DOE - CRD, RBD, LSD

Question 1

Treatment(s)

Answer 1

Various objects of comparison under testing in a comparitive experiement.

eg: - in field experimentation diff fertilizers or diff varieties of cro

Question 2

Experimental Unit

Answer 2

The smallest division of experimental material to which treatments are applied.

Question 3

Block(s)

Answer 3

Sub-group or strata of experimental material that is homogenous within itself and heterogeneous amongst each other.

Question 4

Yield

Answer 4

The measurement of the variable under study on different experimental unit

Question 5

Experimental Error and its reasons

Answer 5

The error caused by external factors that are usually out of experimenters control
- the inherent variability in the experimental material to which treatments are applied
- failure to standardize experimental technique
- lack of representativeness of the sample to population under study

Question 6

precision

Answer 6

the reciprocal of variance of mean
sigma squared is error variance
r/sigma sq

Question 7

efficiency

Answer 7

D1 and D2 with replications r1 and r2 and error variances per unit σ²1 and σ²2 respecitively. ratio of the difference between the two means σ²/r

Question 8

Explain

uniformity trial and contour maps

Answer 8

the fertility of soil does not inc or dec uniformly in any direction but is distrb over the entire field in an erratic manner

by uniformity trial we mean- a trial in which field (exp material) is divided into small units known as plots, and the same treatment is appied on each of the units - and their yields are recorded.

from these yields we can draw a ferility contour map - which gives us a graphic of the variation of the soil fertility - and enables us to form a good idea of the nature of the soil fertility variation.

the fertility contour map is obtained by joining the points of equal ferility through lines.

Accordingly, the field (which is expected to be heterogeneous w.r.t ferility) is divided into relatively homogeneous sub-groups which is known as blocks- to control the experimental error.

uniformity trial gives us some idea about the shape and size of the plots to be used

from the fertility contour map it is generally observed that adjacent plots are more or less alike in fertility than apart. - Thus a homogeneous block can be formed by combining a number of adjacent pairs.

Question 9

Purpose of DOE

Answer 9

• verify the hypothesis in an efficient and economical way
• driving knowledge of cause and effect between factors
• to experiement with all factors at the same time
• to run trials that span the potential experimental region for our factors
• enables us to understand the combined effect of the factors

Question 10

What is DOE?

Answer 10

• branch of applied statistics
• deals with planning, conducting, analysing and interpreting controlled tests to evaluate the factors that control the value of a parameter or a group of parameters.
• a powerful data collection and analysis tool that can be used in a variety of experimental situations

Question 11

3 phases of an experiment

Answer 11

1. Experimental or Planning Phase
2. Design Phase
3. Analysis Phase

Question 12

Experimental or Planning phase

Answer 12

1. Statement of the problem
2. choice of response/study variable
3. deciding the factors to be varied
4. choice of levels of this factors

levels
quantitative/qualitative levels
fixed/random levels

Question 13

Design Phase

Answer 13

1. Setting up the hypothesis
2. Deciding a mathematical model
3. no. of observations to be taken
4. method of randomisation
5. order of experimentation

Question 14

Analysis Phase

Answer 14

1. Data Collection and processing
2. Computation of test statistic
3. Interpretation of the results

Question 15

3 principles of experimental design

Answer 15

1. Replication
2. Randomisation
3. Local Control/ Blocking

Question 16

Why do we have principles of design

Answer 16

To have a better validity of statistical analysis
and
enhance the precision of the experiements
acc to Prof. Ronald. A. Fisher

Question 17

define and give role

Replication

Answer 17

It is the repitition of the treatments under investigation

• It serves to reduce the experimental error
• and it enables us to obtain more precise estimates of the treatment effects
• the most imp purpose is to give an estimate of the experimental error without which we cannot - test the significance of difference b/w any two treatments - or - determine the length of the confidence interval
• randomisation w/o replication is insufficient

Question 18

define and give role

Randomisation

Answer 18

allocation of treatments to experimental units randomly (with equal chance factor

• reduces experimental bias and hence helps in valid estimation of the treatment
• also helps in reducing experiemntal errors
• assure that sources of variation, not controlled in the experiment, operate randomly, so that the avg effect on any group of units is zero

Question 19

define and give role

Local Control (Blocking)

Answer 19

It gives an idea regarding the experimental area

• reduces heterogenity in the field - esxperiments make homo blocks- within and between explain
• by reducing experimental error, it increases the efficiency of the design
• CRD doesnt have blocking in its experimental area so this is not applied there.

Question 20

What is a

Model

Answer 20

A mathematical or statistical model refers to the relationship b/w the input factors(variables) and output responses. In statistics, a model is generally expressed in terms of symbols, usually as a set of equations.
1. Fixed effect Model - each of the factors has fixed effects and only error term is random
2. Mixed or Random Effect Model

Question 21

Hypothesis

Answer 21

an assumption/statement about the population parameters i.e N(μ,σ²)
H0: μ = μ0
H1: μ != μ0

Question 22

Degrees of Freedom

Answer 22

The df corresonding to the no. of independent observations that are available from the data and can be calculated by deducting from the number of values available to the number of constants that are calculated from the data.

For example:
In a sample, if there are n no. of constants grouped into k classes, there have been k-1 df since k-1 fequencies are available, the other has been determined by total size n

Question 23

ANOVA

Answer 23

Acc to Prof. R. A Fisher, ANOVA is the separation of variance ascribable to one group of causes from the variance ascribable to other group.

The ANOVA consists in the estimation of the amount of variation due to each of the independent factors (causes) separately and the comparing these estimates due to assignable factors with the estimate due to chance factor, the latter being known as experimental error.

Question 24

Assumptions of ANOVA

4 in total

Answer 24

1. observations are independent
2. Parent population from which observations are taken is normal
3. Various treatments and env effects are additive in nature
4. Error term (eij) are independent and noramally distributed

Question 25

Comparison of CRD, RBD and LSD

Answer 25

1) analysis 2) experimental material 3) division of exp material 4) **Varying** Quantity of treatments 5) Number of treatments 6) Number of replications 7) random**isation** **of** **treatments** 8) local control 9) treatment of missing value

Question 26

when to use CRD

Answer 26

CRD is appropriate when your experimental units are fairly homogeneous, meaning there's little variation between them. It's often used in laboratory experiments or situations where the experimental material is well-mixed.

Question 27

when to use RBD

Answer 27

RBD is suitable when you have a known source of variation that you want to control for, like a soil fertility gradient. You divide your experimental area into blocks that are homogeneous in terms of that source of variation, and then randomly assign treatments within each block.

Question 28

when to use LSD

Answer 28

LSD is used when you have two known sources of variation that you want to control for, such as rows and columns (or similar factors). It's more efficient than RBD when you have a limited number of treatments and want to control for variation in both row and column directions.

Question 29

# What is a missing plot (observation)

Answer 29

In general in any experiment, we record the data for all the observations in each and every plots. And then we calculate totals and means of the treatments. However, sometimes we do not get data maybe from one or two plots (experimental units) due to some reasons, like no germination of seed, feeding plants by domestic animal, etc. As a result, we miss that data for that plot (unit). This situation is known as missing plot experiment.

Question 30

advgs and disadvgs of CRD

Answer 30

Advantages: * Simple and easy to implement. * High flexibility in terms of the number of treatments and replications. * Suitable for homogeneous experimental materials, such as laboratory experiments. Disadvantages: * May not be as efficient as other designs when there's significant variability between experimental units. * Can become less practical for large numbers of treatments.

Question 31

advgs and disadvgs of RBD

Answer 31

Advantages: * More precise than CRD by controlling for variability between blocks. * Suitable for situations where there are significant differences between blocks (e.g., in field experiments). * More flexible than CRD, allowing for adjustments in the number of treatments and blocks. Disadvantages: * May not be as flexible as CRD for very large numbers of treatments. * Requires careful consideration of block homogeneity to ensure reliable results. * Statistical analysis can be more complex than CRD.

Question 32

advgs and disadvgs of LSD

Answer 32

Advantages: * Efficient for controlling variability in two directions (rows and columns). * Suitable for a limited number of treatments (ideally, equal to the number of rows and columns). * Can be more efficient than RBD when dealing with a small number of treatments. Disadvantages: * Less flexible than CRD or RBD, with the number of treatments limited to the number of rows and columns. * Can be more complex to analyze statistically than CRD or RBD. * Not suitable for a large number of treatments.

Question 33

formula for missing value x in RBD

Question 34

formula for missing value x in LSD

Question 35

Bias in RBD

Question 36

Bias in LSD