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8/6/2019 Sampling Methods Presentation)
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Sampling Methods
and Inferential Statistics
Suparat Walakanon
D5220038
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Presentation Topics
1. Sampling Methods
Population Sample
Sampling Methods
2. Inferential Statistics
Parametric Tests Nonparametric Tests
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What is a population?
A population is the complete collection
of specific types of elements such asscores, people, and other shared
variables to be studied.
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A population must be clearly defined in terms of
the following 3 aspects:
Content research subjects
Extent geographical boundaries
Time the time period under considerationFrankfort-Nachmias and Nachmias (1996)
The first-year SUT undergraduate students enrolled
in English I course in Trimester 1/2010.
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What is sampling?
Sampling is the process of selecting a
small number of elements from a larger
target group of such elements so thatthe data gathered from the small group
will allow judgments or claims to be
made about the populations.
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Sampling Frame
is an actual set of units from whicha sample has been identified,and
should cover all the sampling unitsin the population of interest.
A sampling frame
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Potential Problems of
a Sampling Frame
1. Incomplete frames
- missing names of late enrolled
students
2. Clusters of elements
- samples are located in clusters
(separate groups)
3. Blank foreign elements- inclusion of non-members of the
population in the sample frame
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Sampling Methods
Probability
sampling
Nonprobability
sampling
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Probability Sampling
Simple random sampling
Systematic random sampling
Stratified random sampling
Cluster sampling
Nonprobability Sampling
Convenience sampling Judgment sampling
Quota sampling
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Simple Random Sampling (SRS)
the probability of being selected is equalfor all members of the population
Blind Draw Method (e.g. names placed in a
box and then drawn randomly)
Random Numbers Method (all items in thesampling frame given numbers, numbersthen drawn using table or computer
program)
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Advantages ofSRS
Fair
Unbiased
Disadvantages ofSRS
over- or under-sampling
no guarantee of getting good
representatives
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Systematic random sampling
A sample is obtained be selecting everyK-th e.g. every 15th participant from a list
containing the total population, after a random
start.
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Advantages ofSystematic Random Sampling
Efficiency..do not need to designate (assign anumber to) every population member, justthose early on on the list (unless there is avery large sampling frame).
Less expensivefaster than SRS
Disadvantages ofSystematic Random Sampling
- Small loss in sampling precision
- Potential periodicity problems
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Stratified Sampling
The population is separated into homogeneous
groups/segments/strata and a sample is taken from
each. The results are then combined to get the picture
of the total population.
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Advantages of Stratified Sampling
representativeness of the
composition of the population is
guaranteed.
more complex sampling planrequiring different sample sizes for
each stratum
Disadvantages of Stratified Sampling
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Cluster sampling
method by which the population
is divided into groups (clusters),
any of which can be considered a
representative sample
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Advantages ofCluster Sampling
Economic efficiency faster and less
expensive than SRS
Does not require a list of all members of
the population.
- Cluster specification errorthe morehomogeneous the cluster chosen, the more
imprecise the sample results.
Disadvantages ofCluster Sampling
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Convenience Sampling
A sample is obtained by selecting
individual participants who are easy
to approach.
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Advantages ofConvenience Sampling
convenient
inexpensive
- biased
Disadvantages ofConvenience Sampling
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Purposive Sampling
This method starts with a purpose inthe researchers mind, and thesample is thus selected to includeparticipants of interest and excludethose who do not suit the purpose.
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Advantages ofPurposive Sampling
serves the purpose of the research
is convenient
- subjective- low generalizibility
Disadvantages ofConvenience Sampling
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Quota Sampling
A sample is obtained by identifyingsubgroups to be included, thenestablishing quotas for individuals tobe selected through convenience foreach subgroup.
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Advantage ofQuota Sampling
can ensure that convenience
samples will have desired
proportion of subgroups
- biased
Disadvantage ofQuota Sampling
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INFERENTIAL STATISTICSINFERENTIAL STATISTICS
Hypothesis and Hypothesis Testing
Level of Significance
Directional and Non-directionalHypothesis Testing
Type I and Type II Error
Parametric and NonparametricTests
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Research Hypothesis
A hypothesis is an assumption
about the population parameter.
A parameter is a characteristic of thepopulation, like its mean or variance.
The parameter must be identified
before analysis.
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Hypothesis Testing
Goal: Make statement(s) regardingunknown populationparameter values based on
sample data
Elements of a hypothesis test:
Null hypothesis (H
0) Alternative hypothesis (HA
)
Test statistic
Rejection region(the alpha level)
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Null and Alternative Hypotheses
Null Hypothesis (H0)
- Statement regarding the value(s) of unknownparameter(s).Typically will imply no associationbetween explanatory and response variables in thestudy.
H0:
Alternative Hypothesis(HA
)
- Statement contradictory to the null hypothesis (will
always contain an inequality)
210: QQ !H
210: QQ !H
210: QQ !H
21QQ !
HA : 21 QQ {
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The Alpha Level ()
a probability value that is used to
define the very unlikely sample
outcomes if the null hypothesis is
true
EE
=.05 =.01
the most unlikely 5% (or 1%) of the sample means (the
extreme values) is separated from the most likely 95% (99%)
of the sample means (the central values).
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Critical Region
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Critical Value
Value or values that separate the critical region(where we reject the null hypothesis) from thevalues of the test statistics that do not lead
to a rejection of the null hypothesis
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Critical Value
Critical Value
( z score )
Value or values that separate the critical region(where we reject the null hypothesis) from thevalues of the test statistics that do not lead
to a rejection of the null hypothesis
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Critical Value
Critical Value
( z score )
Fail to reject H0Reject H0
Value or values that separate the critical region(where we reject the null hypothesis) from thevalues of the test statistics that do not lead
to a rejection of the null hypothesis
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Two-tailed,Right-tailed,
Left-tailed Tests
The tails in a distribution are the
extreme regions bounded
by critical values.
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Two-tailed Test
H0: = 100
H1: { 100
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Two-tailed Test
H0: = 100
H1: { 100
E is divided equally betweenthe two tails of the critical
region
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Two-tailed Test
H0: = 100
H1: { 100
Means less than or greater than
E is divided equally betweenthe two tails of the critical
region
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Two-tailed Test
H0: = 100H1: { 100
Means less than or greater than
100
Values that differ significantly from 100
E is divided equally betweenthe two tails of the critical
region
Fail to reject H0Reject H0 Reject H0
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Right-tailed Test
H0: e 100
H1: > 100
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Right-tailed Test
H0: e 100
H1: > 100
Points Right
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Right-tailed Test
H0: e 100
H1: > 100
Values thatdiffer significantly
from 100
100
Points Right
Fail to reject H0 Reject H0
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Left-tailed Test
H0: u 100
H1: < 100
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Left-tailed Test
H0: u 100
H1: < 100
Points Left
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Left-tailed Test
H0: u 100
H1: < 100
100
Values thatdiffer significantly
from 100
Points Left
Fail to reject H0Reject H0
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Conclusions
in Hypothesis Testingalways test the null hypothesis
1. Reject the H0
2. Fail to reject the H0
need to formulate correct wording of
final conclusion
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Type I Error
The mistake of rejecting the null hypothesis
when it is true.
(alpha) is used to represent the probability of a
type I error
Example: Rejecting a claim that the group mean
score equals 96 when the mean really does
equal 96
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Type II Error
the mistake of failing to reject the
null hypothesis when it is false.
(beta) is used to represent the
probability of a type II error
Example: Failing to reject the claimthat the group mean score is 96
when the mean is really different
from 96
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Inferential Statistics
Parametric
Tests
Nonparametric
Tests
normal distribution
ratio or interval scale
random sampling
do not require normality
ordinal or nominal scale
T-test ANOVA Pearsons Chi-square
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t-tests
Compute two sets of mean values
1. one sample t-test2. two independent samples t-test
3. two paired (dependent) samples t-
test
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One group t-test
to examine whether a sample
mean value is different from a
pre-set value
Example:
Is the students TOEFL mean score higher or
lower than 500?
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One group t-test
Formulating a null and research hypothesis
H0: The students TOEFL mean score is about 500.
HA: The students TOEFL mean score is different
from 500.
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Students Individual Scores
500 490 490
530 495 485
440 500 520 450 505 475
460 430 460
485 470 490
465 500 465 510 510 520
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Output Data
Significant at p-value = .011, p < .05
Reject H0
The students TOEFL
mean score is different
from 500
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Dependent-sample t-test
compares the means of individual
participants in one group.
pre-test posttest design
Example:
Is the students individual scores of the pre-test andposttest different?
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Formulating a null and research hypothesis
H0: There is no difference between the mean
scores of the pre-test and posttest.
HA: The students mean scores in the post-
test is higher than those in the pre-test
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Data Output for dependent t-test
Significant at p = .025, p < .05
Reject H0, The students mean scores
in the post- test is higher than those
in the pre-test
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Independent-sample t-test
examines whether the mean values of two
independent groups are significantly different.
A researcher wants to know whether the students of his class
perform better or worse than students in another class in an
English final examination.
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Research Hypothesis
H0 : There is no difference between the mean
scores of the two classes.
HA: The mean scores between two classes are
different
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Not significant
Retain H0
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One-Way ANOVA
The response variable is the variable youre comparing
Thefactorvariable is the categorical variable being used to
define the groups
We will assume ksamples (groups)
The one-wayis because each value is classified in exactlyone way
Examples include comparisons by gender, race, political
party, color, etc.
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One-Way ANOVA
determines whether there is any
significant difference of the mean
values among sample groups
Why not repeated t-tests?
1. One-wayANOVA can handle the comparison for more
than two groups in one time.
2. More tests done, higher risk ofType-I error.
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Research Hypothesis
H0: All the means are equal.
HA: At least two groups have
different mean value.
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ANOVA + Post Hoc tests
ANOVA only tells whether one
pair of mean scores are different
but it does not tell which pair is
different.
Post hoc tests e.g. Sheffe or
Tukeys tests will do this job.
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Non-parametric Test
Pearsons Chi-square
- Goodness-of-fit test
- Test for Independence
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Goodness-of-Fit Test
Compares observed frequencies
within groups to their expected
frequencies.
HO=observed frequencies are
not different from the expected
frequencies.
Research hypothesis: They are
different.
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Test of Independence
Review cross-tabulations (=
contingency tables)
Are the differences in responses of
two groups statistically
significantly different?
One-way = observed vs expected
Two-way = one set of observed
frequencies vs another set.
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Thank you very much