Sampling Methods Presentation)

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 )




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Critical Value

Critical Value

( z score )

Fail to reject H0Reject H0




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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


region


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Two-tailed Test

H0: = 100H1: { 100

Means less than or greater than

100

Values that differ significantly from 100


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 posttest 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

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Sampling Methods Presentation)