dr. anuar abd. rahim blok b, tingkat 1, bilik 42 fakulti pertanian jabatan pengurusan tanah...
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Dr. Anuar Abd. Rahim
Blok B, Tingkat 1, Bilik 42
Fakulti Pertanian
Jabatan Pengurusan Tanah
(Department of Land Management)
Email: [email protected]
Tel: 03-89474857
0122678842
PRT 3202
EERIMENTAL DESIGN AND ANALYSIS
SEMESTER 1 2013/14
EVALUATION
Mid-term 20 %
Assignments 40 %
Final Examination 40 %
PRINCIPLES OF EXPERIMENTAL DESIGN
EXPERIMENT
TREATMENT
EXPERIMENTAL UNIT
REPLICATION
RANDOMIZATION
SAMPLE
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 obtainnew 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 -1
Number of female student 54
Colour of a flower purple
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
= sa
2 (variance between samples)
sd2 (variance within samples)
HYPHOTHESIS TESTINGFOR MORE THAN TWO MEANS
F Distribution
TESTING OF HYPOTHESIS
HYPOTHESIS
Null Alternative
Null Hypothesis
Alternative Hypothesis
Statement indicating that a parameter having certain value
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
df
Sum of Squares
(SS)
Mean Square
(MS)F
Between (B)
Within (W)
Total (T)
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
Below are yield (t/ha) for 5 varieties of corn
Test at α = 0.05 whether there a significant difference among the means
State your hypothesis
Choose your probability level
Choose your statistics
Calculation
Result
Conclusion
HYPOTHESIS TESTING
Analisis Varian (ANOVA)
Sumber
variasi dk
Jumlah kuasa dua
(JKD)
Min kuasa dua
(MKD)F
Antara (A)
Dalam (D)
Jumlah (J)
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)
3. Determine Σci2, Q and r
1. Calculate the total
2. Assign the coefficient for the means
selected to see the difference
CONTRAST
4. Calculate MSQ
5. Calculate F
T1 T2 T3 T4 T5ci
2 Q r
CONTRAST
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 plotnumber 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
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
Paper A
Paper B
1 2 3 4 5 6 7 8 9 10
6 8 4 9 4 7 6 5 6 8
4 5 5 8 1 9 2 3 7 2
Sign test – two samples (paired)
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
Reaction time (min) of two types of medicine are as the following:
Wilcoxon-Mann-Whitney Rank Test
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
Honda Proton Nissan Ford Mazda
187 221 193 204 195
1000 respondents were interviewed on their preference on the type of car Data are as the following:
O E (O-E) (O-E)2
187
221
193
204
195
200
200
200
200
200
dk = 5-1
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
Mechine A
Mechine B
Total
40
60
Total 16 84
O E (O-E) (O-E)2
dk = (row - 1) x (column – 1)
Row Total x Column Total
Overall Total=E
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.
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
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
Season
Year
Location
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.
ANALYSIS OF DATA FROM SERIES OF EXPERIMENTS
Season
Year
Location
EXPERIMENT WITH DIFFERENT SIZES OF EXPERIMENTAL UNITS
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
LOCATION
Test of variance homogeneity
1. Test for two variances
2. Test for more than two variances
TWO VARIANCES
F =higher variancelower variance
Test = 0.05 for the homogeinety of the following variances
S12 = 11.459848
S22 = 17.696970
S32 = 10.106818
df for each variance = 20
More than two variances
2.3026(f) (k log sp2 - log si
2)
1 + [(k + 1) / 3 kf ]
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
SEASON