Overview of Measurement Rasch Model Instrument Construct Findings and Discussion

◦ Summary Statistics Observations◦ Person-Item Map◦ Item Analysis◦ Item Bank

Conclusion

Rasch offers a new paradigm in education longitudinal research.

Rasch is a probabilistic model that offers a better method of measurement construct hence a scale.

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

Rasch read the pattern of an event thus predictive in nature which ability resolves the problem of missing data. Hence, more accurate.

What are the advantages of doing a Rasch analysis?

Results easy to read and clearer to understand A parameter estimate (personal profile) for

each of the individuals from the data. Comparisons between individuals become

independent of the instrument used. Comparisons between the stimuli (items)

become independent of the sample of individuals.

These leads to: Probabilistic models. Separability of parameters. Parameterization in a multiplicative or

additive frame-of-reference. Evaluation of the goodness of fit of the

data to the models.

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.

• 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

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

RASCH MEASUREMENT MODEL IS ABLE TO

MEET ALL THESE R E Q U I R E M E N T S

Q1 Q15 Q16 Q30 Q31 Q50

10111011111111111 11111111111111111111111111111001 =

48

1010010001111111 11111111111111111111111111011111 =

43

10111111111111111 1110111111100100 01101010001101 = 33

10111111111011111 1111111111010100 10110100000011 = 33

10110111111111111 1011111101001110 00010000100001 = 33

10111111111111111 111101100100010 01000000000001 = 27

10111111111111101 110101000100010 00000000001001 = 24

Student.1:

1. But, atypical test result tabulation only rank the students from the highest score in descending order

2. Need to assess beyond raw score. Rasch sorts further according to response pattern in descending order; modified called ‘Rasch-Guttman scale’.

Student.7:

S-03:

S-05:

EASY ITEMS Q3 Q1 Q7 Q5

DIFFICULT ITEMS Q4 Q2

11111011111111111 11111111111111111 111111111110110 = 48

111111111 1111111 11111111111111111 11111001000010 = 43

11111111111111111 1111011011110010 11101010000000 = 33

11111111111111111 0111101111011101 10110100000000 = 33

11010110111101111 1011111101001101 10110110101110 = 33

11111111111111010 0111011101000100 0100 000001000 = 27

11111111111111101 1101110100100100 00000000001000 = 24

SMART

POOR

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

RESPONSESORTED: EASY TO TOUGH

Student.01

S-02

S-03

7 6 4 3 05

S-04

S-05

Theorem 1. Persons who are more able / more developed

have a greater likelihood of correctly answer all the items /

able to complete a given task.

CARELESS

GUESS

PREDICT=1

PREDICT=0

REVERSED

βn= ability

POOR

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

Student.01

S-02

S-03

S-04

S-05

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

Q3 Q1 Q7 Q5δi =ITEM DIFFICULTY

Q2

11111011111111111 11111111111111111 111111111110110 = 48

111111111 1111111 11111111111111111 11111001000010 = 43

11111111111111111 1111011011110010 11101010000000 = 33

11111111111111111 0111101111011101 10110100000000 = 33

11010110111101111 1011111101001101 10110110101110 = 33

11111111111111010 0111011101000100 0100 000001000 = 27

11111111111111101 1101110100100100 00000000001000 = 24

e (βn – δi )

P(Ɵ) = 1 + e (βn – δi )

where;e= Euler’s Number, 2.7183

βn= Person’s ability measure

δi= item difficulty measure

azrilah@gmail.com +60 12320 2821

azrilah@gmail.com +60 12320 2821

01:27 AM 13

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

e.g. On a graduation day, what is the likelihood of a lady liking to a piece of rose as your giving ? Perhaps 30:70Compare 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; a likelihood 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 unit termed ‘logit’.

• INSTRUMENT RELIABILITY• RESPONSE VALIDITY• CALIBRATION• QUALITY CONTROL• QUANTITATIVE

S.D, Cronbach-α, µ, z-Test, PCA• PREDICTIVE MODEL

0.99; ‘Very Good’ instrument reliability in item measuring student learning ability

Valid Responses:99.9%

-ve Person meanμ = -0.03 logitP[Ɵ] LOi= 0.4921

0.66 ‘Poor’ Person separation of 2 groups. 0.31 ‘Poor’ reliability

Cronbach-α :0.33 Poor reliability assessment of student learning

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

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

VERY DIFFICULT= +1.82logitN=243, score=329ave.=1.35, many cannot do

VERY DIFFICULT= +1.82logitN=243, score=329ave.=1.35, many cannot do

EXTREMELY EASY=-7.42logitN=243, score=1215ave.=5, all correct

EXTREMELY EASY=-7.42logitN=243, score=1215ave.=5, all correct

ITEM SD=2.5PERSON SD=0.48ITEM OFF TARGET

ITEM SD=2.5PERSON SD=0.48ITEM OFF TARGET

BOTH y,z BREACHED ITEM NEED REVIEW

BOTH y,z BREACHED ITEM NEED REVIEW

-2 < Z < +2-2 < Z < +20.5 < y < 1.50.5 < y < 1.5 Large +Z due to inconsistency in response. e.g.Poor Person can answer difficult questions

Large +Z due to inconsistency in response. e.g.Poor Person can answer difficult questions

0.32 < x< 0.80.32 < x< 0.8

LOW PT. MEASURE CORELATION . SOME POOR STUDENTS CAN ANSWER ITEMS CORRECTLY WHILST GOOD STUDENTS GOT WRONG

LOW PT. MEASURE CORELATION . SOME POOR STUDENTS CAN ANSWER ITEMS CORRECTLY WHILST GOOD STUDENTS GOT WRONG

Most misfit item:Exceed MNSQ Limit: 0.5 < y < 1.5

Most misfit item:Exceed MNSQ Limit: 0.5 < y < 1.5

High Rating Response Zone 5 – 3. Item in red circles for the respective Persons were under rated

High Rating Response Zone 5 – 3. Item in red circles for the respective Persons were under rated

Low Rating Response Zone 3 – 1. Item in blue circles for the respective Persons were over rated

Low Rating Response Zone 3 – 1. Item in blue circles for the respective Persons were over rated

High Rating Response Zone 5 – 3. Item in red circles for the respective Persons were under rated

High Rating Response Zone 5 – 3. Item in red circles for the respective Persons were under rated

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

3. Validation of instrument construct ◦ Better reflect measure of ability◦ Precision and Accuracy of measurement.

Rasch probalistic model offers an better method to verify the validity of a measurement construct hence precision.

Rasch predictive ability resolves the problem on the need of students taking all the tests; Rasch estimate the likely responses based on anchored items.

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

Rasch offers a new paradigm in engineering education longitudinal research; clearer to read, easy to understand.

saidfudin@gmail.com +60 12240 2821