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1. Mtodos
1.1. Descripcin del mtodo propuesto
1.1.1. Coherencia parcialmente dirigida
Definicin PDC (JUEVES 30 1pm)
Partamos de un conjunto de
mediciones de EEG, registradas con un
S S1 , S 2 , , S M
conjunto de electrodos disponibles
Partiendo de un con
MATH&146
Final Review
Part 1
Linear and Multiple Regression
1
Example 1
For each of the following pairs of variables,
indicate whether you would expect a positive
correlation, a negative correlation, or a correlation
close to zero. Explain your choice.
a)
MATH&146
Exam 3 Review
Lessons 24 34
1
Exam 3
Hypothesis Tests (so far)
Parameter
Hypothesis Test
p
One-Proportion Z Test
p1 p2
Two-Proportion Z Test
p1, p2, , pk
Chi-Square Tests
(mu)
One-Sample T Test
d
Paired T Test
1 2
Two-Sample T Test
1 = 2 = = k
A
MATH&146
Exam 2 Review
Lessons 12 23
1
Example 1
Explain to someone who has not taken a statistics
course what statistical significance means.
One answer:
A result is considered statistically significant if that
result's difference from the null hypothesi
MATH& 146
Lesson 42
Section 6.2
Model Selection
1
Model Selection
The best model is not always the most
complicated. Sometimes including variables that
are not evidently important can actually reduce the
accuracy of predictions.
However, it is not always
MATH& 146
Lesson 41
Section 6.1
Multiple Regression
1
Multiple Regression
The principles of simple linear regression lay the
foundation for more sophisticated regression
methods used in a wide range of challenging
settings.
Multiple regression extends sim
MATH& 146
Lesson 21
Section 2.8
Confidence Intervals
1
Confidence Intervals
Recall that a point estimate is a statistic
calculated from a sample that is used to estimate a
population parameter.
For example, the sample mean, x , can be used to
estimate the
MATH& 146
Lesson 24
Section 3.3
The Chi-Square Distribution
1
One-Way Tables
Previously, we have looked at inference for single
proportions (one group) and for difference of
proportions (two groups).
Now we will develop a method for assessing a null
model
MATH& 146
Lesson 22
Section 3.1
Inference for Single Proportions
1
Trial, Success, and Failure
A single event that leads to an outcome can be
called a trial. If the trial has two possible
outcomes, e.g. heads or tails when flipping a coin,
we typically la
MATH& 146
Lesson 25
Section 3.3
The Goodness of Fit Test
1
Goodness of Fit Test
Suppose that you want to determine whether
observed sample frequencies differ significantly
from expected frequencies specified in the null
hypothesis.
This test can be addres
MATH& 146
Lesson 26
Section 3.4
Testing for Independence of
Categorical Variables
1
Test of Independence
We can check whether one categorical variable is
associated with another categorical variable using
a chi-square test of independence.
For this test,
MATH& 146
Lesson 29
Section 4.2
Paired Data Inference
1
Textbook Prices
Are textbooks actually cheaper online? Here we
compare the price of textbooks at UCLA's
bookstore and prices at Amazon.com.
dept
course
ucla
amazon
diff
1 Am Ind
C170
27.67
27.95
0.28
MATH& 146
Lesson 23
Section 3.2
Difference of Two Proportions
1
Difference of Proportions
Consider the following questions:
Can giving students a reminder cause them to
be a little thriftier?
Do blood thinners have an effect on the survival
of patients
MATH& 146
Lesson 18
Section 2.6
Probabilities Using
the Normal Distribution
1
Areas Between Two Bounds
For a normal distribution, N(,), the area
(probability) between two bounds is
P(a < X < b) = normalcdf(a, b, , )
a
b
2
Example 1
Suppose X ~ N( = 100, =
MATH& 146
Lesson 14
Section 2.3
The Hypothesis Test Procedure
1
Make-Up Final
A (semi) well-known story* goes something like this:
Four students missed the final exam for their statistics
class. They went to the professor and said, "Please,
oh please, let
MATH& 146
Lesson 12
Section 2.1
Randomization Case Study:
Gender Discrimination
1
Example 1
a) Suppose you flip a coin 100 times, getting 51
heads and 49 tails. Would that be evidence of an
unfair coin?
b) Suppose you flip another coin 100 times, getting
MATH& 146
Lesson 11
Section 1.6
Categorical Data
1
Frequency
The first step to organizing categorical data is to
count the number of data values there are in each
category of interest.
We can organize these counts (or frequencies)
into a frequency table,
MATH& 146
Lesson 15
Section 2.3
Randomization Case Study:
CPR Patients
1
Two-Sided Hypotheses
Earlier we explored whether women were
discriminated against (Lesson 12) and whether a
simple trick could make students a little thriftier
(Lesson 13). In these
MATH& 146
Lesson 10
Section 1.6
Graphing Numerical Data
1
Graphs of Numerical Data
One major reason for constructing a graph of
numerical data is to display its distribution, or the
pattern of variability displayed by the data of a
variable.
Three popular
MATH& 146
Lesson 13
Section 2.2
Randomization Case Study:
Opportunity Cost
1
Opportunity Cost
How rational and consistent is the behavior of the
typical American college student?
For this case study, we'll explore whether college
student consumers always
INDEPENDENT
Independent there is no relationship between two variables
Distribution of one variable is same for all categories of another
variable
NOT Independent there is a relationship between two variables
Distribution of one variable is different fo
MATH& 146
Lesson 2
Appendix A.2
Conditional Probability
1
Multiplication Rule (Independent)
Two events are independent if the outcome of
one does not affect the probability of the other
event.
Consider two independent events A and B with
individual probab
MATH& 146
Lesson 5
Section 1.4
Sampling Methods
1
Data Collection
There are two primary types of data collection:
observational studies and experiments.
Generally, data in observational studies are
collected only by monitoring what occurs, while
experimen
MATH& 146
Lesson 3
Sections 1.1 and 1.2
Understanding Data
1
So What Is Statistics?
Let us begin with the Course Description:
"Introduction to the basic principles of probability,
descriptive statistics, and inferential statistics.
Topics include properti
MATH& 146
Lesson 4
Section 1.3
Study Beginnings
1
Populations and Samples
The population is the complete collection of
individuals or objects that you wish to learn about.
To study larger populations, we select a sample. The
idea of sampling is to select
MATH& 146
Lesson 6
Section 1.5
Experiments
1
Experiments
Studies where the researchers assign treatments
to cases are called experiments. When this
assignment includes randomization (such as coin
flips) to decide which treatment a patient receives,
it is
MATH& 146
Lesson 8
Section 1.6
Averages and Variation
1
Summarizing Data
The distribution of a variable is the overall pattern
of how often the possible values occur. For
numerical variables, three summary characteristics
of the overall distribution of th
MATH& 146
Lesson 1
Appendix A.1
Defining Probability
1
Probability
Probability measures the
uncertainty that is associated
with the outcomes of a
particular random process, a
planned operation carried out
under controlled conditions.
Flipping coins or rol
The modern age is called an age of statistics. The
statistics, these days, are most extensively and
effectively used in all fields of social life and as such,
like the ability to read and write, have become an
essential part of human life. Statistics prov