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

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