PUAF 610 TA

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PUAF 610 TA

• Session 4

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Some words

• My email jhlu_at_umd.edu
• Things to be discussed in TA
• Questions on the course and problem sets

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Today

• Problem Sets 1
• Probability
• Sampling
• Standard Error
• STATA

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interval
continuous
numerical proportion
discrete
data
dichotomous
nominal
non-dichotomous
categorical
ordinal
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Measurement scales
All measurement in science are conducted using
four different types of scales "nominal",
"ordinal", "interval" and "ratio Qualitative
data (unordered or ordered discrete
categories) 1. Nominal - numbers are used as
labels for the elements (e.g. gender, party
affiliation, states of a country, etc.) 2.
Ordinal elements in the dataset can be ordered
on the amount of the property being measured and
values are assigned in this same order (e.g.
ratings)
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Measurement scales

• Quantitative data (variables have underlying
  continuity)
• 3. Interval
• A measurement scale in which a certain
  distance along the scale means the same thing no
  matter where on the scale you are, but where "0
  (zero) on the scale does not represent the
  absence of the thing being measured.
  (temperature)
• 4. Ratio
• A measurement scale in which a certain
  distance along the scale means the same thing no
  matter where on the scale you are, and where "0"
  (zero) on the scale represents the absence of the
  thing being measured. (money)

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Events

• Event vs. Observation (any collection of outcomes
  vs. a single observed outcome)
• Simple event any event that cannot be subdivided
  into other events.
• Compound event any event that is composed of two
  or more simple events.
• Sample space an event that contains all possible
  outcomes.

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Events

• Union of events contains simple events that are
  members of either one of the original events.
• Intersection of events contains simple events
  that are members of both of the original events.

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Events

• Mutually exclusive events have neither
  observations nor simple events in common.
• Independent events the probability of one is not
  affected if the other has happened.

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Probability

• Probability deals with the long-term likelihood
  of the occurrence of particular outcomes on
  variables of interest.
• Probability of an event is the ratio of the
  number of outcomes including the event to the
  total number of outcomes (simple events).
• P(A)   Number of outcomes that include A /
  Total number of possible outcomes

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Probability

• probability of event p
• 0 lt p lt 1
• 0 certain non-occurrence
• 1 certain occurrence

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Example

• Choose a number at random from 1 to 5.
• What is the probability of each outcome?
• What is the probability that the number chosen is
  even?
• What is the probability that the number chosen is
  odd?

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Example

• A glass jar contains 6 red, 5 green, 8 blue and 3
  yellow marbles. If a single marble is chosen at
  random from the jar, what is the probability of
  choosing a red marble? a green marble? a blue
  marble? a yellow marble?

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Rules of probability

• Probability of the union of two events
• The probability of event A OR event B is equal to
  the sum of their respective probabilities minus
  the probability of the intersection of the
  events.
• if A and B are mutually exclusive events, then
  P(A or B) P(A) P(B)

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Rules of probability

• Probability of the intersection of two events
• The probability that Both A And B occur is equal
  to the probability A occurs times the probability
  that B occurs, given that A has occurred.
• If events A and B are independent
• then P(A and B) P(A)P(B)

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Rules of probability

• The probability that event A will occur is
  equal to 1 minus the probability that event A
  will not occur.
• P(A) 1 - P(A')

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Rules of probability

• Conditional probability
• The probability of event A given that event B has
  occurred is equal to the probability of the
  intersection of the events divided by the
  probability of event B.

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Example

• Suppose a high school consists of 25 juniors,
  15 seniors, and the remaining 60 is students of
  other grades.
• Whats the relative frequency of students who are
  either juniors or seniors ?

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Example

• Suppose we have two dice. A is the event that 6
  shows on the first die, and B is the event that 6
  shows on the second die.
• If both dice are rolled at once, what is the
  probability that two 6s occur?

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Example

• A box contains 6 red marbles and 4 black marbles.
  Two marbles are drawn without replacement from
  the box.
• What is the probability that both of the marbles
  are black?

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Example

• Suppose we repeat the experiment of but this
  time we select marbles with replacement. That is,
  we select one marble, note its color, and then
  replace it in the box before making the second
  selection.
• When we select with replacement, what is the
  probability that both of the marbles are black ?

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Example

• A student goes to the library. The probability
  that she checks out (a) a work of fiction is
  0.40, (b) a work of non-fiction is 0.30, , and
  (c) both fiction and non-fiction is 0.20.
• What is the probability that the student checks
  out a work of fiction, non-fiction, or both?

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Example

• At Kennedy Middle School, the probability that a
  student takes Technology and Spanish is 0.087.
  The probability that a student takes Technology
  is 0.68.
• What is the probability that a student takes
  Spanish given that the student is taking
  Technology?

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Sampling

• Simple random sampling
• Systematic sampling
• Cluster sampling
• Stratified random sampling
• Multistage sampling

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Sampling distributionof the mean

• When using samples we inevitably face the problem
  of sampling error which is defined as the
  difference between the population mean (µ) and
  the sample mean ( ).
• We can provide a probabilistic estimate of the
  accuracy of the sample mean through a theoretical
  sampling distribution.

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Sampling distribution of the mean

• Central tendency
• The expected value of the mean of the
  distribution of sample means is equal to the
  population mean.
• Variance
• The expected value of the variance for the
  sampling distribution of the mean is
• where s2 is the variance in the population and n
  is the sample size.

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Sampling distribution of the mean
Standard deviation of the sampling distribution
of the mean where s is the standard
deviation in the population (can be approximated
by the sample standard deviation) and n is the
sample size. Standard deviation of the sampling
distribution of the mean is called the standard
error of the mean.
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Sampling distributionof the mean

• As n increases, the standard error decreases.
• As n increases, the shape of SDM becomes more
  like the normal distribution even if the variable
  is not normally distributed in the population.

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Standard error of a proportion
Standard error of a proportion is the standard
deviation of its sampling distribution. Since
proportions have two possible outcomes, the
sampling distribution is binomial, however with
relatively large sample sizes it approximates the
normal distribution.
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Standard errors and statistical precision

• Statistical precision is reflected in standard
  errors as measures of variability of the sampling
  distribution of a statistic.
• Small standard errors imply greater accuracy of
  the estimate.
• When the sample is representative, the standard
  error will be small. 

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STATA

• Beginners Guide to SAS STATA Software (Dept.
  of Agricultural Applied Economics, UGA)
• http//www.aaegrad.uga.edu/stata_sas_guide.pdf
• Learning by practice !

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Stata Commands

summarize univar
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Stata Commands

univar, boxplot graph box
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Stata Commands

univar, boxplot graph box
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STATA commands
hist varname, norm
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Stata Commands
set obs generate varnamerbinomial(1,p) table
varname