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Overview of MeasurementRasch ModelInstrument ConstructFindings and Discussion Summary Statistics Observations Person-Item Map Item Analysis Item BankConclusion

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Rasch offers a new paradigm in educationlongitudinal research.

Rasch is a probabilistic model that offers a

better method of measurement construct hencea scale.

Rasch gives the maximum likelihood estimate(MLE) of an event outcome.

Rasch read the pattern of an event thuspredictive in nature which ability resolves theproblem of missing data. Hence, more accurate.

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What are the advantages of doing a Raschanalysis?Results easy to read and clearer to understand

A parameter estimate (personal profile) foreach of the individuals from the data.Comparisons between individuals becomeindependent of the instrument used.Comparisons between the stimuli (items)become independent of the sample ofindividuals.

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These leads to :Probabilistic models.Separability of parameters.

Parameterization in a multiplicative oradditive frame-of-reference.Evaluation of the goodness of fit of the datato the models.

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When do you need Rasch analysis?Data in hand is ordinal hence qualitative;

but study requires quantitative analysis.Study call for correlation of items.Sample size dealt with is small.A valid scalar instrument of measurement.

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WHAT IS THE INSTRUMENT USED? WHAT IS THE UNIT OF QUANTITY? WHAT IS THE SCALE CONSTRUCT? IS IT OF LINEAR EQUAL INTERVAL? IS THE MEASURE REPLICABLE? IS IT PREDICTIVE ?

R E Q U I R EM E N T O FM E A S U R E M E N T

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D E F I N I T I O N OFM E A S U R E M E N T

RASCH MEASUREMENTMODEL IS ABLE TOMEET ALL THESE

R E Q U I R E M E N T S

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Q1 Q15 Q16 Q30 Q31 Q50

10111 011111111111 11111111111111111 111111111111001 = 48

1010010001111111 11111111111111111 111111111011111 = 4310111111111111111 1110111111100100 01101010001101 = 33

10111111111011111 1111111111010100 10110100000011 = 33

1011 0111111111111 1 0111111 0100 111 0 000 10000 10000 1 = 33

10111111111111111 111101100100010 01000000000001 = 27

10111111111111101 110101000100010 0000000000 1001 = 24

Student.1:

1. But , atypical test result t abulation only rank the students fromthe highest score in descending order

2. Need to assess beyond raw score. Rasch sorts furtheraccording to response pattern in descending order; modifiedcalled Rasch-Guttman scale.

Student.7:

S-03:

S-05:

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EASY ITEMSQ3 Q1 Q7 Q5

DIFFICULT ITEMSQ4 Q2

11111 011111111111 11111111111111111 111111111110110 = 48111111111 1111111 11111111111111111 11111001000010 = 4311111111111111111 1111011011110010 11101010000000 = 3311111111111111111 0111101111011101 10110100000000 = 3311 01011 01111 01111 1 0111111 0100 11 01 1 011 011 010111 0 = 3311111111111111010 0111011101000100 0100 000001000 = 2711111111111111101 1101110100100100 0000000000 1000 = 24

SMART

POOR

Theorem 2 . Easier items / task are more likely to beanswered correctly by all persons.

RESPONSESORTED:EASY TO

TOUGH

Student.01

S-02

S-03

7 6 4 3 05

S-04S-05

Theorem . Persons who are more able / more developedhave a greater likelihood of correctly answer all the items /

able to complete a given task.

CARELESS

GUESS

PREDICT=1

PREDICT=0

REVERSED

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n= ability

POOR

2. Easier items / task are more likely to be answeredcorrectly by all persons.

Student.01

S-02

S-03S-04S-05

1. Persons who are more able / more developed have agreater likelihood of correctly answer all the items / ableto complete a given task.

Q3 Q1 Q7 Q5 i =ITEM DIFFICULTY

Q2

11111 011111111111 11111111111111111 111111111110110 = 48111111111 1111111 11111111111111111 11111001000010 = 43

11111111111111111 1111011011110010 11101010000000 = 33

11111111111111111 0111101111011101 10110100000000 = 33

11 01011 01111 01111 1 0111111 0100 11 01 1 011 011 010111 0 = 33

11111111111111010 0111011101000100 0100 000001000 = 2711111111111111101 1101110100100100 0000000000 1000 = 24

e ( n i )P( ) =

1 + e ( n i )where;e = Eulers Number, 2.7183 n= Persons ability measure

i= item difficulty measure

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8:21 AM 13

Measurement Overview:- Q & A Session: What is an instrument construct ?

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e.g. On a graduation day, what is the likelihood of a lady l ikingto a piece of rose as your giving ? Perhaps 30:70

Compare if you send a bouquet instead. It increases to 60:40;and so forth if you put a Fererro Roche.. the chances gets better.

In Rasch Model, a turn of event is seen as a chance; alikelihood of happenings hence a ratio data. (Steven, 1946)

1090

10-2

-2

3070

6040

5050

991

199

100

102

0 2-1 1

exp

logit

Now, we already have a SCALE with a uni t termed logit .

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INSTRUMENT RELIABILITY RESPONSE VALIDITY CALIBRATION QUALITY CONTROL QUANTITATIVE

S.D, Cronbach- , , z-Test, PCA PREDICTIVE MODEL

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0.99; Very Goodinstrument reliabilityin item measuringstudent learning ability

Valid Responses :99.9%

-ve Person mean

= -0.03 logitP[ ] LOi= 0.4921

0.66 Poor Personseparation of 2 groups.0.31 Poor reliability

Cronbach- :0.33 Poorreliability assessmentof student learning

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1. Poor Students; n=139 (57.20%)

2.Good students; n=104 (42.80%)

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Most misfit item:Exceed MNSQLimit: 0.5 < y < 1.5

High Rating ResponseZone 5 3. Item in redcircles for the respectivePersons were under rated

Low Rating ResponseZone 3 1. Item in bluecircles for the respectivePersons were over rated

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1 Developed the measurement ruler Transform ordinal into equal interval scale Measure item or tasks difficulty

2 Measurement Standard Meet SI unit standard hence measurement

requirement

3Validation of instrument construct Better reflect measure of ability

Precision and Accuracy of measurement.

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Rasch probalistic model offers an better method toverify the validity of a measurement construct henceprecision.

Rasch predictive ability resolves the problem on the

need of students taking all the tests; Rasch estimatethe likely responses based on anchored items .

Rasch gives the maximum likelihood estimate (MLE)of an event outcome.

Rasch offers a new paradigm in engineering educationlongitudinal research; clearer to read, easy tounderstand.

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