STAT-C 3213 (EXPERIMENTAL DESIGN)

STAT 323 (EXPERIMENTAL DESIGNS)

Lecture Note

Chapter 1. Elements of Experimentation

Lesson 1. Estimate of Error

1.1 Replication

1.2 Randomization

Lesson 2. Control of Error

2.1 Blocking

2.2 Proper Plot Technique

2.3 Data Analysis

Lesson 3. Proper Interpretation of Results

Elements of Experimentation

Introduction

In early 1950s, a Filipino journalist, disappointed with the chronic shortage of rice in his country, decided to test the yield potential of existing rice cultivars and the opportunity for substantially increasing low yields in farmers’ fields. He planted a single rice seed- from an ordinary farm- on a well-prepared plot and carefully nurtured the developing seedling to maturity. At the harvest, he counted more than 1000 seeds produces by a single plant. The journalist concluded that Filipino farmers who normally used 50 kg of grains to plant a hectare, could harvest 50 tons (0.05 x 1000) from a hectare of land instead of the disappointingly low national average of 1.2 t/ha.

As in the case of the Filipino journalist, agricultural research seeks answers to key questions in agricultural production whose resolution could lead to significant changes and improvements in existing agricultural practices. Unlike the journalist’s experiment, however, scientific research must be designed precisely and rigorously to answer key question.

In agricultural research, the key questions to be answered are generally expressed as a statement of hypothesis that has to be verified or disproved through experimentation.

These hypotheses are usually suggested by past experiences, observations, and, at times, by theoretical considerations.

For example, in the case of the journalist, visits to selected farms may have impressed him as he saw the high yield of some selected rice plants and visualized the potential for duplicating that high yield uniformly on a farm and even over many farms. He therefore hypothesized that rice yields in farmers’ fields were way below their potential and that, with better husbandry, rice yields could be substantially increased.

Theoretical considerations may play a major role in arriving at a hypothesis.

For example, it can be shown theoretically that a rice crop removes more nitrogen from the soil than is naturally replenished during one growing season, one may, therefore hypothesize that in order to maintain a high productivity level on any rice farm, supplementary nitrogen must be added to every crop.

Once the hypothesis is framed, the next step is to design a procedure for its verification. This is the experimental procedure, which usually consists of four phases

• Selecting the appropriate materials to test

• Specifying the characters to measure

• Selecting procedure to measure those characters

• Specifying the procedure to determine whether the measurements made support the hypothesis

In general, the first two phases are fairly easy for a subject matter specialist to specify. In our example of the maize breeder, the test materials would probably be the native and the newly developed varieties. The characters to be measured would probably be disease infection and grain yield. For the example on maintaining productivity of rice farms, the test variety would probably be one of the recommended rice varieties and the fertilizer levels to be tested would cover the suspected range of nitrogen needed. The characters to be measured would include grain yield and other related agronomic characters.

On the other hand, the procedures regarding how the measurements are to be made and how these measurements can be used to prove or disprove a hypothesis depend heavily on techniques developed by statisticians. These two tasks constitute much of what is generally termed the design of an experiment which has three essential components:

1. Estimate Error

2. Control Error

3. Proper interpretation of results

Lesson 1. Estimate of Error

Consider a plant breeder who wishes to compare the yield of a new rice variety A to that of a standard variety B of known and tested properties. He lays out two plots of equal size, side by side, and sows one to variety A and the other to variety B. Grain yield for each plot is then measured and the variety with higher yield is judge as better. Despite simplicity and commonsense appeal of the procedure just outlined, it has one important flaw. It presumes that any difference between the yields of the two plants is caused by the varieties and nothing else. This certainly is not true. Even if the same variety were planted on both plots, the yield would differ. Other factors, such as soil fertility, moisture, and damage by insects, diseases, and birds also affects rice yields.

Because these other factors affect yields, a satisfactory evaluation of the varieties must involve a procedure that can separate varietal difference from other sources of variation. That is, the plant breeder must be able to design an experiment that allows him to decide whether the difference observed is caused by varietal difference or by other factors. The logic behind the decision is simple. Two rice varieties planted in two adjacent plots will be considered different in their yielding ability only if the observed yield difference is larger than the expected if both plots were planted to the same variety. Hence, the researcher needs to know not only the yield difference between plots planted to different varieties, but also the yield difference between plots planted to the same variety.

The difference among experimental plots treated alike is called experimental error. This error is the primary basis for deciding whether and observed difference is real or just due to chance. Clearly, every experiment must design to have a measure of the experimental error.

Estimate of Error: Replication

In the same way that at least two plots of the same variety are needed to determine the difference among plots treated alike, experimental error can be measured only if there are at least two plots planted to the same variety. (or receiving the same treatment). Thus, to obtain a measure of experimental error, replication is needed.

Estimate of Error: Randomization

There is more involved in getting a measure of experimental error than simply planting several plots to the same variety.

For example, suppose, in comparing two rice varieties, the plant breeder plants varieties A and B each in four plots. If the area has unidirectional fertility gradient so that there is gradual reduction of productivity from left to right, variety B would then be handicapped because it is always on the right side of variety A and always in a relatively less fertile area. Thus, the comparison between the yield performances of variety A and B would be biased in favor of A. A part of the yield difference between the two varieties would be due to the difference in the fertility levels and not to the varietal difference.

Systematic arrangement of plots planted to two rice varieties A and B. This scheme does not provide a valid estimate of experimental error

To such bias, varieties must be assigned to experimental plots that a particular variety is not consistently favored or handicapped. This is can be achieved by randomly assigning varieties to the experimental plots. Randomization ensures that each variety will have an equal chance of being assigned to any experimental plot and, consequently, of being grown in any particular environment existing in the experimental site.

Lesson 2. CONTROL OF ERROR

Because the ability to detect existing differences among treatments increases as the size of the experimental error decreases, a good experiment incorporates all possible means of minimizing the experimental error. Three commonly used techniques for controlling experimental error in agricultural research are:

• Blocking

• Proper plot technique

• Data Analysis

CONTROL OF ERROR: Blocking

By putting experimental units are as similar as possible together in the same group (generally referred as block) and by assigning all treatments into each block separately and independently, variation among blocks can be measured and removed from experimental error. In field experiments where substantial variation within an experimental field can be expected, significant reduction in experimental error is usually achieved with the use of proper blocking.

CONTROL OF ERROR: Proper Block Technique

For almost all types of experiment, it is absolutely essential that all other factors aside from those considered as treatments be maintained uniformly for all experimental units. For example, in variety trial where the treatments consist solely of the test varieties, it is required that all other factors such as soil nutrients, solar energy, plant population, pest incidence, and an almost all plots in the experiment. Clearly, the requirement is almost impossible to satisfy. Nevertheless, it is essential that the most important ones be watched closely to ensure that variability among experimental plots is minimized. This is the primary concern of a good plot technique.

For field experiments with crops, the important sources of variability among plots treated alike are soil heterogeneity, competition effects, and mechanical errors.

CONTROL OF ERROR: Data Analysis

In cases where blocking alone may not be able to achieve adequate control of experimental error, proper choice of data analysis can help greatly. Covariance analysis is most commonly used for this purpose. By measuring one or more covariates- the characters whose functional relationships to the character of primary interest are known- the analysis of covariance can reduce the variability among experimental units by adjusting their values to the common value of the covariates.

Example:

In a rice field experiment where rats damaged some of the test plots, covariance analysis with rat damage as the covariate can adjust plot yields to the levels that they should have been with no rat damage in any plot.

Lesson 3. PROPER INTERPRETATION OF RESULTS

An important feature of the design of experiments is its ability to uniformly maintain all environmental factors that are not a part of the treatments being evaluated. This uniformity is both an advantage and a weakness of a controlled experiment. Although maintaining uniformity is vital to the measurement and reduction of experimental error, which are so essential in hypothesis testing, this same feature greatly limits the applicability and generalization of the experimental results, a limitation that must always be considered in the interpretation of results.

Example:

Consider the plant breeder’s experiment comparing varieties A and B, it is obvious that the choice of management practices (such as fertilization and weed control) or of the site and crop season in which the trial is conducted (such as in a rainy or dry environment) will greatly affect the relative performance of the two varieties. In a rice and maize, for example, it is been shown that the newly developed, improved varieties are greatly superior to the native varieties when both are grown in a good environment and with good management; but the improved varieties are no good, or even poorer, when both are grown by the traditional farmer’s practices.