PPart II; Chapter New Four Sampling and Data Analysis Thiniques

7/23/2019 PPart II; Chapter New Four Sampling and Data Analysis Thiniques

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Chapter Four

Sampling Techniques and Data

Collection Tools

By Teshome A.


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Sampling

Sampling is the process of selecting a small number ofelements from a larger defined target group of elements suchthat the information gathered from the small group will allow

judgments to be made about the larger groups.

In other ward it refers to drawing a sample (a subset) from a

population (the full set). The usual goal in sampling is toproduce a representatie sample .

The purpose of sampling is to gather data about the population

in order to ma!e an inference that can be generali"ed to the

population. Sampling error is an# t#pe of bias that is attributable to

mista!es in either drawing a sample or determining thesample si"e.


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The sampling process

POPULATION

SAMPLE

INFERENCE


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$h# sample%

The following are the major reasons for sampling

Time of researcher and those being sure#ed.

Cost to group or agenc# commissioning the sure#.

&on'interference with population. arge sample couldalter the nature of population eg. opinion sure#s.

Do not destro# population eg. crash test onl# a smallsample of automobiles.

Cooperation of respondents * indiiduals firms

administratie agencies.


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Characteristics of sample

A good sample has following qualities or characteristics:

Representativeness: An ideal sample must be such that itrepresents adequately the whole populations. We wouldselect those units which have the same set of qualities andfeatures as are found in the whole data. It should not lack inany characteristic of the population.

Independence: The second feature of a sample isindependence that is interchangeability of units. !very unitshould be available to be included in the sample.

Adequacy: The number of units included in a sampleshould be su"cient to enable derivation of conclusions

applicable to the whole population. A sample having #$% ofthe whole population is generally adequate.

H!"eneity: The units included in sample must bearlikeness with other units otherwise sample will beunscienti&c.


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T#pes of Sampling +ethods

Random

Simple random

sampling

S#stematic randomsampling

Stratified random

sampling Cluster sampling

Non-random

Conenience sampling

,udgment sampling

-uota sampling

Snowball sampling


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andom and nonrandom sampling

andom sampling/ 0er# unit of the population has the same probabilit# of being

included in the sample.

/ 1 chance mechanism is used in the selection process.

/ 0liminates bias in the selection process/ 1lso !nown as probabilit# sampling

&onrandom Sampling

/ 0er# unit of the population does not hae the same probabilit#

of being included in the sample./ 2pen to selection bias

/ &ot appropriate data collection methods for most statistical

methods

/ 1lso !nown as non'random sampling


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andom Sampling

Simple random samplingis a method of probabilit# samplingin which eer# unit has an equal non"ero chance of beingselected.

Systematic random sampling is a method of probabilit#sampling in which the defined target population is ordered andthe sample is selected according to position using a s!ipinteral.

Stratified random sampling is a method of probabilit#sampling in which the population is diided into different

subgroups and samples are selected from each Cluster random sampling: a sample selected in an# non'

random fashion so that the probabilit# that a unit is drawn intothe sample cannot be calculated.


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Steps in simple random sample

There are si3 major steps in selecting a simple randomsample4Define the target population. Identif# an e3isting sampling frame of the target population

or deelop a new one.0aluate the sampling frame for under coerage oerc

oerage multiple coerage and clustering and ma!eadjustments where necessar#.

1ssign a unique number to each element in the frame.

Determine the sample si"e.andoml# select the targeted number of population

elements


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'ont.

Three techniques are t#picall# used in carr#ing out Step 54 thelotter# method a table of random numbers and randoml#generated numbers using a computer program (i.e. randomnumber generator).

In using the lotter# method (also referred to as the 6blind drawmethod7 and the 6hat model7) the numbers representing eachelement in the target population are placed on chips (i.e.cards paper or some other objects). The chips are then placedin a container and thoroughl# mi3ed. &e3t blindl# select chips

from the container until the desired sample si"e has beenobtained.

Disadantages of this method of selecting the sample are thatit is time'consuming and is limited to small populations.


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'ont.

1 table of random numbers ma# also be used. The numbers ina table of random numbers are not arranged in an# particular

pattern.

The# ma# be read in an# manner i.e. hori"ontall# erticall#

diagonall# forward or bac!ward. In using a table of random numbers the researcher should

blindl# select a starting point and then s#stematicall# proceeddown (or up) the columns of numbers in the table.

The number of digits that are used should correspond to thetotal si"e of the target population.

0er# element whose assigned number matches a number theresearcher comes across is selected for the sample.


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'ont.

1s in using the lotter# method using a table of random

numbers is a tedious time'consuming process and is not

recommended for large populations.

Instead statistical software should be used for large

populations. +ost statistical software and spreadsheet

software hae routines for generating random numbers.

0lements of the populations whose assigned numbers match

the numbers generated b# the software are included in the

sample.

2ne ma# select a number from a table of random numbers for

use as the starting number for the process.


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T#pes of simple random sampling

There are two t#pes of simple random sampling4

Sampling with replacement and

Sampling without replacement.

In sampling with replacement after an element has beenselected from the sampling frame it is returned to the frame and

is eligible to be selected again. In sampling without replacement after an element is selected

from the sampling frame it is remoed from the population andis not returned to the sampling frame.

Sampling without replacement tends to be more efficient thansampling with replacement in producing representatie samples.

It does not allow the same population element to enter thesample more than once. Sampling without replacement is morecommon than sampling with replacement.


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Stratified Sampling

Stratified sampling is a probabilit# sampling procedure in

which the target population is first separated into mutuall#

e3clusie homogeneous segments (strata) and then a simple

random sample is selected from each segment (stratum).

The samples selected from the arious strata are then

combined into a single sample. This sampling procedure is

sometimes referred to as 6quota random sampling.


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'ont.

There are eight major steps in selecting astratified random sample4 Define the target population.

Identif# stratification ariable(s) and determine the number of strata to

be used.

Identif# an e3isting sampling frame or deelop a sampling frame that

includes information on the stratification ariable(s) for each element in

the target population.

0aluate the sampling frame for undercoerage oercoerage multiple

coerage and clustering and ma!e adjustments where necessar#.

Diide the sampling frame into strata categories of the stratification

ariable(s) creating a sampling frame for each stratum.


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'ont.

1ssign a unique number to each element.

Determine the sample si"e for each stratum. The numerical distribution

of the sampled elements across the arious strata determines the t#pe of

stratified sampling that is implemented. It ma# be a proportionate

stratified sampling or one of the arious t#pes of disproportionatestratified sampling.

andoml# select the targeted number of elements from each stratum.

1t least one element must be selected from each stratum for

representation in the sample8 and at least two elements must be chosen

from each stratum for the calculation of the margin of error ofestimates computed from the data collected.


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'ont.

There are two major subt#pes of stratified sampling4

9roportionate stratified sampling and disproportionate

stratified sampling .

Disproportionate stratified sampling has arioussubcategories.


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S#stematic Sampling

S#stematic sampling (or interal random sampling) is aprobabilit# sampling procedure in which a random selection is

made of the first element for the sample and then subsequent

elements are selected using a fi3ed or s#stematic interal until

the desired sample si"e is reached.

The random start distinguishes this sampling procedure from

its non probabilit# counterpart non probabilit# s#stematic

sampling (discussed aboe).

In some instances a sampling frame is not used. The target

population need not be numbered and a sampling frame

compiled if there is ph#sical presentation such as a continuous

flow of population elements at specific locations.


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Steps in s#stematic sampling

:enerall# there are eight major steps in selecting a s#stematicsample4 Define the target population.

Determine the desired sample si"e (n).

Identif# an e3isting sampling frame or deelop a sampling frame of thetarget population.

0aluate the sampling frame for undercoerage oercoeragemultiple coerage clustering and periodicit# and ma!e adjustmentswhere necessar#.

Determine the number of elements in the sampling frame (&).

Calculate the sampling interal (i) b# diiding the number of elements

in the sampling frame (&) b# the targeted sample si"e (n). ;. andoml# select a number r from 6 i r >?i r >@i and so forth until the

frame is e3hausted.


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Cluster Sampling%

2ften it is impossible or impractical to create a sampling

frame of a target population andAor the target population is

widel# dispersed geographicall# ma!ing data collection costs

relatiel# high.

Such situations are ideal for cluster sampling. Cluster

sampling is a probabilit# sampling procedure in whichelements of the population are randoml# selected in naturall#

occurring groupings (clusters).

In the conte3t of cluster sampling a 6cluster7 is an aggregate

or intact grouping of population elements. 0lement sampling isthe selection of population elements indiiduall# one at a

time.


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'ont.

2n the other hand cluster sampling inoles the selection of

population elements not indiiduall# but in aggregates.

The sampling units or clusters ma# be space'based such as

naturall# occurring geographical or ph#sical units (e.g. states

counties census tracts bloc!s or buildings)8 organi"ation'

based such as such units as school districts schools grade

leels or classes8 or telephone'based such as area codes or

e3changes of telephone numbers.

For the most part the cluster sample designs described in thischapter are space'based or area'based sampling procedures.


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Steps in cluster sampling

There are si3 major steps in selecting a clustersample4 Define the target population.

Determine the desired sample si"e.

Identif# an e3isting sampling frame or deelop a newsampling frame of clusters of the target population.

0aluate the sampling frame for undercoerageoercoerage multiple coerage and clustering and ma!eadjustments where necessar#.

Determine the number of clusters to be selected. This ma#be done b# diiding the sample si"e b# estimated aeragenumber of population elements in each cluster..

andoml# select the targeted number of clusters.


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&on andom Sampling

&onprobabilit# sampling is a subjectie procedure in whichthe probabilit# of selection for each population is un!nown

beforehand.

The selection of sample units from a population is not done on

a strictl# chance basis as it is in probabilit# sampling. 1n important feature of nonprobabilit# sampling is that it

offers researchers greater freedom and fle3ibilit# in selecting

the indiidual population units than does probabilit# sampling.

The major non'random sample are4 Conenience Sampling

,udgment Sampling


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#.Conenience Sampling In conenience sampling a researcherBs conenience forms the

basis for selecting a sample of units.

This form of sampling has become er# popular in onlineresearch and is !nown as intercept samplingorpop-up surveys.

?. ,udgment Sampling ,udgment sampling (or purposive sampling) is a procedure in

which a researcher e3erts some effort in selecting a sample thathe or she beliees is most appropriate for a stud#.

In practical situations the researcher will or should be!nowledgeable about the nature of the releant or ideal

population for a stud#.


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'ont. 1lthough a judgment sample will require greater researcher

effort it will generall# be more appropriate than aconenience sample.

@. -uota Sampling

-uota sampling inoles sampling a quota of units to be

selected from each population cell based on the judgmentof the researchers andAor decision ma!ers.

It is the most refined form of nonprobabilit# sampling and

is often used in practice especiall# in studies inoling

personal interiewing. -uota sampling resembles stratified random sampling and

possesses certain features of judgment and conenience

sampling as well.


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'ont.

. 1 snowballing sampling * also !nown as chain referral

sampling* is considered a t#pe of purposie sampling. In

this method participants or informants with whom

contact has alread# been made use their social networ!s

to refer the researcher to other people who could

potentiall# participate in or contribute to the stud#.

Snowball sampling is often used to find and recruit

6hidden populations7 that is groups not easil# accessibleto researchers through other sampling strategies.


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Classification of Sampling

MethodsSampling

Methods

Probability

Samples

Simple

RandomCluster

Systematic Stratified

Non-

probability

QuotaJudgment

Convenience Snoball


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Si"e of sample

For proper stud# of the problem it is necessar# to hae proper

sampling. It means that the sample should be of proper si"e. If

the sample is either too small or too big it shall ma!e the

stud# difficult.

$hat should be the si"e of the sample is a question which

should be answered onl# after ta!ing into account the arious

factors of research problem at hand.

1n optimum sample in sure# is one which fulfills the

requirements of efficienc# representatieness reliabilit# andfle3ibilit#.

The sample should be small enough to aoid unnecessar#

e3penses and large enough to aoid intolerable sampling error.


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Factors affecting sample si"e

The following factors should be considered while deciding

the sample si"e4

!he si"e of the universe: The large the si"e of theunierse the bigger should be the sample si"e.

!he resources available4 If the resources aailable are

ast a large sample si"e could be ta!en. oweer inmost cases resources constitute a big constraint onsample si"e.

!he degree of accuracy or precision desired: The

greater the degree of accurac# desired the larger shouldbe the sample si"e. oweer it does not necessaril#mean that bigger samples alwa#s ensure greateraccurac#.


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'ont.i) #omogeneity or heterogeneity of the $niverse4 If the

unierse consists of homogeneous units a small sample ma#sere the purpose but if the unierse consists ofheterogeneous units a large sample ma# be required.

) Nature of study4 For an intensie and continuous stud# asmall sample ma# be suitable. Eut for studies which are not

li!el# to be repeated and are quite e3tensie in nature it ma#be necessar# to ta!e larger sample si"e.

i) Method of sampling adopted4 The si"e of samples is alsoinfluenced b# the t#pe of sampling plan adopted. Fore3ample if the sample is a simple random sample it ma#

necessitate a bigger sample si"e. oweer in a properl#drawn stratified sampling plan een a small sample ma# giebetter results.

ii) Nature of respondents4 $here it is e3pected a largenumber of respondents will not co'operate and send bac! the

questionnaires a larger sample should be selected.


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Sample error

To use sure#s based on samples it is essentials that one

appreciate the concept of sampling and non'sampling errors.

Sampling errors arises out of the fact that inferences for the

entire population is drawn on the basis of few sample

obserations.

2n the other hand non'sampling errors happens due to errors

of computation at the sate of classification and processing of

data.


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S#stematic errors (non'sampling errors)

S#stematic errors result from decisions that bias the sample selection or

response to the sure#. Four common mista!es are made4 9opulation Specification 0rror4 This error is one of not understanding who

#ou should be sure#ing. 1s a simple e3ample imagine #ou are preparing

a sure# about the consumption of brea!fast cereals. $ho do #ou sure#%

It might be the entire famil# the mother or the children. The famil#

consumes cereal the mother purchases and the children influence herchoice.

Sample Frame 0rror4 1 frame error occurs when the wrong sub'

population is specified from which the sample is drawn. 1 classic frame

error occurred in predicting the


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Selection 0rror4 Selection error results when the respondents self select

their participation... those who are interested respond. Selection error

can be controlled b# going e3tra lengths to get participation. T#pical

steps include initiating pre'sure# contact requesting cooperation

actual sure#ing post sure# follow'up if a response is not receied a

second sure# request and finall# interiews using an alternate modessuch as telephone or person to person.

&on'esponse4 &on response errors occur when non'respondents are

different than those who respond. This ma# occur because either the

potential respondent was not contacted (the# did chec! their e'mail) or

the# refused to respond (the# were all grump# old men or beautiful#oung women afraid of strangers). 1gain the e3tent of this non'

response error can be chec!ed through follow'up sure#s using

alternate modes.


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Determining Sample Si"e

The required sample si"e can be found to reach a desired

margin of error (e)with a specified leel of confidence (< '

)

The margin of error is also called sampling error

the amount of imprecision in the estimate of the

population parameter

the amount added and subtracted to the point estimate to

form the confidence interal


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Gsing

n

)X(Z

=

n*ZX

=

(ampling !rrore

e

Zn

2

22

=

To determine the required sample si"e for the mean #ou must !now4


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If unknown ) can be estimated when using

the required sample si*e formula

Gse a alue for that is e3pected to be at least aslarge as the true

Select a pilot sample and estimate with the sample

standard deiation S

03ample4 If J ?K what sample si"e is needed to estimate

the mean within L margin of error with MN confidence%


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03ercise

1 computer software compan# would li!e to estimate how

long it will ta!e a beginner to become proficient at creating a

graph using their new spreadsheet pac!age.

9ast e3perience has indicated that the time required for a

beginner to become proficient with a particular function of

new software products has an appro3imatel# a normal

distribution with a standard deiation of


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Solution

$e are gien4

s J


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Data collection tools

Data are the obsered alues of a ariable of interest.

There are man# methods used to collect or obtain data for

statistical anal#sis.

Gsuall# data collection tools can be categori"ed in terms of

secondar# and primar# data.

The primar# data collections tools are4

Sure#Aquestioner

Interiew Focus group discussion

2bseration


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Concepts of data anal#sis 2ne of the most important steps in the research process is

anal#sis of data. Data anal#sis refers to turning raw data into

useful information. 9urpose is to proide answers to questions

being as!ed at a program site or research questions

Data anal#sis is a s#stematic search for meaning. It is a wa# to

process qualitatie data so that what has been learned can becommunicated to others.

1nal#sis means organi"ing and interrogating data in wa#s that

allow researchers to see patterns identif# themes discoer

relationships deelop e3planations ma!e interpretationsmount critiques or generate theories.

It often inoles s#nthesis ealuation interpretation

categori"ation h#pothesi"ing comparison and pattern finding.


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Quantitative data analysis Qualitative data analysis

maps data numericall# inorder to anal#"e themstatisticall#

allows #ou to statisticall# test

h#potheses

structures and summariseserbal statements and thusdescribes the data

e3plicitl# considers indiidual

cases and specialcharacteristics Smooth transition from dataanal#sis to interpretation

quantitatie data qualitatie data

!able: %ifference beteen &ualitative and &uantitative data analysis


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T#e Ana$ysis Prcess

+aw ,ata,escriptive(tatements Interpretation


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-uantitatie data anal#sis(estimation)

1 form of Inferential Statistics which consists in estimating a

parameter of a population from a correspondingsample

statistic. The two forms49oint estimationInteral estimation

9oint estimate0stimating the alue of a parameter as a single point from the

alue of the statistic03ample4 the sample mean is the best point estimate of

the mean of a populationConfidence InteralIs a range of values that we are confident contains the

population parameter


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9rinciples of :ood 0stimation

1 statistic that is used to estimate a particular parameter is calledan estimator of that parameter.

1 reali"ed alue of the estimator is called an estimate of theparameter.

For an# parameter there are man# possible estimators. :enerall#

an estimator in wide use has achieed popularit# because itsatisfa#s one or more optimalit# criteria i.e. qualities that a goodestimator is supposed to hae. Eelow are the major criteria usedfor a good estimator.

Gnbiasedness

Consistenc#

0fficienc#

Sufficienc#


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#pothesis testing

1 h#pothesis is a claim or statement about some population

characteristic. 1 test of h#pothesis is a statistical method to determine which

of two contradictor# h#potheses is correct.

There are two components of h#pothesis testing

&ull h#pothesis 1lternatie h#pothesis

The null h#pothesis is denoted b# o is a claim asserting nochange or no effect in the state of nature. Gnless data proidesconincing eidence that it is falseHo is accepted.

The alternatie h#pothesis is a statement that contradicts oand is denoted b# a. It is accepted onl# if data proidesconincing eidence of its truth.


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Steps of h#pothesis testing

The following are the major steps in h#pothesis testing

Step


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'on. Step '( State the null hypothesis) #o The null h#pothesis is

usuall# the h#pothesis that the researcher wants to gathereidence against or is the h#pothesis to be tested . The Hocarries the symbol = ; or at certain times bear two s#mbolssuch as R or thus ma!ingHo composite in nature.

Step *: State the +lternative hypothesis) #a. The

alternatie h#pothesis is usuall# the h#pothesis for which theresearcher wants to gather supporting eidence b# wa# ofobseration that could be obtained from his samplinge3periment.

The alternatie h#pothesis is the opposite of the nullh#pothesis. For a two tailed test the s#mbol used in the Hastatement is and for a one tailed test it is either or U . Thealternatie h#pothesis carries only one symbol at all times.


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'on. Step ,: Specify the level of significance) ( The significance

leel denoted b# Q is the probabilit# of committing a T#pe I0rror4 that of rejecting a null h#pothesis which is in realit# true.

Step .: %etermine the critical region and the appropriate teststatistic( The critical region is the rejection area for the nullh#pothesis. The rejection region coers a total area equal to Q .

The appropriate test statistic is the standardi"ed score of thesample statistic whose single critical alue for a one'tailed test ofsignificance or two critical alues for a two'tailed test determinesthe boundar#Aboundaries between the acceptance and rejectionregions forHo.

The test statistic could be Z , t, !, " , etc. depending on theappropriate sampling distribution of the sample statistic to beused. The critical alue of the test statistic can be read from thestatistical tables.


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'on.

Step /: Compute the e&uivalent test statistic of the

observed value of the parameter( The computed alue of the

test statistic can be generated from an appropriate formula as

determined from the gien conditions of the statistical

e3periment. Step 0( Ma1e your decision either R2J2C! Ho or

ACCEP Ho. The null h#pothesis o, will be rejected if the

computed alue of the test statistic in ST09 M falls within the

rejection region or accepted if it falls within the acceptanceregion forHo.


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-

0rrors in h#pothesis tests

,ust because the sample mean (following treatment) isdifferent from the original population mean does notnecessaril# indicate that the treatment has caused a change.

Vou should recall that there usuall# is some discrepanc#

between a sample mean and the population mean simpl# as aresult of sampling error.

Eecause the h#pothesis test relies on sample data and because

sample data are not completel# reliable there is alwa#s the

ris! that misleading data will cause the h#pothesis test to reach

a wrong conclusion.

Two t#pes of error are possible.


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cont.

T#pe I 0rror

2ccurs when the null h#pothesis is rejected when it is in fact true i.e.

K is wrongl# rejected

T#pe I error is often considered to be more serious and thus more

important to aoid than t#pe II error

The h#pothesis test procedure is adjusted so that there is a guaranteedlow probabilit# of t#pe I error (denoted as #$

T#pe II 0rror

2ccurs when the null h#pothesis is not rejected when it is in fact false

Frequentl# due to sample si"es being too small

The probabilit# of a t#pe II error denoted as%, is generally un&nown

Table 4 T#pe 3 and T#pe 33 0rrors


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Table 4 T#pe 3and T#pe 330rrors

True State % Nature

&e decide t

re'ect t#e

nu$$ #ypt#esis

&e %ai$ t

re'ect t#e

nu$$ #ypt#esis

T#e nu$$#ypt#esis is

true

T#e nu$$#ypt#esis is

%a$se

Type I errr

(re'ectin" a true

nu$$ #ypt#esis)

Type II errr

(%ai$in" t re'ect

a %a$se nu$$

#ypt#esis)

Crrect

decisin

Crrect

decisin

*ecisin


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&nished

Documents

PPart II; Chapter New Four Sampling and Data Analysis Thiniques