The document discusses Rasch measurement model and its advantages. It provides an overview of key Rasch concepts like instrument construct, findings and discussion. It then outlines some key benefits of Rasch analysis - it allows for easier interpretation of results, estimation of individual abilities independent of the instrument, and evaluation of how well data fits the measurement model. Rasch is also described as offering a probabilistic approach and separating item and person parameters.

1.  Overview of Measurement
 Rasch Model
 Instrument Construct
 Findings and Discussion
◦ Summary Statistics Observations
◦ Person-Item Map
◦ Item Analysis
◦ Item Bank
 Conclusion

2.  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.

3. 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.

4. 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.

5. 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.

6. R E Q U I R EM E N T O F
MEASUREM ENT
• 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 ?

7. D E F I N I T I O N OF
MEASUREM ENT
RASCH MEASUREMENT
MODEL IS ABLE TO
MEET ALL THESE
REQUIREMENTS

8. 1. But, atypical test result tabulation only rank the students from
the highest score in descending order
Q1 Q15 Q16 Q30 Q31 Q50
111111111111001 =
10111011111111111
Student.1: 11111111111111111
48
111111111011111 =
1010010001111111 11111111111111111
43
10111111111111111
S-03: 1110111111100100 01101010001101 = 33
10111111111011111 1111111111010100 10110100000011 = 33
10110111111111111
S-05: 1011111101001110 00010000100001 = 33
10111111111111111 111101100100010 01000000000001 = 27
Student.7:10111111111111101 110101000100010 00000000001001 = 24
2. Need to assess beyond raw score. Rasch sorts further
according to response pattern in descending order; modified
called ‘Rasch-Guttman scale’.

9. 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.
EASY ITEMS DIFFICULT ITEMS
SMART Q3 Q1 Q7 Q5 Q4 Q2
CARELESS
Student.0111111011111111111 11111111111111111 111111111110110 = 48
111111111 1111111 11111111111111111 11111001000010 = 43
PREDICT=1
S-0311111111111111111 1111011011110010 11101010000000 = 33
S-0411111111111111111 0111101111011101 10110100000000 = 33
S-0511010110111101111 1011111101001101 10110110101110 = 33
REVERSED
11111111111111010 0111011101000100 0100 000001000 = 27
PREDICT=0
POOR S-02 11111111111111101 1101110100100100 00000000001000 = 24
RESPONSE
SORTED:
7 6 5 4 3 GUESS 0
EASY TO Theorem 2. Easier items / task are more likely to be
TOUGH answered correctly by all persons.

10. 1. Persons who are more able / more developed have a
greater likelihood of correctly answer all the items / able
to complete a given task.
δi =ITEM DIFFICULTY
βn= ability Q3 Q1 Q7 Q5 Q2
Student.01 11111011111111111 11111111111111111 111111111110110 = 48
111111111 1111111 11111111111111111 11111001000010 = 43
e (βn – δi )
S-03
11111111111111111 1111011011110010 P(Ɵ 11101010000000 = 33
)=
S-04
11111111111111111 0111101111011101 1 + e (βn – δi )
10110100000000 = 33
S-05 where;
11010110111101111 1011111101001101 10110110101110 = 33
e= Euler’s Number, 2.7183
POOR S-02 11111111111111010 0111011101000100 β Person’s ability measure
n=
0100 000001000 = 27
11111111111111101 1101110100100100 00000000001000 = 24
δi= item difficulty measure
2. Easier items / task are more likely to be answered
correctly by all persons.

11. zrilah@gmail.com

12. zrilah@gmail.com

13. Measurement Overview:
- Q & A Session
: What is an instrument construct ?
06:49 AM 13

14. In Rasch Model, a turn of event is seen as a chance; a
likelihood of happenings hence a ratio data.(Steven, 1946)
e.g. On a graduation day, what is the likelihood of a lady liking
to 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.
1 10 30 50 60 99
99 90 70 50 40 1
10-2 100 102
exp
logit -2 -1 0 1 2
Now, we already have a SCALE with a unit termed ‘logit’.

15. • INSTRUMENT RELIABILITY
• RESPONSE VALIDITY
• CALIBRATION
• QUALITY CONTROL
• QUANTITATIVE
 S.D, Cronbach-α, µ, z-Test, PCA
• PREDICTIVE MODEL

16. -ve Person mean
μ = -0.03 logit
P[Ɵ] LOi= 0.4921
0.66 ‘Poor’ Person
separation of 2 groups.
0.31 ‘Poor’ reliability
Valid Responses:
99.9%
Cronbach-α :0.33 Poor
reliability assessment
of student learning
0.99; ‘Very Good’
instrument reliability
in item measuring
student learning ability

17. 2.Good students; n=104 (42.80%)
1. Poor Students; n=139 (57.20%)

18. VERY DIFFICULT
= +1.82logit
N=243, score=329 0.5 < y < 1.5 -2 < Z < +2 Large +Z due to inconsistency
ave.=1.35, many in response. e.g.Poor Person
cannot do can answer difficult questions
BOTH y,z
BREACHED ITEM
NEED REVIEW
ITEM SD=2.5
EXTREMELY EASY PERSON SD=0.48
=-7.42logit 0.32 < x< 0.8 ITEM OFF TARGET
N=243,
score=1215 LOW PT. MEASURE CORELATION .
ave.=5, all correct SOME POOR STUDENTS CAN
ANSWER ITEMS CORRECTLY WHILST
GOOD STUDENTS GOT WRONG

19. Most misfit item:
Exceed MNSQ
Limit: 0.5 < y < 1.5
High Rating Response Low Rating Response
Zone 5 – 3. Item in red Zone 3 – 1. Item in blue
circles for the respective circles for the respective
Persons were under rated Persons were over rated

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

21. 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.

22.  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.

23. aidfudin@gmail.com
60 12240 2821