2. • used in determining the significant
differences among the means of more
than two groups
• variation both between and within
each of the group is analyzed to
establish the F value
One-way Analysis of
Variance
(One-Way ANOVA)
3. Example:
A study was conducted to determine
the effect of different stocking
densities on the gel strength of
agar gel produced by Gracilariopsis
bailinae. They used three different
stocking densities: 500, 1000, 2000
g/m². They extracted agar gel and
measured the gel strength in g/cm².
4. The One-Way ANOVA is useful in
this case for the following
reasons:
1. There were more than two means as
independent variable.
means of the gel strength of three
different stocking densities:
500 g/cm², 1000 g/cm² and 2000 g/cm²
5. The One-Way ANOVA is useful in
this case for the following
reasons:
2. There was only one independent
variable involved
stocking density of
Gracilariopsis bailinae
6. Two-Way Analysis
of Variance
(Two-Way ANOVA)
determine the main and
simultaneous effects of two
independent factors on one
or more dependent variables
7. Example:
A group studied the quality of mangoes
produced at different physiological
status (without flush, 25%-50% flush and
75%-90% flush) at different ages (105
DAFI, 110 DAFI and 120 DAFI). They
determined the quality of mangoes in
terms of weight of the mangoes produced.
DAFI- Days After Flower Introduction
8. The Two-Way ANOVA is
useful for the following
reasons:
1. There were more than two means
as independent variables.
means of weights: three
physiologic status for the first
independent variable and three
ages for the second independent
variable (nine means)
9. The Two-Way ANOVA is
useful for the following
reasons:
2. There were two independent
variable.
physiologic status and ages,
whose effect on the dependent
variables of the study were
simultaneously determined
10. Example:
Taxonomic Classiffication and Determine of
the Iodine Content of Seaweeds Collected
along the Coast of Brgy. Sabang, Sibunag,
Guimaras.
Objectives:
1. To collect, classify and identify seaweeds found
along the coast of Brgy. Sabang, Sibunag,
Guimaras.
2. To measure the iodine connent of selected
seaweeds collected along the coast of Brgy.
Sabang, Sibunag, Guimaras.
3. To compare the iodine content of seaweeds
collected along the coast of Brgy. Sabang,
Sibunag, Guimaras.
11. Table 1. Iodine Content (percent) of Seaweeds
Collected in the Coastal Area of Barangay Sabang,
Sibunag, Guimaras.
Gracilaria edulis 1.102 0.876 1.124
Gracilaria salicornia 0.737 0.859 1.056
Gracilaria acerosa 0.769 0.736 0.920
Gracilaria eucheumoides 1.149 0.790 0.721
12. ONE-WAY ANALYSIS OF
VARIANCE
1.H0: There is no significant difference
in the iodine content of seaweeds
collected from the coastal areas of
Barangay Sabang, Sibunag, Guimaras.
H1: There is a significant difference in
the iodine content of seaweeds
collected from the coastal areas of
Barangay Sabang, Sibunag, Guimaras.
2. Level of Significance: α=0.05
13. 3. Degrees of Freedom
d.f for numerator = k-1
d.f for denominator = N-k
k= numbers of groups
N= total number of samples in all groups
d.f for numerator = 4 – 1 = 3
d.f for denominator = 12 – 4 = 8
16. 6. Compute and fill-up the ANOVA Table
Source of Sum of Degrees of Mean F
Variation Squares Freedom Square Radio
(Variance)
Between 0.80250 3 0.026750 0.998283
Groups
Within 0.214364 8 0.026796
Groups
Total 0.294614 11
17. 7. Statistical Decision
Since the computed F-value (0.998283) is less
than the critical region (4.07), there is no
sufficient evidence to reject the null hypothesis.
4.07
0.998283
18. 8. Conclusion
There is no significant difference in the
iodine content of seaweeds collected from
the coastal areas of Barangay Sabang,
Sibunag, Guimaras.
Interpretation
The iodine content is the same or equal
for the four Gracilaria species.
20. The ANOVA Table
Source of Sum of Degrees of Mean F Ratio
Variation Squares Freedom Square
(Variance)
Between SSBET d.f BET MSBET MSBET
Groups
Within SSW d.fW MSW
Groups
Total SST N-1
MDW
22. The ANOVA Table
Source of Sum of Degrees of Mean F Ratio
Variation Squares Freedom Square
(Variance)
Between SSBET d.f BET MSBET MSBET
Groups
Within SSW d.fW MSW
Groups
Total 0.294614 N-1
25. The ANOVA Table
Source of Sum of Degrees of Mean F Ratio
Variation Squares Freedom Square
(Variance)
Between 0.080250 d.f BET MSBET MSBET
Groups
Within SSW d.fW MSW
Groups
Total 0.294614 N-1
MSW
29. The ANOVA Table
Source of Sum of Degrees of Mean F Ratio
Variation Squares Freedom Square
(Variance)
Between 0.080250 d.f BET MSBET MSBET
Groups
Within 0.214364 d.fW MSW
Groups
Total 0.294614 N-1
MSW
31. The ANOVA Table
Source of Sum of Degrees of Mean F Ratio
Variation Squares Freedom Square
(Variance)
Between 0.080250 3 MSBET MSBET
Groups
Within 0.214364 8 MSW
Groups
Total 0.294614 11
MSW
32. e. Mean of Squares (MSBET and MSW)
SSBET
d.f.BET
SSw
d.f.W
MSBET= MSW=
= 0.080250
3
= 0.026750
= 0.214364
8
= 0.026796
33. The ANOVA Table
Source of Sum of Degrees of Mean F Ratio
Variation Squares Freedom Square
(Variance)
Between 0.080250 3 0.26750 MSBET
Groups
Within 0.214364 8 0.026796
Groups
Total 0.294614 11
MSW
35. The ANOVA Table
Source of Sum of Degrees of Mean F Ratio
Variation Squares Freedom Square
(Variance)
Between 0.080250 3 0.26750 0.998283
Groups
Within 0.214364 8 0.026796
Groups
Total 0.294614 11
6. Compute and fill-up the ANOVA Table
36. References:
Amparado, K.M., Pestaño, R., Suelo, J.K.. 2006.
Taxonomic Classification and Determination of the
Iodine Content of Seaweeds Collected along the Coast of
Brgy. Sabang, Sibunag, Guimaras. Unpublished Research
Paper. Philippines Science High School Western Visayas.
Brase, C.H., Brase, C.P,. 1995. Understandable
Statistics Concepts and Methods, D.c., Health and
Company. Lexington, Massachussettes.
Cadomigara, M., 2002. Fundamentals of Research, Methods
and Models Mindset Publishing, Inc. Iloilo City
Milton J.S., McTeer, p.m and Corbet, J.J., 1997.
Introduction to Statistics McGraw-Hill Companies, Inc.
United States of America
