Unit 1-Research methods and science writing.ppt

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Research Methods and
Scientific Writing
Biol 608
Credit hours: 2
Two parts:
1. Research methods
2. Scientific writing

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Reflection, science and research
•The concept of research is closely associated with the processes of
reflection and science.
•We need to know the difference between reflection and science,
before defining research
•Reflection:
–Is a planned, serious thinking about one’s own environment.
–The evolution of organisms is perhaps a result of reflective
thinking by at least a few in a habitat
–Organisms which are capable of reflective thinking possess a
genotype that is different to some degree from the rest of its
kind.
–This genetic difference makes them selected and pass their
genes and subsequent generations become that type.
–That genetic difference can be considered a DISCOVERY
–The discovery can be a changed genotype, a skill or a tool.

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•The ability of a few in a community for reflective thinking, i.e., to think
in an orderly manner has been influential in the cultural evolution of man
–1. Difficult situations can occur and jeopardize the very survival of a
community. These can include, among others:
–Hunger or thirst
–War
–Outbreak of a disease
–Natural calamities like flood, fire, drought, snowstorm, etc.
–2. The difficulty or need may have simple solutions such as feeding,
drinking water, etc. These solutions are habitual or traditional.
–But these solutions may lead to new difficult situations such
as what to feed or drink to keep the community healthier and
fit?
–Should the food or drink be processed before consumption?
–What are the different ways of processing?
–What are the advantages and disadvantages of these ways?
•On the other hand, the difficulty may not have immediate
solution, and it may require serious reflective thinking by a few of
those affected by the problem.

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•The outcome of the reflective thinking can be any one of the fields of
science, including :
•3. Any product of reflective thinking will be put to trial in a community to
be tested, explained, improved and accepted as a tradition or habit.
–Several outcomes of reflective thinking can be processed at once.
One outcome may replace another, or coexist with it.
–Even some products of reflective thinking, which are unexplained or
irrational, may continue to exist if they are useful for some segment of
society.
•e.g. Blind beliefs in religious practices, many of which are
unexplained and irrational, continue to be followed because they
are found to be mentally or physically useful for those who
practice them. Science

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Science
•Science
–Is organized knowledge.
–Involves
•Observation, identification, description, experimental
investigation
•Theoretical explanation of any phenomena that occur in nature
–In other words, science is an organized way of thinking, again for
the well-being and betterment of humanity
–The aim of any good science is to advance the frontiers of human
knowledge, i.e., to add valid information to what is already known
–We need to know one thing:
•What we know in biology or any other field of science is as
little as a fistful and what we do not know is as big as the earth.
Research

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Research
•Research
–Is a method to attain the goal of science, i.e., to:
•Expand the frontiers of knowledge
–It involves the process of organized reflective thinking by the researcher
–Can be done in any field or arts and science, wherever there is a need to
expand the horizon of knowledge
–Almost all industries have their own research and development (R & D)
department to improve the quality and thereby improve sales of their products
–Research in biology has wider implications on human society because;
•It encompasses numerous interrelated fields from agriculture to zoology
•Recently research activities have stressed the need for proper training of
researchers not only on technical aspects but also in ethical aspects
–Biotechnology
–Genetic engineering
–Bioinformatics, etc.

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Basic and applied research
•Based on its objective a research may be classified as basic and applied.
•Basic research is also called pure or fundamental research
–Its objective is the expansion of the existing knowledge
–Driven by a scientific curiosity or interest in a certain scientific question.
–It does not envisage its results to have any social or economic relevance.
No direct commercial value
–A problem for basic research is selected from any source and tackled
with appropriately planned scientific methodology
–Though not applied immediately, it may be applied at a future date
•Examples
–Charles Darwin the theory of evolution
–G. J. Mendel theory of inheritance
–These two theories have become of immense social and
economic importance long after their initial submission

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Questions like:
1. How did the universe begin?
2. How do bacteria reproduce?
3. What is the specific genetic code of fruit flies?
4. Does the earth rotate around the sun or the sun around the
earth?
• All these are basic research and they don’t provide any
immediate benefit to society.
• What is the benefit of knowing how the earth rotates for
today’s economic woes? Nothing.
– Basic research is needed for fundamental insights and new
knowledge. Without this, science cannot progress.
– Basic research lays down the foundation for the applied
science.
–Applied scientific applications are often the result from
discoveries in Basic research.

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•Most research done in universities are pure in nature
•Students in universities need to have an arsenal of basic knowledge
to take up research as their career.
•The trainees need to:
–carry out the research project in a systematic way
–then present their findings in a forum
– and publish them in scientific journal
•On the basis of their performance and on the report of the
independent evaluation of their research thesis or dissertation,
students are awarded a research degree (M. Phil or PhD)

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•Applied research (AR)
–Aim of applied research is practical application of results rather than to
acquire knowledge for knowledge’s sake
–Aspires to improve human condition. Examples:
•Cure of a disease (health)
•Increased food production (food, agriculture)
•Development of biological weapons (defense)
•Improve the energy efficiency of our homes and offices
•Improve modes of transportation, etc.
–These days applied research is receiving more emphasis
• There is a general feeling that the time has come for a shift in
emphasis from purely basic research toward applied science
• This is caused by global overpopulation, global warming, pollution,
overexploitation of the earth’s natural resources.
•The earth’s resources are more limited than we think

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•Applied research (AR) …
A problem for AR is selected from a growing concern and is
analyzed and investigated with well-designed scientific methods
–If the result of such research is applied successfully to the
solution of the problem, it might be patented and exploited
economically
–R & D departments of industries such as pharmaceuticals,
biotechnological industries are involved in applied research, or
they sponsor such researches to be carried out by the universities
and other academic research organizations.
–Some government institutions such as ARARI, Pasteur
Institute, Nutrition Institute, etc. are examples

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•Other types of research:
– Strategic Research – Basic research, but research objects are
chosen in such a way that cooperation with applied researchers
in the same field is fruitful
– Adaptive Research – Adjusting existing technology to
specific environments and circumstances through adaptation
trials and feedback
• These days, most developing countries seek to copy rather than
generate new technologies
• 40 years ago, the Japanese were known to do this
• This time it is the Chinese and others who do this copying
• Other developing countries do the same copying, but the source
countries, which are very much advanced, don’t question them so
much, because they don’t expect them to generate it themselves
• Technology transfer is the word for such a case

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Logic, research, and experiments
•Problems can be solved according two types of reasoning.
■ Deductive reasoning: From general principles to specific
conditions.
■ Inductive reasoning: From specific conditions to general
principles
Examples:
■ Given the general formula for the area of a circle A= r2, what
is the area of a circle whose radius is 6 cm?
■ Given a key describing the beetles in the Amhara region, what
species does a certain beetle belong to?

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•Deductive reasoning:
–Our formal education we receive in school of various
capacities is of deductive type
–Biologists should possess a large store of general
principles and the skills of deductive reasoning to apply
to specific circumstances wherever they are assigned to
work.
–This is traditionally known as the theoretical
background of academicians.
–The more scholarly a person, the more wealth of
knowledge one has and he/she can implement deductive
reasoning satisfactorily

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•Inductive reasoning:
•From the specific to the general
–We are provided with some specific cases and based on these
cases we arrive at some general principles
–Examples:
■ Given the areas and radii of several circles, what general formula
can we give expressing the relationship between the areas and radii
of all circles?
■ Given several specimens of un-described beetles, how would we
describe the species as a whole and express their relation to other
species in a key?
■ Conduct a wheat fertilizer trial in the Amhara region at
representative locations and generalize for the whole region or
develop a regression equation
■Test the newly introduced antimalarial drug artimesinin in
representative communities and declare that it is applicable for the
whole nation

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–Examples continued:
■ Conduct a series of studies on the identity of the causative
agents of the recently occurring diarrhea in Ethiopia, then
come up with a generalization.
■ Which species of trees dominate much of northwestern
Ethiopia? Conduct a case study and conclude about the
dominant species in the area, better sorted into two
(indigenous and exotic)
■What are the causes of pollution in the waters of Lake Tana?
Conduct a series of studies and conclude that the major culprit
is something.

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■ Note that all problems of this type have one thing in
common-they start with a group of observations
• You need to carry out a rigorous study before
generalizing
■ The observations can be either natural phenomena,
like the case of the beetles, or controlled conditions.
■ Under controlled conditions the factors being
studied are made to vary in some systematic
fashion by the application of treatments. Other
factors that might influence the observation are
kept constant. In this case, we have an
experiment.
Experiment

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Experiment
•Question:
– Will the use of a new or different practice affect the
outcome of some particular segment of agricultural
enterprise, and if so, to what extent?
• To answer such a problem, an experiment is
required.
– In the simplest experiment, there may be only two
treatments: the new practice and the old, i.e., two
treatments are tested
– More complex are those experiments in which the
effects of several practices, i.e., treatments, are
studied simultaneously.
Uncertainty

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Uncertainty
■ Finding the area of a circle, no uncertainty in finding the answer.
The answer is definite.
■ But, toss a coin. You are not certain what will happen. Tail or
head? The more often you toss (=large number of observations) the
less uncertainty.
■ Uncertainty is universal in the fields of biology, ecology and
agriculture.
■ No matter how much scientists know about nutrition and
physiology, they cannot predict precisely what will be the gain in
weight of a cow or the yield of a plot of potatoes under given
sets of conditions.
■ Chance variations resulting from a multitude of causes always
make the results vary, no matter how much effort was put into
controlling all relevant factors.
■ Thus chance affects biological events.
Chance itself is driven by internal variations that naturally
exist between individuals who look the same superficially.
2nd session
from here

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Uncertainty …
■ We agree chance events affect our observations
–What should we do about them?
–We need statistics to quantify the uncertainty in our predictions
• Why do we analyze data anyway?
– To quantify uncertainty. Uncertainty=experimental error=within variation.
•Differences of this sort among crop or animal units result from
genetic and environmental differences beyond the control of
the experimenter.
■ They are not errors in the sense of being wrong, but they
represent the variability among experimental units, we call
this the experimental error.
■ Because of this variability, it is difficult to evaluate a
new practice by comparing the results of two treatments:
i.e. new practice (=treatment) versus old practice (=control)

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Uncertainty
■ So an experiment with a single replication provides a very poor
measure of treatment effect, it provides no measure of experimental
error. We should measure the within variation.
■ Experimental error is estimated by applying treatments to at least
two experimental units (two replicates); usually more. Also the
controls need replication.
■ An appropriate Statistical Test shows if the treatment effects are
significantly different from the controls.
■ Two main principles in all experimental designs: (We will see this in
detail in later chapters. The principles will be more than two)
■ Replication:
Treatment is repeated twice or more. Number of replicates depends
on magnitude of differences one wishes to detect and the
variability of the data.
■ Randomization:
Assign treatments to experimental units randomly. It assures
unbiased estimate of treatment effects and experimental error.

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The Scientific Method
Scientific investigations involve the following
major steps:
■ Formulation of a hypothesis:
• A tentative explanation or solution for a problem.
• This is alternative hypothesis in standard statistics
■ Planning an experiment:
• to objectively test the hypothesis
■ Careful observations, collection and analysis of data
from the experiment
■ Interpretation of experimental results
• This leads to confirmation, rejection, or alteration of the
hypothesis.

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The Scientific Method …
Characteristics of a well-planned experiment (1):
■ Review previous work on the subject to avoid
overlooking a better procedure. Adjust as necessary.
■ Simplicity: experimental design as simple as possible
■ Degree of precision: An appropriate design and
sufficient replication to increase precision
■ Absence of systematic error: obtain an unbiased
estimate of each treatment effect (e.g. by
Randomization)

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The Scientific Method …
Characteristics of a well-planned experiment (2):
– Calculate the degree of uncertainty
• Statistics is needed for this
– Wider range of validity of conclusions:
● An experiment replicated in time and space would
increase the range of validity of the conclusions that
could be drawn from it.
● A factorial set of treatments is another way for
increasing the range of validity of an experiment.
– In a factorial experiment the effects of varying
levels of one factor are evaluated under varying
levels of a second factor (e.g. 2 temperature levels,
3 food levels, 5 replicates result in 30 experimental
units)

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Steps in experimentation
• Research procedure depends on:
■ Subject matter
■ Objectives of the research.
• The research might be:
■ Descriptive and may involve a sampling survey (e.g.
monitoring of species population densities)
■ Or it might involve a controlled experiment
• To accomplish a research successfully:
■ Define the problem - State the objectives
– Once the problem is understood, you should be able to formulate
questions or hypotheses.
– This may be in the form of questions to be answered, or
hypothesis to be tested, which, when answered, will lead to
solutions.

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Steps in experimentation …
• To accomplish a research successfully:
– Select treatments
– The success of the experiment rests on the careful
selection of treatments
– Select representative materials
– The material used in the experiments should be
representative of the population on which the treatments
will be tested
– Select an experimental design
– The design should be as simple as possible.
» Selection of the unit for observation and the number
of observations
– For example:
» In experiments with animals, this means deciding on
the number of animals in an experimental unit and
the number of experimental units.

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■ Control of the effects of the adjacent units on each other
– This is usually accomplished by randomization of
treatments
– Consider the type of data to be collected, which depends on
objectives
– Plan statistical analysis, which depends on the type of
experiment and experimental design.
■ During the experiment:
• Avoid fatigue in collecting data.
• Recheck observations that seem out of line (outliers).
• Organize the data in such a way that it will be easy for
analysis

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■ Analyze the data and interpret the results:
• Analyze data
• Interpret results in light of questions addressed or
hypotheses tested
• Consider the size of the treatment effects, statistics
do not prove everything!!
• Consider the consequences of making a wrong
decision.
• Do not jump to conclusions. If the conclusion appears
out of line with previously established facts be careful
and investigate the matter further.

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Prepare a complete, readable, and correct report of the research.
• There is no such thing as negative result.
• If the hypothesis is rejected, there is no difference among the
treatments.
• Check with your colleagues and provide for review of your
conclusions

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Experimental Designs
• In biological research
– Natural events are observed and described
– Those events are explained
– Solutions are found to problems of the natural world
– To do these, scientists use scientific methods
– Investigations may be:
• Case study, Cross-sectional study or Longitudinal study
– Case study:
• One or a few occurrences of an event are observed and
described
• The event may occur any where in the world
– Among humans
– Plants or animals
– In the atmosphere
– Fresh water or ocean

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– Example:
• The event may be a human subject, with abnormality,
which may be physical, physiological or psychological
• The natural corollary of a case study is the proposition of
a hypothesis to explain the observed event
• Cross-sectional study
– A study of defined population by observing samples collected
from that population. This is Survey
– The variables are not manipulated. You study them as they are.
– Correlations, associations, etc. among the variables are
investigated
– That does not mean that a particular variable is the cause of an
event

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Longitudinal study
• This is an experimental investigation proper
• We manipulate variables and factors in experimental units and
observe effects.
• Such study helps us to provide tangible evidence to
demonstrate causative agent of events
• Example:
• Suppose a physician observes a few persons with oral
cancer and also notes all these persons have tobacco
chewing habit.
• He would report the description of the cases of occurrence
of oral cancer in these persons and even might hypothesize
that tobacco-chewing is the causative agent.
• However, there is no proof that this habit actually caused
oral cancer. There may be other reports of oral cancer
occurrence in person without this habit. This is simply a
case study.

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Cross-sectional study:
– Next step is cross-sectional study of a population of persons
who have the tobacco chewing habit
– Samples from such population will be screened for oral cancer,
symptoms of oral cancer, several biochemical parameters, etc.
– Simultaneously samples from a control population of those
without this habit may be screened for the same factors
– Comparing incidence of oral cancer and other factors helps to
ascertain the association among the factors
– Correlation analysis among various variables is also possible
– However, this one alone cannot provide evidence that tobacco-
chewing causes oral cancer
– The results simply add strength to the hypothesis

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Longitudinal study (LS)
– Only LS with well-designed experiments would provide
substantial evidence to demonstrate that tobacco-chewing is the
cause of oral cancer
– Difficult to conduct such an experiment on human subjects
– But animal models such as monkeys, which can be induced
into tobacco-chewing habit, can be used

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Observation
– The basic requirement in biological research is observation
– Observe. Be observant.
• What happened/ is happening in nature?
• Then this observation leads to an attempt to explain the event and
answer questions such as:
– What, how and if possible why
– Often explanations appear in the form of a hypothesis
– Example
• Large scale mortality of fish in a lake
– We are concerned and want to have an explanation for the event
– Then we would test the quality of the water, especially for pollution
– We analyze samples of water from the lake for physico-chemical
properties and may find out a high level of cadmium, a heavy metal
– We suspect that this is the reason for the death of fish
– We hypothesize that cadmium at high level is toxic to fish
– But this is one of several hypotheses
– Others include: bacteria, virus, etc., or a combination of them might be the
cause

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Hypothesis and null hypothesis
– Hypothesis is put forth as a solution to a problem or as an
explanation for an event
– Hypothesis is a statement predicting that an event will occur
under the stated condition
• Examples
1. Prolonged exposure of men to lowered oxygen pressure
will cause increased haemoglobin level in them
– This hypothesis might arise as a result of similar
observation in men of high ground
2. Cadmium inhibits growth in plants
3. Ginger has antimicrobial activity
4. Lantana camara has cytotoxic activity
5. Eucalyptus oil has antibacterial activity
hypotheses

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• A hypothesis should be one that can be tested
• But it is difficult to prove every hypothesis beyond any doubt
• All that we can do is conduct well-designed, controlled experiment to collect
evidence to support our hypothesis
• The data we collect are not the end of the matter
– The data collected are subject to statistical analysis, which would test a null
form of our hypothesis, the NULL HYPOTHESIS (NH)
– What does the statistical analysis do?
• The result of statistical test of significance calculates the probability
for occurrence of the null hypothesis
• If that probability is very low, i.e., lower than the chosen level of
significance, we reject the NH
• Rejection of NH implies that we have collected evidence that
supports our hypothesis. In this case, we cannot reject our hypothesis.
• But that does not mean that our hypothesis is acceptable beyond any
doubt
– This is because we have been based on a few samples

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• But if the statistical test gives us a probability of the occurrence
of the NH equal to or greater than the Level of Significance, then
we cannot reject the NH
– Failure to reject the NH entails that we have not collected
enough evidence to support our hypothesis
– So we accept NH and reject alternative hypothesis
– In other words, we have to reject our hypothesis, at least for the
time being, until we are able to provide sufficient evidence

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– A NH is a hypothesis of no difference, hence the name null-hypothesis
– NH may be stated in words or symbols. Examples:
1. No observed difference between observed mean and population mean
2. No significant difference between the two observed means
3. No significance difference among observed means
4. No significant difference between the observed correlation coefficient and
population correlation coefficient:
5. No significant difference between the observed variances
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• Advantage of NH==== Testability
– NH is testable hypothesis with two options to decide about it
• Reject it or Fail to reject it
– Our ultimate intention is to prove our alternative
hypothesis, so we need to produce evidence to reject NH
– NH should be testable. This does not mean those that cannot be
tested are totally false
– Un-testable hypothesis may be true or false
– We, as experimental biologists, are concerned about testable
hypotheses

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• Basic principles of experimental designs:
– 1. Observation 2. Experimentation
– Observation of events happening in nature is the basis for any
hypothesis
– Experiment is the basic scientific method of testing the
hypothesis that tries to explain an event
– Experiment is also a way of observation of events (results)
under controlled conditions
– The purpose of the observation is to demonstrate or prove
– the functions,
– relationships,
– causes,
– effects, etc. of one or more factors that exist in nature

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• Basic principles of experimental designs …
– In biological experiments in field or laboratory, we manipulate
(change by removing or adding or altering) one or more factors
in samples obtained from a population and observe the resulting
changes in required parameters
– On the basis of these observations, we infer about the population
– For inferences to be valid, we must have a correct lay out and
design of the experiment before the commencement of the
experiment
– The designs vary with the specific field of biology (ecology,
toxicology, ethology, genetics, immunology, molecular biology, etc.)
– In this class it is impossible to go into the details of designing
experiments in each field of biology
– We discuss only the general aspects, which apply to all or most
of the designs

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– Three basic steps we have to take at the beginning of any
biological experiment
• 1. Aim (objective): First we must define and record the
objective of the experiment
• 2. Plan: we must write down the strategy we adopt in the
conduct of the experiment. The planning includes:
» Defining the population
» Sampling procedure
» Sample size
» Determination of dosage (treatments)
» Mode of treatment
» Control or check
» Randomization
» Methodology for the evaluation of parameters
» Collection and analysis of the data

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• 3. Procedure: we must clearly state in writing the experimental
procedure, i.e., how we conduct the experiment in practice
» Example:
– How to collect the sample of fish, water, air, plant, animal, or
their parts, etc., must be specified
– How to transport the sample from the field to the laboratory
– How to sacrifice the experimental animals, if there is a need
– All physical activities, operational details and requirements
(equipment, glassware, apparatus, instruments, chemicals,
etc.) expected to be used should be thought of in advance
– The time, the specific time to start and end the experiment
• Before we venture into experimental designs, it would be useful
if we understand the meaning and usage of certain
terminologieswe can come across in any
experimental designs

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Basic principles of experimental designs …
Terminologies:
1. Experimental unit
2. Sampling unit
3. Experimental error (EE)
4. Discrimination
5. Replication
6. Generalization
7. Controls
8. Randomization
9. Measurement

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• Basic principles of experimental designs … Terminologies
– 1. Experimental unit and sampling unit
• Experimental unit and sampling unit are different
• Experimental unit (EU)
– Refers to the material used such as laboratory animal, cage, culture
plate, agriculture field, a plot in the garden, a pot in the greenhouse,
etc.
– A treatment is applied to an experimental unit
• Sampling unit (SU)
– May be an experimental unit itself or it may be a fraction of it
– For example, to test the toxic effect of a heavy metal on fish, we
may have two aquaria, one treated with a heavy metal and the other
without (control)
– Each aquarium may have a number of fish, say 50.
– At specific intervals, we may sample fish from each tank for
haematological, histological and biochemical analysis
– In this experimental setup, the EU is the aquarium and not the fish
in it. The fish are SU, part of experimental unit.

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• Basic principles of experimental designs …Terminologies
• 2. Experimental error (EE)
• EE is residual variance. It is variation among observations
made on the experimental units, which are treated alike.
– e.g.We inject a certain dosage of hormone into each of six mice
– The treatment is same to all six experimental units, the response
(e.g. level of glucose in the serum) may not be the same
– This is variation among the observations
• Two sources of EE
– 1. Natural variability among experimental materials
» Natural or inherent variability in experimental materials due to
genetic variability, age, sex, health, physiology, immunology,
parasitemia, etc.
– 2. The lack of consistency in or during the conduct of the
experiment
» Lack of uniformity in experimentation due to erroneous recording,
instruments, chemicals and reagents, etc.
» Changes occur on living things, errors may come from them
Within an
experimental unit
which receives same
treatment

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• 3. Discrimination
• Any experiment we design should provide
answer to a specific hypothesis
• It should not give result that can explain more
than one hypothesis
• In other words, experiments should discriminate
between different hypotheses
It should answer a
specific question

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• 4. Replication
– We all know this fact: no two individuals are identical, even
those that are genetically identical and those treated the same
– Gene expressions greatly vary in tissues, even within supposedly
identical individuals
– Also differences occur due to factors such as:
– Time of day
– Age
– Physiological state (sex, reproductive cycles, diseases)
– Biological variables are highly unpredictable
– Even so-called constant variables are regulated by homeostatic
mechanism, to remain within a wide but acceptable range of values

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• 4. Replication …
– So any inference in any experiment based on one observation is
invalid.
– Example:
• Test a hypothesis that bitter-gourd lowers blood sugar level
in man and conduct an experiment using one person
• Prepare an aqueous extract of a known quantity of bitter-
gourd and administer the extract orally to a diabetic patient
after measuring the initial blood sugar
• After half an hour, the blood sugar level may show a
lower value
– Can we infer that the bitter-gourd has the potency to
lower blood sugar?
» Certainly not.
» Problems for this inference include:

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– 4. Replication …
– Numerous questions can be raised against the above inference:
• Is there a statistically significant difference between the initial
and the final blood sugar level? There is no answer for this
question.
• A sample of n=1 is never a sample at all. DF=0.
– Suppose a 2nd volunteer diabetic was there to whom the extract
was administered
– The result might have been:
» slightly higher than the initial or it may be the same
• This means response to a treatment may vary with different
individual units of a sample
• This natural variance can be accounted for only if the
treatment is replicated, i.e., the same treatment is
administered to different sampling units
Natural variation (variance
can be quantified)

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• 4. Replication …
– How many times a treatment should be replicated, i.e., what
sample size should it be?
• The answer to this question:
– depends on the expected variance of the data, before and after
treatment
– It also depends on the accuracy we desire to have in our final
prediction
– The higher the accuracy required, i.e., the narrower the range of
the prediction, the larger is the size of the sample
– If the number of replicates is very small, our inferences will be
inconclusive and invalid
– On the other hand, too many replicates may yield diminishing
returns, that means they can cause high cost.

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– Two ways to increase the amount of information to be gained from an
experiment
• Blocking – this eliminates the effect of extraneous factor
• Replication – increases the volume of data
• Example:
– for simple experiment where one population is studied, if we
increase sample size from 3 to 28 observations, the information
we get from the experiment will increase.
– for more complex designs: the same thing can be accomplished
by executing the entire experiment more than once.
» This situation is called Replication.
» If we want to determine the difference among four
varieties of maize in the field, then we need to test each
variety in more than one plot, preferably 4 or more
More like clustering
Replication: repeats experiments

55
• Conceptually, replication does not present any difficulties,
but computationally, it does
• If an experiment requiring a two-way-analysis of
variance is replicated, it will then require a three-way
analysis of variance, since replication, itself may be a
source of variation in the data.
• When we replicate it in space and time dimensions, these
dimensions themselves become another source of
variation.
• So the analysis should include replicates as a factor

56
• 5. Generalization
• The aim of any biological investigation is to make an
inference about the population from the sample, i.e.,
estimation of population parameters using sample statistics
• We attempt to generalize what we observed in a sample or
series of samples
• We must be careful when we generalize
– What we observe in a few fish from a laboratory stock may
not apply to wild fish in a lake
– Also we should be cautious while using observations made
on laboratory bred guinea pigs for, say, extrapolation to
other mammals, especially humans

57
– 6. Controls
• All biological experiments should have appropriate controls
• If you apply a treatment and measure the response, the result might have
come from other (confounding) factors and bias, and not from your
treatment
• You need to ensure that the result has come from the treatment and not from
any other source
– Even the method of treatment itself unless regulated can create difference and
serve as another unintended source of variation. Eliminate such chances.
– Variation in handling of animals, plants, etc., medium in which the treatment is
prepared.
– A proper control can help us avoid such a problem
• Example: testing a plant extract to reduce blood glucose level in rabbits
– The experiment would be to prepare the extract and administer to
rabbits
– We must ensure that the effect did not come from other sources such as the
medium in which the extract was prepared and the technique of administering
– To do this we need a control

58
– 6. Controls …
• Use genetically and physiologically similar rabbits
• Divide them into two (with treatment and placebo)
Treatment (plant extract) Placebo (no plant extract)
Plant extract prepared in
physiological saline
Physiological saline without the
plant extract
Certain pH level Certain pH level
Certain temperature level Certain temperature level
So the rest of the handling process is exactly the same between the two
groups. The only difference is the extract, whose effect is being
investigated. If the contents of the two columns vary, then that is no
experiment

59
– 6. Controls …Types of control
– A) Positive control
• A positive control is the one in which the factor being tested is
added in the placebo.
– Example: we wish to know the effect of removal of pituitary
gland on the blood glucose level of a species of fish
– Here the experimental fish are hypophysectomized.
– We will have two types of control in such experiments
» 1) fish that were sham operated, to eliminate the effect of
the operation procedure itself
» 2) hypophysectomized fish injected with extract of
pituitary or implanted with pituitary. This 2nd one is a
positive control because it has something added that is
missing in the experimental animal
A better example: 3 fertilizer levels
against untreated control (check)

60
– A) Positive control
• Positive scientific control groups are where the control group is expected to
have a positive result, and allows the researcher to show that the set-up was
capable of producing results.
• Generally, a researcher will use a positive control procedure, which is
similar to the actual design with a factor that is known to work.
– For example, a researcher testing the effect of new antibiotics upon
Petri dishes of bacteria may use an established antibiotic that is known
to work.
– If all of the samples fail, except that one, it is likely that the tested
antibiotics are ineffective.
– However, if the control fails too, there is something wrong with the
design.
– Positive scientific control groups reduce the chances of false negatives.

61
– B) Negative control
• A negative control is the one in which the factor being tested is
removed from the basic factor that is being tested.
• Comparison of the two treatments, experimental and control,
helps us judge the efficacy of the extract in lowering the blood
sugar level in rabbits.
• Establishing strong scientific control groups is arguably a more
important part of any scientific design than the actual samples.
• Failure to provide sufficient evidence of strong control groups
can completely invalidate a study, however, high significance-
levels indicate low probability of error.
A better example: 3 fertilizer
levels against untreated
control (check)

62
– B) Negative control
• Negative Scientific Control is the process of using the control
group to make sure that no confounding variable has affected the
results, or to factor in any likely sources of bias.
• It uses a sample that is not expected to work.
– In the antibiotic example, the negative control group would be
a Petri dish with no antibiotic, allowing the researcher to prove
that the results are valid and that there are no confounding
variables.
– If all of the new medications worked, but the negative control
group also showed inhibition of bacterial growth, then some
other variable may have had an effect, invalidating the results.
– A negative control can also be a way of setting a baseline.

63
– 6. Controls … Types of control”
– Negative and positive controls are also called Baseline controls
– They both are opposite of experimental units (the ones tested)
– All the rest conditions should be maintained the same
– Examples of baseline controls
» normal, Healthy, Untreated animals, Untreated plants, etc.
– C) Known standard control
– This is used to control the possible experimental errors
– Suppose we want to test immunohistochemically the presence of a hormone,
pancreatic peptide, in the pancreas of fish
– We may use antiserum raised in rabbits against avian pancreatic polypeptide
– Result may be negative.
– we may infer that the pancreas of fish lacks pancreatic polypeptide
– But to ascertain that we followed correct procedure, and the antiserum we
obtained was potent enough to cross-react with the polypeptide, we must have a
control test run in pancreas of a bird or mammal, which are known for certain to
give positive results

64
– 6. Controls …Types of control”
– D) Blind controls
– Useful when we know what results are expected to occur
– Example:
• experiment designed to determine the effect of growth promoting hormone,
the result expected is obvious
– If we have a prior knowledge of the likely results, we may falsify
the data
– This problem can be overcome by a blind design in which a
person (a technician), who is not informed which plant received
which treatment is entrusted with the task of evaluating the results
– So the bias towards an expected result can be avoided
– Not only the person who evaluates (the researcher) the results is
blind as to what treatment is given to which subject, but also the
subjects are blind to the nature of the treatment they receive

65
D) Blind controls
– Example: a medical study with two groups, one set of patients with real
medicine and the other a placebo, in order to rule out the placebo effect.
– In this particular type of research, the experiment is double blind.
• Neither the doctors nor the patients are aware of which pill they are
receiving, curbing potential research bias.
– In social sciences, control groups are the most important part of the
experiment, because it is practically impossible to eliminate all of the
confounding variables and bias.
• For example, the placebo effect for medication is well documented,
and the Hawthorne Effect is another influence where, if people know
that they are the subjects of an experiment, they automatically change
their behavior .

66
• D) Blind controls
– A double blind experiment is an experimental method used to
ensure impartiality, and avoid errors arising from bias.
– It is very easy for a researcher, even subconsciously, to influence
experimental observations, especially in behavioral science, so this
method provides an extra check.
– For example, imagine that a company is asking consumers for
opinions about its products, using a survey.
– There is a distinct danger that the interviewer may subconsciously
emphasize the company’s products when asking the questions.
– This is the major reason why market research companies generally
prefer to use computers, and double blind experiments, for
gathering important data.

67
– THE BLIND EXPERIMENT
– The blind experiment is the minimum standard for any test involving
subjects and opinions, and failure to adhere to this principle may result in
experimental flaws.
– The idea is that the groups studied, including the control, should not be
aware of in which group they are placed.
– In medicine, when researchers are testing a new medicine, they ensure that
the placebo looks, and tastes, the same as the actual medicine.
– There is strong evidence of a placebo effect with medicine, where, if people
believe that they are receiving a medicine, they show some signs of
improvement in health.
– A blind experiment reduces the risk of bias from this effect, giving an
honest baseline for the research, and allowing a realistic statistical
comparison.
– Ideally, the subjects would not be told that a placebo was being used at all,
but this is regarded as unethical.

68
– THE DOUBLE BLIND EXPERIMENT
– The double blind experiment takes this precaution against bias one-step
further, by ensuring that the researcher does not know in which group a
patient falls.
– Whilst the vast majority of researchers are professionals, there is always a
chance that the researcher might subconsciously tip off a patient about the
pill they were receiving.
– They may even favor giving the pill to patients that they thought had the
best chance of recovery, skewing the results.
– Whilst nobody likes to think of scientists as dishonest, there is often
pressure, from billion dollar drug companies and the fight for research
grants, to generate positive results.
– This always gives a chance that a scientist might manipulate results, and try
to show the research in a better light.
– Proving that the researcher carried out a double blind experiment reduces
the chance of criticism.

69
– 7. Randomization : protection against extraneous factor .
• Ensures that each experimental unit gets equal chance of being assigned
to a treatment, in all aspects (including space and time)
• All treatments have equal chance of being assigned to each unit in the
experiment
• An experiment may contain two or more groups receiving different
treatments
• Allotment of sampling units to the different groups should be random
• Example:
– procure 20 mice with known similar genetic background for an experiment to
test the effectiveness of a drug to reduce heartbeat rate
– We divide the 20 mice into two groups of 10 each, one for drug treatment and
one for placebo
• How do we select the 1st 10 and the 2nd 10 mice?
– Catching blind-fold the mice from the cage is not really a random sampling
because those mice which allow themselves to be caught earlier than the others
are somehow less active than the ones which don’t allow themselves
– The best way is to assign numbers to each of the mice and pick the numbers by
lottery. The first 10 numbers would form one group, the remaining ten numbers
form the 2nd group.

70
– 7. Randomization …
• Which group receives which treatment should also be determined at random,
say, by toss of a coin.
• Then comes within a group.
– Which of the ten mice should get injected with the drug first?
– It looks that there is little difference between the mice, so why worry?
– But, what about the person who injects them?
– He may get tired as he continues injecting, so the amount of material
that the last one gets may be different and handling of the animal may
change with time
– Time matters. The mice should be randomly injected
– If the experimental procedure is more complex involving steps such as
surgery, the difference due to elapse of time becomes more pronounced
and this needs randomization in time.
– Randomization in time pertains not only to the order of treatment
application at the beginning of the experiment but also to the order of
observations or measurements or data recording
• Randomization is also necessary when there is variation in space.

71
7. Randomization …
– Randomization is also necessary when there is variation in space.
– Example:
• Arranging experimental cages, aquarium tanks, pots, etc. in the laboratory
can make a lot of difference with respect to light, aeration, etc.
– A pot placed close to the window might receive more light and air than
pots kept away from the window
– Unless we have the facility to maintain uniform lighting, aeration,
humidity, temperature, etc. variations arise and affect the results
• Agricultural field plots (every piece of land differs in many different
variables including soil fertility, light, slope, aspect, moisture, soil physical
and chemical properties, biotic factors, vegetation, precursor plants, etc.)
– Randomization is more important in field experiments because of the
heterogeneity of soils. While soils in adjacent areas are more
homogeneous, those far apart are not
– Most of these field conditions cannot be regulated artificially, we need
to use randomization
• Randomization is becoming more and more important and complex in the
field of molecular biology where microarray experiments are routinely
conducted to ascertain the function of genes in relation to environmental
factors

72
– 8. Measurement
• Results of an experiment need to be measured using some kind of scale like:
– Ordinary metric scale
– Digital balance
– Sophisticated spectrophotometer
• Whatever scale used, we need to be concerned about the accuracy and precision
of measurements
• Accuracy is closeness of measured value to the true value
– Remember there is always a true value although we may lack the capacity
to find it
– And unfortunately, the true value is never known. We can’t say for sure it is
accurate.
– Example: we measure the length of a fish to be 4.3 cm.
– This value is obtained using a scale that gives values up to a tenth of a
centimeter
– If we still use a finer scale, we may measure it to a hundredth or thousands
of cm

73
– 8. Measurement …
• But how can we be certain that our measurements are accurate?
• Suppose we know the true value of the length of the fish is 4.25 cm
• Any measurement that is close (e.g. 4.3) to the true value can be more
accurate when compared to values far away (e.g. 4.0 or 4.5 cm)
– Precision is the reproducibility of a measurement or numerical
result
• Example:
– we weigh a fish using digital balance and get 10.6 g
– Weigh the same fish again and get 10.5 g, a third measure gives 10.9 g
– Our results are not precise
• Now use another balance and get 10.6 g, 10.5 g and 10.5 g
• Now we can say our results are more precise than the previous values
• We can describe the second balance as a precision instrument because it
gives reproducible measurement values. Precision is practical and more
valuable than accuracy

Local control
•Controls extraneous factors
•Divide field into several homogeneous parts,
known as blocks and then each block is divided
into parts equal to the number of treatments
•It applies to any field of study
•Soil variation
•Populations vary (rich, poor; male, female;
educated, not educated; rural, urban, etc.)
•So whole set of apply treatments to each
group .
•This is essentially blocking.
74

75
A few common
experimental
designs

76
A few common experimental designs
• All experimental designs require a thorough understanding of the basic
principle of statistics, especially inferential statistics
• At the end of the experiment, we collect data, analyze it, and infer about the
population from which the sample was obtained
• Biologists need to think about the statistical test to be used before the start
of the experiment
• Sir R.A. Fisher (1890-1962), whose contribution to the design of
experiments is well known, said the following in his presidential address in
1938 in a statistical conference:
– To consult a statistician after the experiment is completed is to ask him
to conduct post mortem examination. That is more like asking: what
the experiment died of.
• We will talk about certain experimental designs which are based on
statistical principles
– But we only discuss principles and applications, not detailed
statistical procedures

77
A few common experimental designs …
• 1) One group design
– A random sample is collected from the population and its statistics (e.g.
mean) is compared with the population parameter (e.g. µ)
– Example:
» A sample of alcoholics may be examined for blood cholesterol
level
» This sample mean may be tested for significance against population
mean. The population mean is a quantity known earlier.
– Procedure (7 steps)
» 1. statement of the problem=hypothesis
» 2. null hypothesis:
0
: 

 
X
Ho

78
A few common experimental designs …
• 1) One-group design …
– 3. Level of significance: 0.05 or 0.01
– 4. Sampling distribution of sample means. Computation of the standard
error of the mean either from population SD (σ) or sample SD (s) as:
– 5. Location of the sample statistics in the sampling distribution as:
– 6. Decision about the rejection of the Ho. Minimum Z required for
rejecting Ho..
n
X

  or
)
1
( 

n
S
SX
SX
X
Z
)
( 


Level of significance One-tailed test Two-tailed test
0.05 1.64 1.96
0.01 2.32 2.58
If the calculated Z> the tabulated Z, reject Ho

79
• 7. Inference: differences between and µ is significant if Ho is
rejected, and not significant if Ho fails to be rejected.
• The given hypothesis is discussed based on the above decision
• Example:
– A certain random sample of 100 men from a hill-tribal village gave
a mean height of 167 cm with a standard deviation of 5 cm.
Discuss the suggestion that this tribal village do not form a part of
the Dravidian race whose mean height was claimed to be 170 cm.
• Answer: Z=6 which is greater than both 1.96 and 2.58 for
α=0.05 and 0.01.
• So the NH is rejected. There is significant difference between
the sample mean and the population mean.
X

80
Step 1. Statement of the hypothesis: Mean height of the village men ( ) is
significantly different from the population mean ( )
Step 2.
Step 3. Assumption of a sampling distribution of of samples from the
population and computation of the SE of the mean as:
Step 4. Location of the observed mean in the sampling distribution in terms of the
Z-score as:
Step 5. Decision about the Ho: Since the calculated Z (6) > the table Z (1.96, at
α=0.05, two-tailed test), we reject the
significant difference between the observed mean and the population mean,
with a significance of P<0.05. The calculated Z is greater than even 2.58 (Z
value required to reject Ho at 0.01 significance level (alpha level) of the two-
tailed test.
Step 6. Inference: Since the null hypothesis is rejected, the suggestion that the men
of the hill-tribal village whose mean height is 167 cm do not form a part of
Dravidian race whose mean height is 170 cannot be rejected.
X

,
05
.
0


;
0


 
X
Ho
two-tailed test (no direction specified)
s
X '
5
.
0
95
.
9
5
1
100
5
1






n
S
SX
0
.
6
5
.
0
3
5
.
0
170
167
)
(






SX
X
Z

;
0


 
X
Ho
there is a

81
• 2) Two-group design
– Samples may be obtained from two different populations, and their statistics
and may be used to compare the population parameters and
– Or a sample may be divided randomly into two and allotted to experimental and
control groups in order to assess the effect of the experimental treatment
– Statistical analysis varies with sample size (large or small)
• Comparison of means of two large samples
– Example: samples of one-year-old adult male Tilapia mossambica were
collected one from each of two geographically isolated lakes, and their body
lengths were measured to the nearest millimeter. From the data below, determine
whether there is statistically significant difference between males of the two
populations in terms of body length. Remember your biostatistics course.
X1 X 2 2
1
42
225
74
1
2
1
1



n
S
X Inference: There is no statistically
significant difference between the mean
lengths of the two geographically
isolated populations of one-year-old
male Tilapia mossambica
Z test
46
148
78
2
2
2
2



n
S
X

82
2) Two-group design …
• Step 1. Statement of the problem: To test whether there is a significant difference
between and
– Ho: μ1– μ2=0 (i.e., the mean of the population from which sample 1 was drawn
is not different from the mean of the population from which the sample 2 was
drawn)
– α=0.05 (two-tailed)
• Step 2. Sampling distribution of the difference between means,
with a mean of 0, and SE of difference between means
• Step 3. Location of the observed difference between means in the sampling
distribution in terms of Z score, as:
• Step 4. Decision about Ho: Minimum Z required to reject Ho at α=0.05, two-
tailed test is 1.96. The calculated Z (1.365) < table Z (1.96). Therefore, we fail to
reject the Ho: μ1-μ2=0.
• Step 5. Two geographically isolated fish same length.
X1 X 2
X
X 2
1

93
.
2
56
.
8
55
169
41
225
1
1 2
2
2
1
2
1
2
1









n
S
n
S
S X
X
365
.
1
93
.
2
)
78
74
(
)
(
)
(
2
1
2
1
2
1








S
X
X
X
X
Z



83
• 2) Two-group design …
– Student’s t-test
– Comparison of means of two small samples (uncorrelated groups)
– Example:
• Two horticultural plots were divided each into six equal subplots. Organic
fertilizer was added to Plot 1 and chemical fertilizer to was added to Plot 2.
The yield of fruits from Plot 1 and Plot 2, in kg/subplot, was given below.
Can we say the yield due to organic fertilizer was higher than due to
chemical fertilizer?
• Inference: the yield due to organic fertilizer (Plot 1) was significantly
higher than that due to chemical fertilizer (Plot 2).
Plot 1 6.2 5.7 6.5 6.0 6.3 5.8
Plot 2 5.6 5.9 5.6 5.7 5.8 5.7

84
2) Two-group design … Student’s t-test. Comparison of means of two
small samples (uncorrelated groups)
Step 1. calculate the following statistics for the above data
Step 2. Hypothesis: Ho: μ1- μ2=0; α=0.05 (one-tail)
DF= 6+6-2=10
Step 3. Assumption of a sampling distribution of difference between
means, with a mean of μ1- μ2=0 and SE of difference between
means computed as follows.
Plot 1 Plot 2
n1=6 n2=6
08
.
6
1

X 716
.
5
2

X
279
.
0
1

S 116
.
0
2

S

85
2) Two-group design … Student’s t-test. Comparison of
means of two small samples (uncorrelated groups)
Pooled variance:
Standard error:
134
.
0
5
045
.
0
5
045
.
0
1
1
045
.
0
12
)
01
.
0
(
6
)
08
.
0
(
6
6
6
6
6
2
2
1
2
2
2
2
1
2
2
2
2
1
1
2 )
116
.
0
(
)
279
.
0
(
















n
S
n
S
n
n
S
n
S
n
S
P
P
P
SE

86
2) Two-group design … Student’s t-test. Comparison of
means of two small samples (uncorrelated groups)
Step 4. Location of the observed difference between means in the
sampling distribution in terms of t, is calculated as follows:
Step 5. Decision about Ho. Table value of t at α=0.05 and 10
DF=1.812
Since the calculated t > the table t, Ho: μ1- μ2=0 is rejected. There is
a significant difference between the means of the two plots
Step 6. Inference. The yield due to organic fertilizer (Plot 1) is
significantly higher than that due to chemical fertilizer (Plot 2).
72
.
2
134
.
0
716
.
5
08
.
6
2
1





SE
t X
X

87
• 3) Matched-pair data analysis design
– In this design only one group of sample is used
– The data may be collected before and after an experimental treatment
– Or data may be collected after the control treatment and again after the
experimental treatment
• In this design each sample unit serves for both control and experimental
treatments
• The pair of data obtained are matched, i.e., the difference between each pair
is obtained and tested weather the mean difference is significant.
– Example:
• A pharmaceutical company developed a drug which, it claims, increases
haemoglobin content in aged people. The haemoglobin content (g/100 ml) of
10 subjects is measured before and after administration of the drug. On the
basis of the following data determine whether the company’s claim is valid.
• Inference: The sample mean difference is significant. The drug is effective
in increasing the haemoglobin content in aged people. The claim of the
company is valid.

88
3) Matched-pair data analysis design …
Step 1. Same subject gives pairs of data. e.g.
• Values obtained before and after treatment
• Values obtained after control treatment and after experimental treatment
• Values obtained at two different periods – now and a gap of a day, a
month, a year, etc
Step 2. Significance of the mean difference ( ) is tested using t-test
Step 3. Ho: -μD=0; n-1 degrees of freedom (n=number of pairs of
data); sampling distribution of mean differences ( ) with a
population mean of μD=0.
Step 4. Computation:
a. D= matched difference between n paris of values-if the after value is greater
than before value the difference is shown as +; if the after value is less
than the before value, the difference is -. This + or – sign should be taken
into account while calculating ΣD and D-
b. ΣD
c. Mean difference, = ΣD /n
D
D
D
D
D

89
d.
e.
f.
5.
6. Table t at a specific alpha level and n-1 DF (one-tail, if direction is
specified, two-tailed if not)
7. Decision. If calculated t>table t, reject Ho.
8. Inference. Based on the decision, the given Ho is discussed.
 
n
SD
D
D
 

2
    
 

 D
D
D
D and
D
D
2
2
..
..
,
1
,..
..
..
..


n
S
difference
mean
of
SE SD
S
S D
D
D D
t
is
this
D
t
0
..,..
...
,...






90
Example
Step 1. Ho: -μD=0, α=0.05, one-tailed with DF=10-1=9
Step 2. Computation
=2, S=1.1
Step 3. Assumption of sampling distribution of with a mean of μD=0
and SE computed as:
Step 4. Location of the observed mean difference in the sampling
distribution in terms of t as:
D
D
41
.
5
37
.
0
2




SE
D
t D

37
.
0
1
10
1
.
1
1





n
SD
SE

91
Step 5. Decision about the Ho: -μD=0
Table t at α=0.05 (one-tail) and 9 DF=1.833.
Calculated t (5.42)>table t; reject Ho.
Step 6. the sample mean difference is significant. The drug is
effective in increasing the hemoglobin content in aged people.
The claim of the company is valid.
Doing the same using Excel.
D

92
• 4. Multiple-group design
– Application of ANOVA would enable a variety of multiple group designs
– Some of them are:
• One-way classification design
• Randomized (complete) block design
• Factorial design or two-way classification design
• Latin square design
• Split-plot or nested design
– Application of analysis of covariance is more useful in the design of
experiments because it incorporates correlation and regression between variables
into ANOVA
– 1) One-way classification design with fixed effects (Model 1)
– A simple and very common design in which two or more groups are
compared, specifically, it is described as one-way classification,
completely random design with fixed effects.
– It is one-way because only one factor is studied.
– The factor may be studied at different levels, the levels considered as
groups, or k groups

93
• 4. Multiple-group design
– 1) One-way classification design with fixed effects
(Model 1)
• One-way ANOVA is used to test for differences among
two or more independent groups.
• Typically, however, the one-way ANOVA is used to test
for differences among at least three groups, since the
two-group case can be covered by a t-test (Gosset,
1908).
• When there are only two means to compare, the t-test
and the ANOVA F-test are equivalent; the relation
between ANOVA and t is given by F = t2.

94
• 4. Multiple-group design … One-way classification design with fixed effects
• Example:
• Suppose we are interested in studying the effect of temperature on bacterial growth
• In this study the factor is temperature with several levels. The growth of bacteria
measured in terms of number of colonies/plate is the dependent variable
• Temperatures such as 25o, 30o, 35o, 40o and 45o at which the bacteria are cultured are
the levels, 5 groups (k=5).
• At each temperature level, we may have a number of replicates, i.e., culture plates,
which refer to the sample size in each level of group
• The number of replicates in different groups may be equal or unequal
• The samples of k groups (levels) are independent of one another
• The allotment of a culture plate is random, hence the name completely random
design
• On the other hand we decide the number of levels
• We would have selected any number of temperatures, say, 0o to 100o, we choose
only 5 specific temperatures
• These temperatures are not selected randomly, hence fixed
effects, meaning the factor levels are deliberately chosen by the
investigator because of their significance

95
– Using the same design, the growth of bacteria (number of
colonies/plate), may be studied in a number of bacterial species at a
particular temperature, say 37o.
• Here the levels of the factor are the number of species (fixed effects)
• Each species is cultured in replicates at 37o.
– The question in both approaches is:
• Do samples of each level come from a population having the same
characteristic?
• Bacteria cultured at 25o, 30o, 35o, 40o and 45o are assumed to have
come from the respective populations of bacteria cultured at 25o, 30o,
35o, 40o and 45o
– This is the alternative hypothesis which claims a difference
– While the null hypothesis claims that they come from one
population (one temperature level), meaning no effect in
temperature

96
– Example:
• The following data represent the weight gain (kg) of a species of edible fish
cultured in diet formulations (D1, D2, D3 and D4) for a period of 3 months.
Analyze these data for significant difference among the diet formulations in
terms of gain in weight:
• Inference: there is significant difference among the diet formulations in
terms of weight gain
Diet 1 Diet 2 Diet 3 Diet 4
4 8 5 1
5 7 7 4
1 9 8 1
3 6 6 3
2 10 9 1

97
• 4. Multiple-group design …
– 2) One-way classification with random effects:
– It is also possible to have one-way classification, completely random design
with random effects
– The design we discussed above:
• We selected the levels of treatment (the temperature or the species)
• Thus the design was described to have FIXED EFFECTS. We fix the treatment.
• Instead, if the levels of treatment are selected at random from a large set of
options, the experimental design is said to have RANDOM EFFECTS.
• Example: If the five temperatures were selected randomly from a wide range of
all possible temperatures in which the bacteria can grow, then the bacteria
cultured at each of the random temperatures would represent a population of
bacteria growing in that temperature
• Note that these populations from which the samples were drawn have
themselves been selected randomly from a large number of populations.
• So the design is said to have random effect
• The method of handling the data is the same as the fixed effect discussed above

98
– 2) One-way classification with random effects:
• Random-effects models (Model 2):
– Random effects models are used when treatments are not
fixed.
– This occurs when factor levels are sampled from a larger population.
– Because the levels themselves are random variables, some
assumptions and the method of contrasting the treatments differ from
ANOVA model 1.
– Most random-effects or mixed-effects models are not concerned with
making inferences concerning the particular sampled factors.
– For example, consider a large manufacturing plant in which many
machines produce the same product.
– The statistician studying this plant would have very little interest in
comparing the three particular machines to each other.
– Rather, inferences that can be made for all machines are of interest,
such as their variability and the mean.
– However, if one is interested in the realized value of the random
effect best linear unbiased prediction can be used to obtain a
"prediction" for the value.

99
– 3) Two-way classification design or factorial design
– This is a situation when two factors are involved in the
experiment
– Completely random design with fixed effects or factorial
experiment
– In a factorial experimental design, the effect of two or more
factors operating on a third factor is investigated
– The first two factors may be in two or more levels
• Example: We may be interested to know the effects of
temperature and pH on bacterial growth.
• The levels of the factor temperature may be two, say, 30o and
40o and the levels of the pH may also be two, say, pH 4 and
pH 10.

100
• 3) Two-way classification design or factorial design …
• The most commonly used type of factorial ANOVA is the
22 (read "two by two") design, where there are two
independent variables and each variable has two levels
or distinct values.
• Factorial ANOVA can also be multi-level such as 33, etc. or
higher order such as 2×2×2, etc..
• Since the introduction of data analytic software, the
utilization of higher order designs and analyses has
become quite common.

101
– 3) Two-way classification design or factorial design …
– ANOVA enables us to separate and evaluate the following:
– Effect of the two factors (temperature, pH)
– Interaction of the two factors
– A) Randomized block design (RBD)
• This design is also known as Randomized Complete Block Design
(RCBD)
• This design is used mainly to reduce error due to natural
variations.
– Variations (or changes in a certain characteristic, such as soil
fertility status) naturally have a gradient or direction
• It involves the arrangement of the experiment in the form of
blocks
• The assignment of experimental units to each block is random

102
– A) Randomized block design (RBD)
– Example:
• Suppose we want to compare the yield of four varieties of maize, A,
B, C and D.
• A simple RBD with four replications is to have an agriculture field
divided into 4 blocks of equal size, each block having 4 sub-blocks of
equal size.
• The four varieties of maize are grown in all the four blocks
• Also the allotment of a maize variety to each sub-block of a block is
random
• Such a randomization would result in minimum variation within blocks
and maximum variation between blocks. Blocks become another source
of variation
• It reduces the total random error (chance variation) due to variations
between blocks
Seats
by
chance

103
– A) Randomized block design (RBD) …
– An illustration of RBD (RCBD) field lay out (next slide):
• This design has basically been developed for agricultural research
• Ever since, however, it has become adopted in numerous other
experimental conditions
• If replications of several treatments in an experiment are to be carried out
in one day, the treatments have to be performed over a period of several
days
– In such a case, the days are classified as blocks
– If an experiment is done in different laboratories, the laboratories
become blocks
– Generally, whenever experimental conditions are heterogeneous,
these conditions are subdivided into more homogeneous blocks
– The blocks can be age groups, genotypes, environmental factors,
income levels, education level, sex, whatever grouping is available.

104
Variety

105
• Example : A field experiment to compare six melon cultivars with four
replications, each arranged as follows:

106
Mixed design model
 When one wishes to test two or more
independent groups (treatments)
subjecting the subjects to repeated
measures, one may perform a factorial
mixed-design ANOVA, in which one
factor is a between-subjects and the
other is within-subjects variable.
 This is a type of mixed-effect model.

107
– 4) Latin square design (LSD)
• This design is a versatile design
• Introduction:
– We saw how blocking can be used to eliminate the
variability due to one extraneous factor from the
experimental error
– In principle, two or more extraneous sources of variation
can be handled in the same way
– The problem with this is that this will inflate the size of the
experiment beyond practical bounds
– If we continue blocking for every extraneous factor, then
we will have a huge experiment which is not practical at all
– This will give as many experiments as the number of
extraneous factors, which increases costs and difficulty of
operation
4th session

108
– 4) Latin square design (LSD) …
• If we have 4 levels of factor A and 4 of B, replicated 4 times,
then we will have: 4*4*4=64
– This is a huge task (demanding resources and time)
• Latin square eliminates some of these problems at least in
part
• We can still use only 16 observations instead of 64.
• Also this implies that through proper design experiments can
be made to yield a wealth of information with minimal
expense

109
– 4) Latin square design (LSD)
• Also common in agricultural research
• Useful when we want to control (capture) the variations in
an experiment that is related to rows and columns in the
field
• LSD can be adopted in many experimental situations in the
greenhouse or in the laboratory
• In a field study, LSD consists of a row-and-column design
for n treatments in n rows and n columns
• Each treatment occurs once in each row and once in each
column
• Let us consider an experimental situation in which Latin square
design can be adopted.

110
• Suppose we are interested in testing the effectiveness of extracts of 4
plants, A, B, C and D (say, herbal formulations, of which one or more
could be controls) in controlling blood sugar level in diabetic patients.
– Testing a single extract requires one whole day
– Let us also assume that there are only four diabetic patients (I, II, III
and IV) who have agreed to be subjects of our experiment, and that
they will be available with us on four consecutive Sundays (1, 2, 3
and 4).
– The experimental unit in this set-up is a “patient-Sunday”.
– If we adopt the Latin square design, the rows would represent the
patients and the columns the consecutive Sundays
– On each Sunday all the four extracts are tested
– The decision as to which patient would receive which plant extract
on which Sunday is made by random procedure
– Example: on the 1st Sunday, patient II would receive the extract of
plant C
Column: Sundays
Rows: Patient
Treatment: Extracts

111
Columns
1 2 3 4
Rows I A B C D
II C D A B
III D C B A
IV B A D C

112
Consecutive Sundays
1 2 3 4
Patient I A B C D
II C D A B
III D C B A
IV B A D C

113
• LSD is more useful in field studies where we would like to
control variations in two-dimensional space, i.e., different
directions, rows and columns.
• Treatments (e.g. different fertilizers, pesticides, etc.) are
allotted at random within rows and columns, with each
treatment once per row and once per column
• What do we notice in LSD?
– Three factors are tested (present case: patient, Sundays and plant
extract)
– In two-way ANOVA only two factors are tested, although interaction
term is later added at the time of data analysis
– LSD is always a square, i.e., the rows and columns should be equal

114
• Statistical analysis is similar to two-way ANOVA.
• Total SS, row SS, column SS are calculated in the same way
• But, here we have an extra SS which measures the variability
due to the variable represented by the letters A, B, C, D,
namely the new treatment SS.
– Formula:
– Where TA is the total of observations corresponding to treatment A,
TB is the total of observations corresponding to treatment B, and so
forth.
– But also for the letters A, B, C and D, you can calculate SS as
usually done in ANOVA (instead of the above formula)
– Finally the error sum of squares is again obtained by subtraction
T
T
T r
r
Tr
SS B
A
2
2
2
.
1
...)
(
1
)
( 2





115
• ANOVA of Latin square design (format)
Source of
variation
Degrees of
freedom*
Sum of
squares (SS)
Mean
square
(MS)
F
Rows (R) r-1 SSRows SSR/(r-1) MSR/MSE
Column (C) r-1 SSColumn SSC/(r-1) MSC/MSE
Treatments
(Tr)
r-1 SSTreatment SSTr/(r-1) MSTr/MSE
Error (E) (r-1)(r-2) SSError SSE/((r-1)(r-2))
Total (Tot) r2-1 SSTotal
*where r=number of treatments= rows= columns

116
• Sample ANOVA table
Source of
variation
Degrees of
freedom
Sum of
squares
(SS)
Mean
square
(MS)
F
Rows 3 40.77 13.59 5.91†
Columns 3 125.39 41.80 18.16†
Treatments 3 160.57 53.52 23.26†
Error 6 13.81 2.30
Total 15 340.54
† Table F at 0.05 Level of Significance and at 3, 6 degrees of freedom is 4.76

117
– 4) Latin square design (LSD) … Raw data example
Discounts Lotteries Coupons Two-for-
one sales
A
48
B
38
C
42
D
53
Northeast
B
39
C
43
D
50
A
54
Southeast
C
42
D
50
A
47
B
44
Northwest
D
46
A
48
B
46
C
52
Southwest
Suppose in a breakfast-food study, a market research organization gets
data shown above, where the values are weekly sales in $10 thousands

118
– In the above table:
– Deals with the sales of breakfast in the US influenced by three
factors:
• 1. Regions (rows)
• 2. Promotional techniques (such as discount, lotteries, etc.)
(columns)
• 3. Packaging techniques (A, B, C, and D) (in the body of the data
table)
• SS for rows and columns will be calculated as usual
• Also total SS follows the same way
• What makes this matter different is the third factor: in this case
the packaging
• It may be done in a different way: the values of each package may
be collected and tabulated for calculation

119
Packaging
A B C D
48 38 42 53
54 39 43 50
47 44 42 50
48 46 52 46

120
– 4) Latin square design (LSD) … ANOVA table
Source of variation Degrees of
freedom
Sum of
squares
(SS)
Mean
square
(MS)
F
Rows (regions) 3 17.25 5.75 0.9
Columns (promotion
method)
3 114.75 38.25 5.9*
Treatments
(packaging)
3 174.75 58.25 9.0*
Error 6 39.00 6.5
Total 15 345.75
Conclusion: differences in promotion and packaging, but not the
different regions, affect the breakfast food’s sale (P<0.05).
Split-plot design

121
– 4) Split-plot design (SPD)
• This design is useful for two factors, one of which may have to be
applied to larger experimental units and the other factor, which requires
smaller areas within the larger units.
– Example:
• We may be interested to know the effects of 5 different
fertilizers (A, B, C, D and E) on the growth of genotypically
different plant species (1, 2, 3, 4, …, 10)
• An experimental field is divided into 5 main plots. Each
main plot is applied with one fertilizer, referred to as main-
plot factor
• The allotment of fertilizers to the main plots is done
randomly
• Then each of the 5 main plots is subdivided into 10 equal
sized subplots

122
– 4) Split-plot design (SPD) …
• Each subplot in a main-plot is planted with a genotypically
different plant (variety)
• The different plant varieties are allotted to the subplots in each
main-plot randomly
• The split plots design can be adopted in a variety of
experimental situations such as environmental conditions,
disease trials, and nutrient trials on different plants
• The ANOVA of a SPD data involves:
– Comparison of variation between treatments applied to
main plots to random variations between main plots.
– Comparison of variation between treatments applied to
subplots, and variation of the interaction, to random
variation between subplots

123
• An experiment in which an extra factor (second) is introduced into a study
by dividing the large experimental units (whole unit) for the first factor into
smaller experimental units (sub-units) on which the different levels of the
second factor will be applied.
• Each whole unit is a complete replicate of all the levels of the second factor
(RBD).
• The whole unit design may be CRD, RCBD or LS design.
• Randomization - The first factor levels are randomly assigned to the whole
units according to the rules for the whole unit design (i.e., CRD, RCBD or
LSD design). While the second factor levels are randomly assigned sub-
units within each whole unit according to the rules of a RCBD. The name of
the split-plot design is prefixed with the design name associated with the
whole plot design, i.e., Randomized Complete Block Split-Plot Design. The
design for the sub-plot is never given, but is assumed since it must by
definition be RBD.

124
• ADVANTAGES
• 1. Since sub-unit variance is generally less than whole unit
variance, the sub-unit treatment factor and the interaction are
generally tested with greater sensitivity.
• 2. Allows for experiments with a factor requiring relatively
large amounts of experimental material (whole units) along
with a factor requiring relatively little experimental material
(sub -unit) in the same experiment
• 3. If an experiment is designed to study one factor, a second
factor may be included at very little cost
• 4. It is the design (univariate) for experiments involving
repeated measures on the same experimental unit (whole unit),
while the repeated measures in time are the sub-unit.
If
we
want
to
repeat
same
factor
several
times
as
maiplot,
i.e.,
repeated
measures Repeated
measures can
be sub-plots

125
DISADVANTAGES
1. Analysis is complicated by the presence of two experimental error
variances, which leads to several different SE for comparisons 
2. High variance and few replications of whole plot units frequently leads to
poor sensitivity on the whole unit factor. 
POSSIBLE APPLICATIONS
1. Experiments in which one factor requires larger experimental units than the
other factor
2. Experiments where greater sensitivity may be desired for one factor than
for the second factor
3. Introduction of a new factor into an experiment which is already in
progress.

126
Here we have
mainplot A and
subplot B
We have 3 levels
of A, and 2 levels
of B, and two
replications. .

127
Source df
Whole-Plot Analysis
Factor A a-1
Whole-Plot Error a(r-1)
Split-Plot Analysis
Factor B b-1
A x B (a-1)(b-1)
Split-Plot Error a(b-1)(r-1)
Total abr-1

128

129

130

131

132

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