Saturday : 0830

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LECTURE
Saturday 0830 1020 am Location
A 104
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LAB.
Tuesday 1400-1700 Location Makmal
Biometri, Blok D
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EVALUATION
Lab and Quiz 20
Mid Term Exam (17 Oktober) 40
Final Examination 40
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TESTS
Mid Term Exam
Final Exam
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PRINCIPLES OF EXPERIMENTAL DESIGN
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Population
SAMPLE
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Parameter

• Statistic

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Difference

• When describing a population, one may use a
  parameter or a statistic. However, they differ in
  the quality of information. A parameter is a
  numerical value that is equivalent to an entire
  population while a statistic is a numerical value
  that represents a sample of an entire
  population. To distinguish between whether
  something is a parameter or a statistic, you
  might ask yourself if the data you are looking at
  includes the entire population that you are
  examining or some of the people from the entire
  population. For instance, 'What percentage of
  people in your household like sweet potatoes?' is
  a question that can easily be answered by polling
  everyone at home, which would be a parameter.
  But, in order for this question, 'How many people
  in the world like sweet potatoes?' to be answered
  as a parameter requires that you ask every single
  person in the world not likely. This is where a
  representative sample becomes important. And,
  when there is a sample of the population, there
  is a statistic to be found.

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VARIABLES
Characteristics of the experimental unit that can
be measured
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VARIABLES
QUANTITATIVE
QUALITATIVE
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DISCREET
CONTINUOUS
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DATA
Characteristics
Count
Status
Measurement
Digital
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Examples
Variable
Data
Weight
75 kg
Speed of a lorry
35 km hr -1
Number of female student
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purple
Colour of a flower
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STATISTICS

• Central Tendency
• Dispersion

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Distribution of Data

• Normal Curve or
• Bell Curve

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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
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Examples
Complete Randomized Design (CRD)
Randomized Complete Block Design (RCBD)
Latin Square Design
Split Plot Design
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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.  
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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.
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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.
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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.
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  F s2, calculated from sample mean
s2, calculate from variance between
individual sample   sa2 (variance between
samples) sd2 (variance within samples)
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HYPHOTHESIS TESTING FOR MORE THAN TWO MEANS
F Distribution
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TESTING OF HYPOTHESIS
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HYPOTHESIS
Null
Alternative
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Null Hypothesis
Statement indicating that a parameter having
certain value
Alternative Hypothesis
Statement indicating that a parameter having
value that differ from null hypothesis
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Critical area Probability level Critical value
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Critical area

• area to reject null hypothesis

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Probability level

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Critical value
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Analysis of Variance (ANOVA)
Sum of Squares (SS)
Source of Variation
Mean Square (MS)
F
df
Between (B)
Within (W)
Total (T)
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Below are yield (t/ha) for 5 varieties of corn
Variety V1 V2 V3
V4 V5
3.8 5.2
8.8 10.9 7.3
4.6 5.0 6.3
9.4 8.6
4.6 6.7 7.4
11.3 7.2
4.8 6.1 8.3 12.4
7.8
Test at a 0.05 whether there a significant
difference among the means
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HYPOTHESIS TESTING
State your hypothesis
Choose your probability level
Choose your statistics
Calculation
Result
Conclusion
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Analisis Varian (ANOVA)
Jumlah kuasa dua (JKD)
Min kuasa dua (MKD)
Sumber variasi
F
dk
Antara (A)
Dalam (D)
Jumlah (J)
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ANALYSIS VARIANCE FOR ONE FACTOR EXPERIMENT
ARRANGED IN DIFFERENT EXPERIMENTAL DESIGNS
CRD
RCBD
LATIN SQUARE
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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, Tukeys test,
Scheffes test, Student Newman-Keuls test
(SNK), Dunnetts 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.
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MEANS SEPARATION
LSD
Tukey
CONTRAST
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ta/2
LSD
2 MS (within) r
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TUKEY (HSD)
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CONTRAST
1. Calculate the total
2. Assign the coefficient for the means
selected to see the difference
3. Determine Sci2, Q and r
4. Calculate MSQ
5. Calculate F
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CONTRAST
T1 T2 T3 T4 T5
?ci2 Q r
MSQ F
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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.  
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LOG TRANSFORMATION
conducted when the variance or standard
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(x1)
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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

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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)
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NON-PARAMETRIC TEST

• Sign test one sample

• Sign test two samples

• Wilcoxon-Mann-Whitney

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NON-PARAMETRIC TEST

• A non parametric test is a hypothesis that does
  not require specific conditions concerning the
  shape of the populations or the value of any
  populations parameters. Non parametric tests are
  sometime called distribution free statistics
  because they do not require the data fit a normal
  distribution.

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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 lt 98.0 at
0.05
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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.
1 2 3 4 5 6 7 8 9 10
Judge
Paper A
6 8 4 9 4 7 6 5 6 8
Paper B
4 5 5 8 1 9 2 3 7 2
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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
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CHI SQUARE
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CHI SQUARE
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YATES CORRECTION
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CHI SQUARE

• Test of Goodness-of-fit

• Test of Independance

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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
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2
O E (O-E) (O-E)2

200 200 200 200 200
187 221 193 204 195
dk 5-1
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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 10
30 6 54
Total 40 60
Mechine A Mechine B
Total 16 84
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2
O E (O-E) (O-E)2

dk (row - 1) x (column 1)
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Row Total x Column Total
E

Overall Total
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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.
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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
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TWO FACTORS EXPERIMENT
Main effect
Interaction Effect
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TWO FACTORS EXPERIMENT

• CRD

• RCBD

• Split plot

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TWO FACTORS EXPERIMENT
ANOVA
CRD
RCBD
Split Plot
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TWO FACTORS EXPERIMENT
COMPARISON OF MEANS
LSD
Tukey
Contrast
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EXPERIMENT WITH DIFFERENT SIZES OF EXPERIMENTAL
UNITS
ANALYSIS OF DATA FROM SERIES OF EXPERIMENTS
Year
Location
Season
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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 lt sub-plot Error term
is separated for main plot and sub-plot.
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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.
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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.
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EXPERIMENT WITH DIFFERENT SIZES OF EXPERIMENTAL
UNITS
ANALYSIS OF DATA FROM SERIES OF EXPERIMENTS
Year
Location
Season
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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
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Test of variance homogeneity
1. Test for two variances
2. Test for more than two variances
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TWO VARIANCES
higher variance
F

lower variance
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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
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?2 2.3026(f) (k log sp2 - ? log si2)
1 (k 1) / 3 kf
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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