Chapter 18: The Normal
Approximation for Probability
Histograms
Probability histogram, empirical, converge and
The Central Limit Theorem
Probability Histograms
Probability histogram is a graph that
represents chances by area.
Example 1: Gambler playing th
Chapter 10: Regression
Regression line, regression method, the graph of
averages, regression effect, regression fallacy
Introduction
The regression method describes how one
variable depends on another
Example: We have height and weight data
for 471 men ag
Summary of Chapter 6
Chance error, bias or systematic error, outliers
Summary
No matter how carefully it was made, a
measurement could have turned out a bit different.
This reflects chance error. Before investigators rely
on a measurement, they should est
Chapter 13: Probability. What
are the Chances?
Chance, frequency theory, conditional probabilities,
unconditional probabilities, multiplication rule,
independent and dependent things
Introduction
You say that the rain is:
Likely
Probable
Possible
Is ther
Chapter 5: The The Normal
Approximation
for
Data
Percentiles and interquartile range
(Continued)
Percentiles
The average and SD are a good summary
of the data that follows the normal curve.
They are less satisfactory for other kinds of
data.
Example: The
Chapter 9: More about
Correlation
Features of the correlation coefficient, changing
SDs and ecological correlation
Some Exceptional Cases
The correlation coefficient is useful for football
shaped scatter diagrams.
For other diagrams r can be misleading.
Summery of Chapter 10
Regression estimates, regression line, graph of
averages, regression effect and regression
fallacy
Associated with an increase of one SD in x, there is
an increase of only r SDs in y, on average. Plotting
these regression estimates g
Summery of Chapter 11
Residual, r.m.s. error, residual plot,
homoscedastic and heteroscedastic diagram
When the regression line is used to predict y from x,
the difference between the actual value and the
predicted value is a residual, or prediction error
Syllabus
MATH 114
Foundations of Statistics
Spring 2014
Instructor: Alona Kryshchenko
Office: KAP 416B
Telephone: (323) 6498113
Email: [email protected]
Office hours: Monday 23pm, Wednesday 10:30am12:30pm at KAP 416B (starting from
the second w
Binomial formula
The chance that an event will occur exactly k
times out of n is given by binomial formula
n!
k!(n
In this formula:
n  number of trials
k  number of times the event is to occur
p  probability that the event will occur on any
particul
Chapter 21: The Accuracy of
the Percentage
Inference, the bootstrap, confidence interval
The bootstrap
So far we talked about taking SRS from the
population which composition is known.
What to do if we do not know the
composition? (the usual case)
The boo
Chapter 17: The Expected
Value and Standard Error
Expected value, standard error, the square root
law and observed value
The Expected Value
Expected value of the sum of draws made at
random with replacement for a box equals
(number of draws)*(average of
b
Chapter 20: Chance Errors in
Sampling
Sample percentage, population percentage, SE
for percentage and correction factor.
The expected value and
standard error of the
How to find the likely size of a chance error in
percentage
percentage, for a simple rand
Chapter 10: Regression
(continued)
Regression effect, regression fallacy
The Regression Fallacy
Example: A preschool program tries to boost
childrens IQs. Children were tested when they
enter the program and again when they leave. On
both occasions, the a
The SD Line
The SD line goes through the point of
averages and it passes all the points which
are an equal number of SDs away from the
average, for both variables.
To plot SD line:
Plot point of averages
Slope: SD of y/SD of x , for positive
correlation

Summary of Chapter 14
When figuring chances, one helpful strategy is to
write down a complete list of all the possible ways
that
the chance process can turn out.
If this is too hard, at least write down a few
typical ways, and count how many ways there ar
Chapter 19: Sample Surveys
Population, sample, inference, parameters, statistics,
selection bias, nonresponse bias, quota sampling,
simple random sample, multistage cluster sampling
Introduction
A class of individuals of interest is called the
population