Establishmment of Norms chapter 5

8/7/2019 Establishmment of Norms chapter 5

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Establishmment ofEstablishmment of

NormsNorms1.) Giving the test to a representative sample of1.) Giving the test to a representative sample ofindividuals.individuals.2.) Calculating the average score (mean) at2.) Calculating the average score (mean) ateach level.each level.3.) Preparing a table of equivalence that the3.) Preparing a table of equivalence that thetransformation of the raw scores into derived stransformation of the raw scores into derived s


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1.) Giving the test to a representative1.) Giving the test to a representativesample of individuals.sample of individuals.

2.) Calculating the average score (mean)2.) Calculating the average score (mean)at each level.at each level.

3.) Preparing a table of equivalence that3.) Preparing a table of equivalence thatthe transformation of the raw scores intothe transformation of the raw scores intoderived scores can be made morederived scores can be made moreconvenientconvenient


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Interpreting NormsInterpreting Norms

Norms are widely used in manyNorms are widely used in manystandardized achievement testsstandardized achievement tests

prepared.prepared. These tests have to be validated andThese tests have to be validated and

standardized.standardized.


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Age NormsAge Norms

Are based n the average scoresAre based n the average scoresearned by pupils at different ages.earned by pupils at different ages.

They are interpreted in terms of ageThey are interpreted in terms of ageequivalents.equivalents.

Age norms are commonly used inAge norms are commonly used intests in reading indicated as readingtests in reading indicated as readingage), in mental ability ( mental age )age), in mental ability ( mental age )and achievement tests in arithmetic.and achievement tests in arithmetic.


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Characteristics of age normsCharacteristics of age norms

Represent test performance inRepresent test performance inunequal units.unequal units.

Can be used more meaningfully inCan be used more meaningfully inthe elementary level.the elementary level.

Do not represent what the child canDo not represent what the child canactually do.actually do.


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PERCENTILE NORMSPERCENTILE NORMS

Are not the same as percentageAre not the same as percentagescores because percentiles arescores because percentiles are

derived scores which are expressedderived scores which are expressedin terms of the percentage ofin terms of the percentage ofpersons while percentage scores arepersons while percentage scores areexpressed in terms of percentage ofexpressed in terms of percentage of

items.items.


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Percentile norms are more widelyPercentile norms are more widelyused than other norms.used than other norms.

They are easy to compute and canThey are easy to compute and canreadily be understood.readily be understood.


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STANDARD SCORE NORMSSTANDARD SCORE NORMS

Indicate the pupils relative positionIndicate the pupils relative positionby showing how far his raw score isby showing how far his raw score isabove or below average.above or below average.

Express the pupils performance inExpress the pupils performance interms of standard units from theterms of standard units from themean.mean.

Is represented by the normalIs represented by the normalprobability curve or what isprobability curve or what iscommonly called the normal curve.commonly called the normal curve.


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The mathematical CharacteristicsThe mathematical Characteristics

of a NormalCu

rveof a NormalCu

rve It is divided into standard deviationIt is divided into standard deviation

unitsunits

Each portion under the curve has aEach portion under the curve has afixed percentage of cases.fixed percentage of cases.


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Standard deviation permits us toStandard deviation permits us toconvert raw scores into a commonconvert raw scores into a commonscale of equal units ( SD units )scale of equal units ( SD units )which can readily be interpreted inwhich can readily be interpreted interms of a normal curve.terms of a normal curve.


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ZZ--scoresscores

Are linearly derived standard scores.Are linearly derived standard scores.

To compute a z score, find theTo compute a z score, find the

difference between the individualsdifference between the individualsraw score and the mean of theraw score and the mean of thenormative group, and then divide thenormative group, and then divide thedifference by the SD of a normativedifference by the SD of a normative

group.group.


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Example:Example:

Formula: z =Formula: z = XX--MM Z=Z= 4848--6060

SD 5SD 5

Given: M=60 SD = 5 Z=Given: M=60 SD = 5 Z=--2.42.4

Tinas score X1 =Tinas score X1 = 7070--6060

55

X1= +2X1= +2

Ronalds Score : X1 = 48Ronalds Score : X1 = 48


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TT-- ScoresScores

Refer to any set of normallyRefer to any set of normallydistributed standard scores that hasdistributed standard scores that hasa mean of 50 and a standarda mean of 50 and a standarddeviation of 10.deviation of 10.

TT-- scores are obtained by multiplyingscores are obtained by multiplyingzz--scores are obtained by multipying zscores are obtained by multipying z

scores by 10 and adding the productscores by 10 and adding the productto 50.to 50.


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Formula: TFormula: T--score = 50 + 10(z)score = 50 + 10(z)

Applying this formula to the two zApplying this formula to the two z--

scores we computed earlier:scores we computed earlier:

T=50 + 10(2) = 70T=50 + 10(2) = 70

T=50+10 (T=50+10 (--2.2)=282.2)=28


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One very good features of standardOne very good features of standardscores is they have equal units ofscores is they have equal units ofmeasures and their size is the samemeasures and their size is the samefrom distribution to distribution.from distribution to distribution.

Thus comparisons of test resultsThus comparisons of test resultstaken by the same individuals cantaken by the same individuals can

best be done by using standardbest be done by using standardscores.scores.

Establishmment of Norms chapter 5

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