Download Standardized Testing

Standardized Testing
Basic Terminology
• Evaluation: a judgment
• Measurement: a number
• Assessment: procedure to
gather information
Norm- and CriterionReferenced Tests
• Normreferenced
– General ability
– Compares people
to people
– Selecting top
candidates
• Criterionreferenced
–
–
–
–
Mastery
Basic skills
Prerequisites
Grouping for
instruction
What Do Test Scores
Mean?
•
•
•
•
•
Standardized test
Norming sample
Frequency distributions
Central tendency
Variability
Frequency Distribution
Histogram
3
2.5
2
Students 1.5
1
0.5
0
40
45
50
55
60
65
70
75
Scores on Test
80
85
90
95
100
Central Tendency
• Mean
– The arithmetic average
• Median
– The middle score
• Mode
– The most frequently occurring score
Variability
• Range
• Standard deviation
– Indicates how much the scores
vary from the mean
Calculating the Standard
Deviation
•
•
•
•
•
•
•
Calculate the mean: c
Subtract the mean from each score: (c-c)
Square each difference: (c-c)2
Add all the squared differences:S(c-c)2
Divide by the number of scores: S(c-c)2
N
Find the square root :
S(c-c)2
N
Sample Problems
Calculate the mean, median, mode,
range, and standard deviation for
the following sets of scores
• Reading
–
–
–
–
–
–
–
–
–
95
90
85
80
75
70
65
60
55
• Arithmetic
–
–
–
–
–
–
–
–
–
76
78
77
71
75
79
74
72
73
Calculations
• Reading
c
c-c (c-c)2
–
–
–
–
–
–
–
–
–
95
90
85
80
75
70
65
60
55
20
15
10
5
0
-5
-10
-15
-20
400
225
100
25
0
25
100
225
400
S(c-c)2 = 1500
• Arithmetic
c
c-c (c-c)2
–
–
–
–
–
–
–
–
–
76
78
77
71
75
79
72
73
74
+1
+3
+2
-4
0
+4
-3
-2
-1
1
9
4
16
0
16
9
4
1
S(c-c)2 = 60
Calculations continued
Reading
Arithmetic
S(c-c)2
N
S(c-c) 2
N
=166.67
S(c-c)2
=6.67
N
=12.91
S(c-c)2
N
= 2.58
Standard deviations
Completed Calculations
–
–
–
–
–
Reading
Mean = 75
Mode = none
Median = 75
Range = 40
Standard
deviation = 12.91
–
–
–
–
–
Arithmetic
Mean = 75
Mode = none
Median = 75
Range = 8
Standard
deviation = 2.58
Normal Distributions
• The “bell curve”
• Mean, median, mode all at the center
of the curve
• 50% of scores above the mean
• 50% of scores below the mean
Normal Distribution with Standard Deviations
Percent of the
population
34%
2%
34%
14%
-3SD
-2SD
-1SD
2%
14%
0
+1SD
+2SD
+3SD
Standard Deviation Units
Types of Scores
• Percentile rank
• Grade-equivalent
• Standard scores
– z scores
– T scores
– Stanine scores
Interpreting Test Scores
•
•
•
•
•
Reliability
True score
Standard error
Confidence intervals
Validity
Types of Standardized
Tests
• Achievement Tests
– Measure previous learning
• Diagnostic Tests
– Identify strengths and weaknesses
• Aptitude Tests
– Measure abilities
Issues in Testing
• Widespread testing
• Accountability and high
stakes testing