Utilization and Interpretation of Test Results

1. Utilization & Interpretation of Test Results

2. Interpreting Test Scores

3. Types of Test Score Interpretations

5. Types of Test Scores
•Raw and Percentage Scores
•Percentile Rank
•Standard Scores
Standard
Scores
Z- score
T-score
Stanine

6. Raw and Percen%age
Scores
• Ex:
• Ana scored 24/30
• Philip scored 40/50
Both actually got 80%.
This student got 90%.
This student got 88%.
Criterion-referenced interpretation

7. Percen%ile Rank
• Refers to the percentage
of students (who took
the same test) you
SURPASSED.
The higher the
percentile rank, the
better your
performance.
Ex: In a class with 44
students, your
percentile rank is 80,
how many students
scored LOWER than
your score.
35 students
Norm-referenced interpretation

8. Percen%ile Rank
• Refers to the percentage
of students (who took
the same test) you
SURPASSED.
The higher the
percentile rank, the
better your
performance.
Ex: In a class with 28
students, you are the
third to the highest.
What is your
percentile score?
25/28 students scored
lower than you
Percentile rank: 89

9. Standard Scores
•A derived score which utilizes the normal
curve
Norm-referenced interpretation

10. The Normal Curve

11. Normal vs Skewed Distributions

12. Positively Skewed Distribution
•Skewed to the right
• Concentrated on low scores

13. Negatively Skewed Distribution
• Concentrated on high
scores
•Skewed to the left

14. The Normal Curve
𝒛 =
𝒙 − ഥ
𝒙
𝒔
Z- score
raw score
mean
score
standard deviation
What does a negative standard score mean?

15. Example
•JB got a score of 42 in a 50-
item Math test where the mean
of the class is 36 and the
standard deviation is 3.
•Find JB’s standard score.
𝒛 =
𝒙 − ഥ
𝒙
𝒔
𝒛 =
𝟒𝟐 − 𝟑𝟔
𝟑
𝒛 = 𝟐

16. Example
•KC has a standard score of -1.5
in a 60-item English test where
the mean is 38 and the
standard deviation is 2.
•Find KC’s score in the test.
𝒛 =
𝒙 − ഥ
𝒙
𝒔
−𝟏. 𝟓 =
𝒙 − 𝟑𝟖
𝟐
𝒙 = 𝟑𝟓

17. T-score
Z-score T-score
T= 10z+50
Z-score T-score
Mean 0
Standard dev. 1
50
10
Fif-T

18. Z-scores and T-scores
50 60 70 80
40
30
20

19. Example
•JB got a score of 42 in a 50-
item Math test where the mean
of the class is 36 and the
standard deviation is 3.
•Find JB’s T- score.
𝒛 = 𝟐
𝑻 = 𝟏𝟎𝒛 + 𝟓𝟎
𝑻 = 𝟕𝟎

20. Z-scores and T-scores
70

21. Stanine = Sta9
Z-score Stanine
Stanine =
2z + 5
Z-score stanine
Mean 0
Standard dev. 1
5
2

22. Z-scores and Stanine scores
5 7 9
3
1

23. Example
•JB got a score of 42 in a 50-
item Math test where the mean
of the class is 36 and the
standard deviation is 3.
•Find JB’s stanine score.
𝒛 = 𝟐
𝒔𝒕𝒂𝒏𝒊𝒏𝒆
= 𝟐𝒛 + 𝟓
= 𝟗

24. Z-scores and Stanine scores
5 7 9
3
1

25. Measures of Central Tendency
•Mean ( ҧ
𝑥)=
𝑀+𝐸+𝐴
𝑁
→ the average
•Median (෤
𝑥)= 𝑀, 𝐸,
𝐷+𝐼
2
, 𝐴, 𝑁→ the middle
value
•Mode (ො
𝑥)= Mooooooode → the most
frequent value

26. Example:
•Given the scores of 10 kindergarten pupils:
•12, 15, 15, 15, 16, 17, 18, 18, 20, 20
•Find the mean, median and mode.

27. Measures of Variability
•Range = 𝐻 − 𝐿→ highest – lowest
•Variance (s2)= average square deviations
from the mean
• →
σ(𝑥− ҧ
𝑥)2
𝑛−1
•Standard deviation (s)= the square root of
the variance

28. Example:
Given the
scores of 10
kindergarten
pupils:
12, 15, 15, 15,
16, 17, 18, 18,
20, 20
Find the
standard
deviation.
What is the
standard score
of the pupil
who got 17?

29. The Normal Curve

30. “Score is just a
number before
a teacher
interprets it…”