B.Ed. 104 unit4.4-statistics

1. MAEER’s
MIT SaintDnyaneshwarB.Ed.College,
Alandi(Devachi),Pune.
B.Ed. 104
ASSESSMENT AND EVALUATION FOR
LEARNING
Unit 4- INTERPRETING TEST SCORES
(Statistics): (4.4)
By.
Asst.Prof. Gangotri V. Rokade

2. UNIT4 INTERPRETINGTESTSCORES
(1 CREDIT)
Statistical measures to interpret the test scores (Meaning,
Characteristics, and Uses)
4.1 Measures of Central Tendency : Mean, Median, Mode
4.2 Measures of Variability : Quartile Deviation, Standard
Deviation
4.3 Percentile and Percentile Rank
4.4 Co-efficient of correlation by Spearman’s Rank Difference
method
4.5 Standard Scores: Z and T (Concept Only)
4.6 Graphical representation of data : Histogram, Frequency
polygon
4.7 Normal Probability Curve : Properties, Uses
4.8 Skewness and Kurtosis

3. UNIT 4 INTERPRETING TEST SCORES
4.4 Co-efficient of correlation by Spearman’s Rank Difference
method
Meaning of Correlation:
Correlation means inter relationship between two or more
variables.
Types of Correlation:
1. Positive correlation
2. Perfect positive correlation
3. Zero correlation
4. Negative correlation
5. Perfect or ideal negative correlation

4. Types of Correlation:
1. Positive correlation:
If increase or decrease in one variable also
causes increase or decrease respectively in other
variable, then the two variable are said to be
positively correlated.
e.g. E.g. If a speed of a vehicle is 40 km/hr then it will
cover 40 km distance in one hour and if the speed is
doubled i.e. 80 km/hr then the distance travelled in one
hour will also get doubled i.e. 80 km.
Inc in
first
variable
Inc. In
Second
variable

5. Types of Correlation:
2. Perfect Positive correlation:
If increase or decrease in one variable also
causes increase or decrease respectively in other
variable in the same proportion, then the two
variable are said to be positively correlated.
e.g. E.g. Price of 1kg sugar is Rs. 80/- then price of 2 kg
will be Rs.160/- Thus the price of the sugar increases
( or decreases) in the same proportion as its weight
increases ( or decreases)
Inc in
first
variable
Inc. In
Second
variable
same proportion

6. Types of Correlation:
3. Zero Correlation:
If increase or decrease in one variable has no
bearing on the other variable then there is zero
correlation between the two factors.
e.g. E.g. Weight of a student and his/her achievement,
Height of a person and his intelligence etc
Inc in
first
variable
No
Inc. In
Second
variable

7. Types of Correlation:
4. Negative correlation:
If increase in one variable causes decrease in
other variable, then the two variable are said to
be negatively correlated.
e.g. E.g Price of commodity or items increases then its
demand in the market decreases
Inc in
first
variable
Dec. In
Second
variable

8. Types of Correlation:
5 Perfect Negative correlation:
If increase in one variable causes decrease in
other variable in the same proportion, then the
two variable are said to be negatively correlated.
e.g. E.g. A vehicle moving with a speed of 40km/hr will
take two hrs to reach the destination. If the speed of a
vehicle is 80km/hr then it will take only one hour to
reach the destination.
Inc in
first
variable
Dec. in
Second
variable
same proportion

9. Coefficientof Correlation
• A constant which denotes the extent of correlation that
exists between the two variable, is known as Coefficient
of correlation. It is denoted by ‘r’.
• The limits of Correlation coefficient extend from -1 to +1

10. Interpretationof Coefficientof Correlation
Value of r Correlation
0.00 Zero Correlation
0 to 0.19 Negligible correlation
0.20 to 0.39 Low correlation
0.40-0.59 Medium order
0.60 to 0.79 Good/high correlation
0.80 to 0.89 Very good/high correlation
0.90 to 0.99 Excellent/highest order
1.00 Perfect or ideal correlation

11. Computation of coefficient of correlation
1. Spearman’s rank difference method
2. Pearsons’s product-moment method

12. Spearman’s rank difference method
students Writing skill
Rank (R1)
Reading skill
Rank ( R2)
D= R1-R2 D2
A 2 1 1 1
B 1 3 -2 4
C 6 5 1 1
D 5 6 -1 1
E 3 2 1 1
F 7 4 3 9
G 4 7 -3 9
ƩD2= 26
6ƩD2 (6x 26) 156 156
ꝭ = 1 - ----------- = 1 - ----------- = 1 - ---------- = 1 - -------- = 1 – (0.464) = 0.536
N( N²- 1) 7( 7² -1) 7 (48) 336

13. Spearman’s rank difference method
students score Raw rank Final rank
A 26 1 1
B 25 2 2
C 22 3 (3+4)/2 = 3.5 3.5
D 22 4 3.5
E 18 5 5
F 16 6 (6+7)/2 = 6.5 6.5
G 16 7 6.5
H 14 8 8
I 12 9 9
J 11 10 10

14. Spearman’s rank difference method
students Scores in
English
Scores in
Hindi
Ranks in
English
(R1)
Ranks in
Hindi
(R2)
D=
( R1-R2)
D²
A 30 30 2.5 1 1.5 2.25
B 16 26 10 5 5 25.0
C 18 18 8.5 10 -1.5 2.25
D 30 28 2.5 2.5 0 0
E 32 28 1 2.5 -1.5 2.25
F 28 26 4 5 -1 1.0
G 26 25 5 7.5 -2.5 6.25
H 18 26 8.5 5 3.5 12.25
I 25 22 6 9 -3 9.0
J 24 25 7 7.5 -0.5 0.25
6ƩD2 (6x 60.5 ) 363
r = 1 - ----------- = 1 - --------------- = 1 - ---------- = 1 – 0.367 = 0.633
N( N²- 1) 10( 10² -1) 990

15. students Scores in
Maths
Scores in
Music
Ranks in
Maths
(R1)
Ranks in
Music
(R2)
D=
( R1-R2)
D²
A 45 15
B 40 22
C 48 12
D 40 22
E 35 17
F 34 24
G 38 18
H 38 17
I 25 32
J 20 33
K 33 24
L 22 33
6ƩD2 (6x 530.50 ) 3183
ꝭ = 1 - ----------- = 1 - --------------- = 1 - ---------- = 1 – 1.855 = - 0.855
N( N²- 1) 12( 12² -1) 1716