
Test Pos
P = 0.89
1/270(0.89) =
0.0033
Test Neg
1/270(0.11)=
0.00041
Downs Syndrome
Actually present
P = 1/270
P = 0.11
Test Pos
P = 0.25
Downs Syndrome
not present
269/270(0.25)
= 0.249
P = 269/270
Test Neg
BPS  5th Ed.
P = 0.75
Chapter 12
269/270(0.75)
Statistical Concepts and Methods for the Social Sciences
STATS 221

Fall 2012
STAT/SOC/CSSS 221
Picturing Distributions with Graphs
Chapter 1
BPS  5th Ed.
1
Chapter 1
What is this course about
The course will discuss, in a nonmathematical way,
the most important concepts and techniques of
statistics from the point of view of appl
Statistical Concepts and Methods for the Social Sciences
STATS 221

Fall 2012
Chapter 24
OneWay Analysis of Variance:
Comparing Several Means
Outline
Problem description.
F test.
Analysis of Variance  ANOVA.
Conditions for ANOVA.
Problem description
Often, the studies are aimed to compare more
than two population in order to chec
Statistical Concepts and Methods for the Social Sciences
STATS 221

Fall 2012
Chapter 23
Inference for Regression
Outline
Conditions for inference.
Estimating regression parameters.
Testing linear relationship and correlation.
Inference for regression slope.
Inference about prediction.
Linear regression
We are interested in describ
Statistical Concepts and Methods for the Social Sciences
STATS 221

Fall 2012
Chapter 22
Two Categorical Variables:
The Chisquare Test
Outline
Association between two categorical variables.
Hypothesis of independence: expected counts.
Chisquare distribution.
Chisquare test.
Goodness of t.
Contingency tables
We are interested in
Statistical Concepts and Methods for the Social Sciences
STATS 221

Fall 2012
Chapter 19 and Chapter 20
Inference about a Population
Proportion.
Comparing Two Proportions
Outline
Estimating a population proportion and a
dierence between proportions.
Condence intervals for a proportion and for a
dierence between proportions.
Signica
Statistical Concepts and Methods for the Social Sciences
STATS 221

Fall 2012
Chapter 18
TwoSample Problems
Outline
Comparing two population means.
Condence interval for the dierence between
means.
Twosample ttest.
Setup
We want to compare the responses to two
measurements or to compare the
characteristics of two populations.
We
Statistical Concepts and Methods for the Social Sciences
STATS 221

Fall 2012
Chapter 17
Inference about a population
mean
Outline
Conditions for inference.
tdistribution.
Onesample condence interval based on the
tdistribution.
The onesample ttest.
Paired ttest (matched pairs t procedures).
Simple conditions for inference abo
Statistical Concepts and Methods for the Social Sciences
STATS 221

Fall 2012
Chapter 15
Thinking about inference
Outline
Conditions for inference in practice.
Behavior of condence intervals.
Behavior of signicance tests.
Power of a test.
Type I and Type II errors.
Simple conditions to check:
SRS of size n from the population of in