lecture
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LECTURE. Saturday : 0830 – 1020 am Location : A 104. LAB. Tuesday: 1400-1700 Location : Makmal Biometri, Blok D. EVALUATION. Lab and Quiz 20 %. Mid Term Exam (17 Oktober) 40 %. Final Examination 40 %. - PowerPoint PPT PresentationTRANSCRIPT
LECTURE
Saturday : 0830 – 1020 am
Location : A 104
LAB.
Tuesday : 1400-1700
Location : Makmal Biometri, Blok D
EVALUATION
Lab and Quiz 20 %
Mid Term Exam (17 Oktober) 40 %
Final Examination 40 %
TESTS
Mid Term Exam
Final Exam
PRINCIPLES OF EXPERIMENTAL DESIGN
Population
SAMPLE
Parameter
Statistic
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.
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
STATISTICS
Central Tendency
Dispersion
Distribution of Data
Normal Curve or
Bell Curve
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 standard 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
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.
NON-PARAMETRIC TEST
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
We analyzed the data over crop seasons using a fertilizer trial with 5 Nitrogen rates tested on rice for 2 seasons, using RCBD with 3 replications.
ANOVA
Source of Variation d.f SS MS Computed F
Dry season
Replication 2 0.0186 0.0093
Nitrogen 4 14.5333 3.6333 6.43*
Error 8 4.5221 0.5653
Wet season
Replication 2 1.2429 0.6215
Nitrogen 4 13.8698 3.4674 10.91**
Error 8 2.5414 0.3177
TWO VARIANCES
F =higher variancelower variance
Combine ANOVA:
ANOVA
Source of Variation d.f SS MS Computed F
Season(s) (s-1)
Rep. within season s(r-1)
Treatment t-1
S X T (s-1)(t-1)
Error s(r-1)(t-1)
Total srt-1
Reps. Within season SS = (Rep.SS)D + (Rep.SS)W
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