Based on the results of your item analysis, do you think this test is suitable for the purpose for which it was designed? Are there any possible revisions you might recommend?

HUDE 225

Take Home

Directions: You are a psychologist working at a local high-school, and the principal wants to create a pre-assessment of 9th grade students’ algebra ability, in order to identify those in need of remedial instruction.

A team of math teachers constructs the test, and pilots it with one class of students. After these data are collected, the principal asks you to perform an item analysis, in order to provide information about the suitability of the test.

Below is item-response data for 10 participants on 5 selected-response items from the test.  All of these items are dichotomous and each are designed to tap the same ability: algebra.  Additionally, all of the items feature four possible answer choices.

Your task is to compute all relevant CTT and IRT statistics that we have learned in classfor these particular items. You may use all course materials, and any computer programs (e.g., Excel, SPSS, JMP) or a hand calculator to assist you. Round your answers to two decimal places.

Also—you are the only psychologist in this particular school, so please do your own work. This activity is worth a total of 70 points.

Data:

Examinee Items Score
1 2 3 4 5
1 1 1 1 1 1 5
2 1 1 1 0 1 4
3 1 1 1 1 1 5
4 0 0 0 0 0 0
5 1 1 0 1 1 4
6 0 0 0 0 1 1
7 0 1 0 0 0 1
8 1 1 1 1 1 5
9 0 0 1 0 0 1
10 1 0 0 0 0 1
P (5 points)          
Q (5 points)          
Variance (5 points)          
Standard deviation

(5points)

         
D (5 points)            
Point-biserial correlation

(5 points)

           

 

Inter-Item Covariance Matrix (5 points: .5 point per covariance)
 Item Number 1 2 3 4 5
1          
2          
3          
4          
5          

 

Inter-Item Correlation Matrix (5points: .5 point per correlation)
Item Number 1 2 3 4 5
1 1        
2   1      
3     1    
4       1
5         1

 

 

 

Test Statistics (6 points)

Average Score  
Composite Variance  
Composite SD  
Cronbach’s Alpha  
Standard Error of Measurement  
Standard Error of Estimate  

 

 

 

Item-Characteristic Curves (Paste below, 5 points):

(Note: Because of the small sample-size, your principal is only requiring a 1pl IRT model)


 

Test Information Function (Paste below- 1 point):

 

 

Item difficulty parameters (5 points):

Item b
1  
2  
3  
4  
5  

 


 

Item-Analysis Report: Based on the results of your item analysis, do you think this test is suitable for the purpose for which it was designed? Are there any possible revisions you might recommend? Explain your answer using relevant statistics you calculated above as support.  Remember, students may be placed in remedial algebra based on their score on this test, so your report is important. (13 points).

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