PRT 3202
EERIMENTAL DESIGN AND ANALYSIS
SEMESTER 1 2013/14
Dr. Anuar Abd. Rahim
Blok B, Tingkat 1, Bilik 42
Fakulti Pertanian
Jabatan Pengurusan Tanah
(Department of Land Management)
Email: anuar_ar@upm.edu.my
Tel: 03-89474857
0122678842
EVALUATION
Assignments
40 %
Mid-term
20 %
Final Examination
40 %
PRINCIPLES OF EXPERIMENTAL DESIGN
EXPERIMENT
TREATMENT
EXPERIMENTAL UNIT
SAMPLE
REPLICATION
RANDOMIZATION
VARIABLES
CONTROL
RESPONSES
EXPERIMEMTAL ERROR
TYPES OF EXPERIMENT
SELECTION OF TEST SITE
UNIFORMITY OF EXPERIMENTAL SITE
PROCEDURE OF PLANNING AN EXPERIMENT
TYPES OF MEASUREMENT/DATA
HYPHOTHESIS TESTING
METHODS OF ERROR CONTROL IN EXPERIMENT
PLOT SIZE AND SHAPE
UNIFORMINTY OF EXPERIMENTAL PLOT
EXPERIMENT
Experiment is an investigation to obtain
new information or proving the result of
earlier experiment
TREATMENT
Procedure whose effect a material to be
tested and compared with other treatments
Example: Type of fertilizer
- NPK Blue and NPK Yellow
EXPERIMENTAL UNIT
This is the unit of material that receives a
treatment or where the treatment is given
Example :
- a plant
- an animal
- a square meter plot
REPLICATION
Repetition or appearance of a
treatment more than once in an
experiment
RANDOMIZATION
Arrangement of treatments of experimental
unit so as that each experimental unit has
the same chance to be selected to receive a
treatment
VARIABLES
Characteristics of the experimental unit that
can be measured
VARIABLES
QUANTITATIVE
QUALITATIVE
DISCREET
CONTINUOUS
DATA
Characteristics
Count
Status
Measurement
Digital
Examples:
Variable
Data
Weight
75 kg
Speed of a lorry
35 km hr
Number of female student
54
Colour of a flower
purple
-1
EXPERIMENTAL DESIGNS
Arrangement of
experimental unit that
contains treatments and replications into
various designs to estimate and control
experimental error so as to interpret results
accurately. The major among experimental
designs is the way in which experimental
units
are
classified
or
grouped.
An
experimental design can be simple or
complex. It is, however, advisable to choose a
less complicated design that best provides the
desired precision.
A pot experiment was conducted to
determine the effect of N rate(0,
45, 90, 135 and 180 kg N ha-1) with
four replications on yield of maize
cobs
Examples:
Complete Randomized Design (CRD)
Randomized Complete Block Design (RCBD)
Latin Square Design
Split Plot Design
Complete Randomized Design
It is used when an area or location or
experimental materials are homogeneous.
For completely randomized design (CRD),
each experimental unit has the same
chance of receiving a treatment in
completely randomized manner.
Randomized Complete Block Design
In this design treatments are assigned at
random to a group of experimental units
called the block. A block consists of uniform
experimental units. The main aim of this
design is to keep the variability among
experimental units within a block as small
as possible and to maximize differences
among the blocks.
Latin Square Design
Latin square design handles two known sources
of
variation
among
experimental
units
simultaneously. It treats the sources as two
independent blocking criteria: row-blocking and
column-blocking. This is achieved by making
sure that every treatment occurs only once in
each row-block and once in each column-block.
This helps to remove variability from the
experimental error associated with both these
effects.
ANALYSIS OF VARIANCE (ANOVA)
Analysis of variance (ANOVA) is to determine the
ratio of between samples to the variance of within
samples that is the F distribution. The value of F is
used to reject or accept the null hypothesis. It is
used to analyze the variances of treatments or
events for significant differences between treatment
variances, particularly in situations where more
than two treatments are involved. ANOVA can on
only be used to ascertain if the treatment
differences are significant or not.
F
=
s2, calculated from sample mean
s2, calculate from variance between individual sample
=
sa2 (variance between samples)
sd2 (variance within samples)
HYPHOTHESIS TESTING
FOR MORE THAN TWO MEANS
F Distribution
TESTING OF HYPOTHESIS
HYPOTHESIS
Null
Alternative
Null Hypothesis
Statement indicating that a parameter
having certain value
Alternative Hypothesis
Statement indicating that a
parameter having value that
differ from null hypothesis
Critical area
Probability level
Critical value
Critical area
 area to reject null hypothesis
Probability level
Critical value
Analysis of Variance
(ANOVA)
Source of
Variation
Between (B)
Within (W)
Total (T)
df
Sum of
Squares
Mean
Square
(SS)
(MS)
F
Below are yield (t/ha) for 5 varieties of corn
Variety
V1
3.8
4.6
4.6
4.8
V2
5.2
5.0
6.7
6.1
V3
8.8
6.3
7.4
8.3
V4
10.9
9.4
11.3
12.4
V5
7.3
8.6
7.2
7.8
Test at α = 0.05 whether there a significant
difference among the means
HYPOTHESIS TESTING
State your hypothesis
Choose your probability level
Choose your statistics
Calculation
Result
Conclusion
Analisis Varian (ANOVA)
Sumber
variasi
Antara (A)
Dalam (D)
Jumlah (J)
dk
Jumlah
kuasa dua
Min kuasa
dua
(JKD)
(MKD)
F
ANALYSIS VARIANCE FOR ONE FACTOR
EXPERIMENT ARRANGED IN DIFFERENT
EXPERIMENTAL DESIGNS
CRD
RCBD
LATIN SQUARE
COMPARISON OF MEANS
Comparison of means is conducted when HO is being rejected
during the process of ANOVA. When HO is rejected, there is at
least one significant difference between the treatment means.
There are various methods of to compare for significant
difference between the treatments means. The means of more
than two means are often compared for significant difference
using Least Significant Difference (LSD) test, Duncan New
Multiple Range (DMRT) test, Tukey’s test, Scheffe’s test, Student
–Newman-Keul’s test (SNK), Dunnett’s test and Contrast.
However, more often than not, such tests are misused. One of
the main reasons for this is the lack of clear understanding of
what pair and group comparisons as well as what the structure
of treatments under investigation are. There are two types of
pair comparison namely planned and unplanned pair.
MEANS SEPARATION
LSD
Tukey
CONTRAST
LSD
= tα/2
2 MS (within)
r
TUKEY (HSD)
CONTRAST
1. Calculate the total
2. Assign the coefficient for the means
selected to see the difference
3. Determine Σci2, Q and r
4. Calculate MSQ
5. Calculate F
CONTRAST
T1 T2
T3
T4
T5
ci2
Q
r
MSQ
F
DATA TRANSFORMATION
Data that are not conformed to normal
distribution need to be transformed to
normalize the data. Usually discrete data
are required to be transformed so as
various statistical analyses can be carried
out.
LOG TRANSFORMATION
conducted when the variance or
stanadard deviation increase
proportionally with the mean
Examples
 number of insects per plot
 number of eggs of insect per plant
 number of leaves per plant
If there is zero, convert all the data
to log(x+1)
SQUARE ROOT TRANSFORMATION
 conducted for low value data or occurrence
of unique/weird situation
Examples
•number of plants with disease
•number of weeds per plot
If there is zero, use x + 0.5
 can also be used for percentage data 0 – 30
or 70 - 100
ARC SINE TRANSFORMATION
 conducted for ratio, number and percentages
Criteria 1: If percentages fall between 30-70, no
transformation
Criteria 2: If percentages fall between 0-30 atau
70-100, use square root transformation
Criteria 3: If di not qualifies for criteria 1 and 2
use 1 or 2, use arc sine
When there is 0
(1/4n)
When there is 100
(100 - 1/4n)
NON-PARAMETRIC TEST
 Sign test – one sample
 Sign test – two samples
 Wilcoxon-Mann-Whitney
Percentage octane content in petrol A are as
the following:
97.0, 94.7, 96.8, 99.8, 96.3, 98.6, 95.4,
92.7, 97.7, 97.1, 96.9, 94.4
Test

= 98.0 compare to
 < 98.0 at  = 0.05
Sign test – two samples (paired)
Two types of paper was judged by 10 judges to determine which
which paper is softer based on the scale 1 to10. Higher value
indicate is more soft.
Judge
1 2 3 4 5 6 7 8 9 10
Paper A
6 8 4 9 4 7 6 5 6 8
Paper B
4 5 5 8 1 9 2 3 7 2
Wilcoxon-Mann-Whitney Rank Test
Reaction time (min) of two types of
medicine are as the following:
Medicine P : 1.96, 2.24, 1.71, 2.41, 1.62, 1.93
Medicine Q : 2.11, 2.43, 2.07, 2.71, 2.50, 2.84, 2.88
1. Arrange all data
2. Determine R1
3. Determine U
4. Determine Z
CHI SQUARE
CHI SQUARE
YATE’S CORRECTION
CHI SQUARE
 Test of Goodness-of-fit
 Test of Independance
Test of Goodness-of-fit
1000 respondents were interviewed on
their preference on the type of car
Data are as the following:
Honda
Proton
Nissan
Ford
Mazda
187
221
193
204
195
O
E
187
200
221
200
193
200
204
200
195
200
(O-E)
dk = 5-1
(O-E)2
2
Test of Independance
Test on the statement that defected
materials
obtained
from
two
machines (A and B) is independent
from the machines that generate
them
Defect
Normal
Total
Mechine A
10
30
40
Mechine B
6
54
60
16
84
Total
O
E
(O-E)
(O-E)2
dk = (row - 1) x (column – 1)
2
Row Total x Column Total
E
=
Overall Total
FACTORIAL EXPERIMENT
Factorial experiment is conducted for more
than one factor with the intention to check
not only the effect of each factor but whether
there is interaction or not among the factors.
It is one in which the treatment consists of all
possible combinations of the selected levels
of two or more factors.
TWO FACTORS EXPERIMENT
A factorial experiment (3 x 3) to
evaluate the effect of N rate (0, 90,
dan 180 kg N ha-1) and source of N
[Urea, (NH4)2SO4 dan KNO3] with 4
replications
TWO FACTORS EXPERIMENT
Main effect
Interaction Effect
TWO FACTORS EXPERIMENT
 CRD
 RCBD
 Split plot
TWO FACTORS EXPERIMENT
ANOVA
CRD
RCBD
Split Plot
TWO FACTORS EXPERIMENT
COMPARISON OF MEANS
LSD
Tukey
Contrast
EXPERIMENT WITH DIFFERENT SIZES OF
EXPERIMENTAL UNITS
ANALYSIS OF DATA FROM
SERIES OF EXPERIMENTS
Year
Location
Season
EXPERIMENT WITH DIFFERENT SIZES OF
EXPERIMENTAL UNITS
Split Plot Design
For factorial experiment with two factors where the experimental
materials do not allow for the treatment combinations to be arranged
in the usual manner.
Contains main plot and sub-plot. Sub-plot is arranged within the
main plot
First factor is arranged in the main plot and the second factor is
arranged in the sub- plot
Treatments in the main plot and sub-plot are arranged randomly
Precision: main plot < sub-plot
Error term is separated for main plot and sub-plot.
EXPERIMENT WITH DIFFERENT SIZES OF
EXPERIMENTAL UNITS
EXPERIMENT WITH REPEATED DATA
For perennial crops rubber and oil palm
data can be repeated from the same
experimental unit in different years or
seasons.
REPEATED MEASURES
An experiment was conducted to
determine the effect of N rate (0, 50,
100 dan 150 kg ha-1) on maize yield
using RCBD with 4 replictions
N content (g kg-1) in the leaf tissue
was sampled at 25 days and 40 days
after planting.
EXPERIMENT WITH DIFFERENT SIZES OF
EXPERIMENTAL UNITS
ANALYSIS OF DATA FROM
SERIES OF EXPERIMENTS
Year
Location
Season
LOCATION
An experiment on the effect 7 varieties
on the yield of sweet corn using RCBD
with 3 replications was conducted at 11
locations
Test  = 0.05 whether there is an effect
of location, varieties and interaction on
the yield of sweet corn
Test of variance homogeneity
1. Test for two variances
2. Test for more than two variances
TWO VARIANCES
F =
higher variance
lower variance
More than two variances
Test  = 0.05 for the homogeinety of the
following variances
S12 = 11.459848
S22
= 17.696970
S32
= 10.106818
df for each variance = 20
2 = 2.3026(f) (k log sp2 -  log si2)
1 + [(k + 1) / 3 kf ]
SEASON
An experiment on the effect of rate of N
(0, 30, 60, 90, 120 and 150 kg N ha-1) on
yield of paddy was conducted using
RCBD with 4 replications and 3 seasons
of planting
Test at  = 0.05 whether period, rate of
N and interaction influence the yield of
padi