FRIEDMAN TWO-WAY ANALYSIS
OF VARIANCE (X2r)
PRETEST- Problem
Friedman Two-Way Analysis of Varaince (X2r) Jegie 198
Problem
Table 16 presents the perception of teachers, parents and pupils regarding
interpersonal intelligence of the pupils of a certain school.
Table 16
Perceived Interpersonal Intelligence
Indicators Teachers Parents Pupils
1. Modest in all occasion both public and 4.70 4.83 4.59
Private places.
2. Easily imitate gestures from others 4.75 4.81 4.65
specially from a person they idolized.
3. Give reactions from the novels viewed. 4.77 4.82 4.69
4. Share opinion. 4.65 4.79 4.57
5. Give firm decision. 4.74 4.77 4.50
Solve the problem by getting the following requirements:
1). Specific Problem
2). Null Hypothesis
3). Alternative Hypothesis
4). Statistical Method Used
5). Level of Significance
6). Region of Rejection
7). Computation of the value of H
8). Decision
9). Conclusion
PRETEST- Answers
Friedman Two-Way Analysis of Varaince (X2r) Jegie 199
I - Specific Problem
Is there any significant difference in the respondent’s perceptions regarding interpersonal
intelligence of the pupils in a certain school?
II - Null Hypothesis
There is no significant difference in the respondent’s perceptions regarding interpersonal
intelligence of the pupils in a certain school.
III - Alternative Hypothesis
There is a significant difference in the respondent’s perceptions regarding interpersonal
intelligence of the pupils in a certain school.
IV - Statistical Test:
Use Friedman Two-Way Analysis of Variance
V- Level of Significance:
Assume : = 0.05
VI - Critical Region:
Degrees of freedom (df) = K – 1 where :
= 3 –1 k = number of town houses
= 2 X2 0.05 = 5.991
VII- Calculation
X2 r = 10.00
VIII- Decision
Since the computed value of X2 r = 10.00 is greater than the critical value at
0.05 which is equal to x2 0.05 = 5.991, therefore accept the alternative hypothesis.
IX – Conclusion
There is a significant difference in the respondent’s perceptions regarding interpersonal
intelligence of the pupils in a certain school.
FRIEDMAN TWO WAY ANALYSIS OF
VARIANCE
Jegie 200
FRIEDMAN TWO WAY ANALYSIS OF VARIANCE
Definition
It is used to determine the significant difference in the mean rank
levels of 2 or more variables for a descriptive design.
Formula:
X2r = 12 R2i - 3 N (k + 1)
N k ( k + 1)
Where:
X2r = Friedman Two Way Analysis of Variance
N = number of rows
k = number of columns
Ri = ranks in the ith column
12 = constant
Steps
1. Rank the mean responses of the subjects where the
lowest mean value ranks 1.
2. Total the ranks of each variables to get R .
3. Compute the value of X2r by using the formula.
4. Compute the degrees of freedom (df) by using the
formula, df = k – 1.
5. Choose the level of probability, either 0.01 or 0.05 and
refer to the chi-square table to determine if the
obtained computed value of X2r is significant or not. If
the obtained value is equal to or greater than the
tabular value in the table, it is significant; if the
computed value is less than the tabular value in the
table, it is insignificant.
FRIEDMAN TWO WAY ANALYSIS OF
VARIANCE
Jegie 201
Problem
Table 17
Mean Rank Level’s Differences of Responses on the
Adequacy of Instructional Materials as Perceived by Qualified
and Nonqualified Science and Mathematics Mentors in Different SUC Levels in a Certain Region
Levels of SUC Qualified Mentors (X1) Nonqualified Mentors (X2)
1 3.6 3.8
2 3.4 3.4
3 2.8 3.0
4 2.7 2.9
Solution
I Specific Question
Is there a significant difference in the mean rank levels of the adequacy of instructional
materials as perceived by the qualified and nonqualified science and mathematics
instructors and professors in SUCs in a certain region?
II Null Hypothesis
There is no significant difference in the mean rank levels of the adequacy of instructional
materials as perceived by the qualified and nonqualified science and mathematics
instructors and professors in SUCs in a certain region.
III Alternative Hypothesis
There is a significant difference in the mean rank levels of the adequacy of instructional
materials as perceived by the qualified and nonqualified science and mathematics
instructors and professors in SUCs in a certain region.
IV Level of Significance
Use = 0.05
FRIEDMAN TWO WAY ANALYSIS OF
VARIANCE
Jegie 202
V Statistical Method Used
Friedman Two Way Analysis of Variance
VI Rejection Region
Df = k – 1 = 2–1 = 1 ( where k is the number of column)
X2 0.05 = 3.841,
VII Computation
Levels of SUC Qualified Mentors Nonqualified Mentors
X1 R1 X2 R2
1 3.6 1.0 3.8 2.0
2 3.4 1.5 3.4 1.5
3 2.8 1.0 3.0 2.0
4 2.7 1.0 2.9 2.0
Total R1 = 4.5 R2 = 7.5
1. Rank the observed value in rows taking the lowest value
as rank 1.
For Row 1 = 3.6 as Rank 1 and 3.8 as Rank 2
For Row 2 = 3.4 as Rank 1.5 and 3.4 as Rank 1.5
For Row 3 = 2.8 as Rank 1 and 3.0 as Rank 2 etc.
2. Get the sum of the ranks per column as R1 = 4.5
and R2 = 7.5.
3. Substitute the computed values to the formula.
12
X2r = R2 i - 3 N (k + 1)
N k ( k + 1)
X2r = 12 R21 + R22 - 3 N (k + 1)
N k ( k + 1)
FRIEDMAN TWO WAY ANALYSIS OF
VARIANCE
Jegie 203
Where N = number of rows = 4
k = number of columns = 2
R1 = 4.5
R2 = 7.5
X2r = 12 (4.5)2 + (7.5)2 - (3) (4) (2 + 1)
(4) (2) ( 2+1)
X2r = 12 (4.5) (4.5) + (7.5)(7.5) - (3) (4) (2 + 1)
8(3)
X2r = 12 20.25 + 56.25 - (12) ( 3 )
24
X2r = 12 76.50 - (12) ( 3 )
24
X2r = 918 - (12) ( 3 )
24
X2 r = 38.25 - 36.00
X2 r = 2.25
VIII Decision
Since the computed value of X2r = 2.25 is less than the tabular value at 5 percent
level of significance X2 0.05 = 3.841, therefore accept the null hypothesis.
IX Conclusion
There is no significant difference in the mean rank levels of the adequacy of instructional
materials as perceived by the qualified and nonqualified science and mathematics
instructors and professors in SUCs in a certain region.
POST TEST- Problem
Friedman Two-Way Analysis of Variance ( X2 r ) Jegie 204
Problem
Table 18 shows the teachers, parents, and pupils perception on visual-spatial
intelligence of the pupils of a certain school.
Table 18
Perceived Visual-Spatial Intelligence
Indicator Teachers Parents Pupils
1. Learn to use appropriate dress 4.62 4.73 4.54
for an occasion.
2. Appreciate the use of accessories 4.63 4.72 4.64
like jewelry.
3. Produce decorative objects using 4.48 4.66 4.58
recycled materials.
4. Make use of color combination in 4.66 4.58 4.61
any art works
5. Appreciate paintings made by 4.67 4.66 4.57
Filipino painters.
Solve the problem by getting the following requirements:
1). Specific Problem
2). Null Hypothesis
3). Alternative Hypothesis
4). Statistical Method Used
5). Level of Significance
6). Region of Rejection
7). Computation of the value of H
8). Decision
9). Conclusion
POST TEST- Problem
Friedman Two-Way Analysis of Variance ( X2 r ) Jegie 205
I - Specific Problem
Is there any significant difference in the respondent’s perceptions regarding visual-spatial
intelligence of the pupils in a certain school?
II - Null Hypothesis
There is no significant difference in the respondent’s perceptions regarding visual-spatial
intelligence of the pupils in a certain school.
III - Alternative Hypothesis
There is a significant difference in the respondent’s perceptions regarding visual-spatial
intelligence of the pupils in a certain school.
IV - Statistical Test:
Use Friedman Two-Way Analysis of Variance
V- Level of Significance:
Assume : = 0.05
VI - Critical Region:
Degrees of freedom (df) = K – 1 where :
= 3 –1 k = number of town houses
= 2 X2 0.05 = 5.991
VII- Calculation
X2 r = 1.60
VIII- Decision
Since the computed value of X2 r = 1.60 is lesser than the critical value at
0.05 which is equal to x2 0.05 = 5.991, therefore accept the null hypothesis.
IX – Conclusion
There is no significant difference in the respondent’s perceptions regarding visual-spatial
intelligence of the pupils in a certain school.
