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inference are made
entire collection
of entities that we
POPULATION
want information
about
"all"
subset of population
SAMPLE
what we examine to
less complicated, less
gather information
costly, and time-saver
"randomly selected"
Plural Sense: collection of facts
and figures or processed data
(numerical figures)
based on population
average - ratio and
POPULATION MEAN: μ
intervals
PARAMETERS
POPULATION
characteristics
PROPORTION: P
Example
POPULATION
STANDARD DEVIATION:
σ
dispersed
SUMMARY MEASURES
POPULATION
proximity and spread
dispersed
VARIANCE:σ^2
out
based on sample
SAMPLE MEAN: x̄
STATISTICS
SAMPLE PROPORTION: p̂
Example
SAMPLE STANDARD
DEVIATION: s
SAMPLE VARIANCE: s²
categorical data that
cannot be measured on
QUALITATIVE
a natural numerical
scale
characteristic or
attribute that is
measured for the unit
age, number of siblings,
TYPE
under consideration
DISCRETE
recorded on a natural
finite or countable
number of values
number of courses
example
failed, time spent
studying
occurring numerical
QUANTITATIVE
scale and performs
arithmetic operations
infinitely many values
CONTINUOUS
at any point of a given
example
height, weight, weekly
allowance
interval
qualitative variable
gives names/ labels to
various categories
without a sense of
order
NOMINAL
categories are of equal
importance
data are limited to
frequency counts and
percentages
VARIABLE
sex, employment
status, farm type,
example
tenure status, yes or no
question
qualitative variable
inherent ordering
difference between
categories cannot be
measured and has no
meaning
ORDINAL
Module 1
n = number of trials
Symbols
Basic Concepts in
Inferential Statistics
limited to frequency
counts and percentages
Statistics
LEVEL OF
MEASUREMENT
example
p = probability
of failure
p1^x = 0.1
x = probability
of success
X = probability of events
quantitative variable
Singular Sense: branch of
science (theory and methods)
intervals between
categories have
meaning
xi = number of times
outcomes k occurred in
n trials
INTERVAL
cannot perform
multiplication or
division
2 possible outcomes
MEAN
number of trials are
fixed; n > 1
BINOMIAL
DISTRIBUTION
E[X] = np
FORMULAS
VARIANCE2 (standard
deviation)
constant for each trial
(independent) means
doesn't affect other trials
V[X] = [np (1-p)]
P(X<x) = P(X=x) + P(X=x)...
may also depends
if the x is too big
P(X>x) = 1 - P(X<x)
IQ scores, degree
Celsius, fahrenheit
example
SD[X] = √[np (1-p)]
quantitative variable
has an absolute zero
point = absence
all POSSIBLE outcomes
are known in advance
X ~ binomial (n,p)
P(X=x) = (nCx)(p^x)(1-p)^(n-x)
highest educational
attainment, satisfaction
rating, student
classification
associated with discrete
random variable, which
can take on distinct,
countable, sometimes
infinite number of
values
PROBABILITY
MASS
FUNCTION
P(X>x) = P(X=x) + P(X=x)...
RANDOM EXPERIMENT/
STATISTICAL
EXPERIMENT
DISCRETE PROBABILITY
DISTRIBUTION
properties
RATIO
outcomes are
unpredictable
ACCURATE
OBSERVATION
repeatable
KEYWOARDS
SAMPLE SPACE
more than 2 outcomes
number of trials are given
RANDOM VARIABLE
constant for each trial
(independent) means
doesn't affect other trials
PROBABILITY
MASS FUNCTION
realized value of a
variable that is
measured and recorded
DATA
rule that quantifies each of the outcome (let
x be.... = {0,1,2,..}
Common Probability
Distributions
ESTIMATOR
BRANCHES OF
STATISTICS (objectives:
to define and to infer)
INFERENTIAL
STATISTICS
bell-shaped
formula for computing
ESTIMATION
finding a value or range
of values for an
unknown parameter of
interest
numerical value
ESTIMATE
range of plausible
values
between 0 and 1
P-value
extreme or even more
extreme
CONFIDENCE INTERVAL
ESTIMATION
statement about the
parameter
associated with
continuous random
variables, which can
take any value on an
interval
NORMAL DISTRIBUTION
TEST OF HYPOTHESIS
verifying a claim
interval becomes
CONFIDENCE INTERVAL
if a confidence
coefficient is attached
to it
format
CONTINUOUS
PROBABILITY
DISTRIBUTION
smallest standard error
obtained by selecting
the appropriate
statistic
symmetric in mean =
median = mode
maximum = mean
minimum asymptotic
tails
measured by variance
or standard error
single value
POINT ESTIMATION
COMMON PROCEDURES
IN STATISTICAL
INFERENCE
closeness to the
different possible
values
PRECISE
BASIC CONCEPTS
conclusions apply
whether it is a
population or sample
data
tools used to analyze
the information from
the sample to make
generalizations from
the population
PROPERTIES
kelvin
tools used to describe a
mass of data
Module 2
bias = zero, then the
estimator is unbiased
measured by bias
collection of
observation on one or
more variables
DESCRIPTIVE STATISTICS
PROBABILITY
DISTRIBUTION
most quantitative falls
in ratio
example
set of all possible outcomes of a random
experiment (Ω)
MULTINOMIAL
DISTRIBUTION
gives probabilities of
occurrence of the
possible outcomes of a
random experiment
closeness to the true
value
can multiply or divide
1-α
α = level of significance
0% = no confidence
100% = certain
level of confidence
90%, 95%, 99%
higher degree of
confidence = wider
interval
point estimate (+-)
standard error
FORMAT: Ho: Population
Parameter = null value
HYPOTHESIS
NULL HYPOTHESIS
reject Ho
each unit in the population has a known and
nonzero chance of selection
PROBABILITY MASS
FUNCTION
z = look at the z-table
always less than
point estimator of the
population is the
sample mean (x̄ )
x̄ /n
POINT ESTIMATOR
normally distributed
or approximates a
normal distribution
SIMPLE RANDOM
SAMPLING
draw lots
STRATIFIED RANDOM
SAMPLING
example
indicates accuracy
length is the precision
(standard error)
GOALS
STAT 101
collect data for decision
making
equal chances
contradictory
statement that will be
accepted if the Ho is
rejected
ALTERNATIVE
HYPOTHESIS
reject a true Ho
take a sample in every
groups(cluster)
SYSTEMATIC SAMPLING
x̄ +- Margin Error
Formulating the
hypothesis
FORMAT
Test procedures
SAMPLING METHOD
CLUSTER SAMPLING
CONFIDENCE INTERVAL
ESTIMATOR
Sampling frame
make the group (clusters)
chosen a sample
create a list
ERROS
STEPS IN HYPOTHESIS
TESTING
Decision
Computing the test
statistic and p-value
probabilities of sampling are unknown
known variance: z-test
Decision and Conclusion
test
should not be used for statistical inference
NONPROBABILITY
SAMPLING
unknown variance: t-test
examples
known variance
Should be normally
distributed
judgement sampling
selected purposively
accidental sampling
taken as volunteers
convenience sampling
Parametric test
unknown variance
Histogram
HYPOTHESIS TESTING
bell-shaped
Graphical Method
Wilcoxon signed-rank
test
Nonparametric test
Chi-square distribution
sample variance (s^2)
Q-Q Plot
POINT ESTIMATOR
Normal distribution
POPULATION VARIANCE
Parametric
Test
HYPOTHESIS TESTING
mean
ESTIMATION AND TEST
OF HYPOTHESIS ON ONE
POPULATION
POINT ESTIMATOR
standard deviation
Inference on Single
Population
Module 4
SAMPLING
DISTRIBUTION
plotted points lie close
tto a straight line
capable of detecting
normality even for a
small sample size (3 2000)
Shapiro-Wilk
normality test
Statistical Method
sample proportion (p̂ )
Other: Chi-square test
for normality,
Kolmogorov-Smirnov
Test, and Jarque-Bera
test or SkewnessKurtosis test
compare the sizes of
boxes
Assumptions
standard error
Graphical Method
n(p) and n(1-p) are both
at least five
spread of the whiskers
(range)
Boxplot
approximation to
normal distribution
binomial exact interval
Q1, median, Q3, range,
outliers
POPULATION
PROPORTION
for any sample size
Variances of the
population are equal
PARAMETRIC
STATISTICAL TESTS
CONFIDENCE INTERVAL
ESTIMATOR
z-interval
use if the number of
success(x) and the
number of failures (n-x)
are both at least 5
"continuity correction"
in R-commander
Mean
Module 3
binomial exact test
test
two population
Assumptions
Median
NON PARAMETRIC
STATISTICAL TESTS
SEVERAL PROPORTION
Tests
free-system for
statistical analyses and
graphics
Introduction to
R-Software
(language)
simple and intuitive
operating system:
Windows, Linux, MASOS
R-Graphical User
Interface (GUI)
Bartlett's Test
type the commands
very sensitive; should
be all normally
distributed
Levene's Test
Ordinal or Nominal
test
Statistical Method
three population
F-test
HYPOTHESIS TESTING
three population
Test
approximate Z-test
assumptions
F-test
T-test
Assumptions for
Parametric Tests
HYPOTHESIS TESTING
chi-square goodness-offit test
Test
Ratio or interval
for a larger sample size
Wilcoxon Signed-Rank
test
TYPE I ERROR
every kth unit
POPULATION MEAN (µ)
PARAMETRIC
if p-value > α
preferred by researchers (quantitative research)
Sample mean's
SAMPLING
DISTRIBUTION
theorem
fail to reject Ho
TYPES
PROBABILITY
SAMPLING
if p-value </= α
COURSES OF ACTION
less sensitive
obtained haphazardly
The [parameter of
interest] has a sufficient
evidence that [Ha],
when in fact [Ho]
failed to reject a false
Ho
TYPE II ERROR
FORMAT
The [parameter of
interest] has a NO
sufficient evidence that
[Ha], when in fact [Ha]
