1

SA’ADATU RIMI COLLEGE OF EDUCATION, KUMBOTSO

SCHOOL OF SCIENCE EDUCATION

DEPARTMENT OF BIOLOGY

BIO 212 RESEARCH METHODS AND BIOMETRY

Meaning, purpose and relevance of research methods and biometry

Research method refers to the techniques for investing phenomenon through

experimentation. An experiment is carried out in order to investigate a

phenomenon which can lead to the acquisition of new knowledge or it can be

carried out to confirm or to correct a previous finding.

Biometry, Biometrics or Biostatistics is the application of statistics to a wide

range of topics in biology and its related discipline particularly agriculture and

medicine to distinguish it from statistics used in other field of human endeavour

e.g. economics business, education etc. The subject encompasses the design

layout, conduct of experiments, collection, compilation and analysis of

numerical data as well as interpretation of the results and drawing valid

conclusion for a particular situation time.

Biometry or Biostatistics is relevant to the field of Biology Agriculture and

Medicine; where the subjects of inquiries are variable in nature and the extent of

variation coupled with the relative importance of the different causes of the

variations are the primary concerns. Three, eminent scientist Sir R.A. Fisher,

S.D. Wright and J.B.S. Haldane, were the founding fathers of Biometry.

TYPES OF RESEARCH

Generally, research is divided into two main types these are: -

2

1. Qualitative Research

2. Quantitative Research

Qualitative Research: is a type of research that aim to investigate a question

without attempting to quantifiable measure variable or look to potential

relationship between variables. Example of qualitative research include case

study.

Quantitative Research: is a systematic empirical investigation of quantitative

properties and phenomena and their relationships, there by asking a narrow

question and collecting numerical data to analyse using a statistical methods.

Example include: experimental, correlational and survey.

Choice of Research Topic

The most successful research topics are narrowly focused and carefully defined.

Before a researcher chose a research topic, several factors are taken into

consideration. Some of them have to do with your particular interests,

capabilities and motivation. Other focused on areas that will be of great interest

to both the academic and private sectors.

The chemistry professor and author, Robert Smith in his book Graduate

Research: A guide for students in sciences (1984) listed some point to be

consider in finding and developing a research topic:

a) Can it be enthusiastically pursued?

b) Can interest be sustained by it?

c) Is the problem solvable?

d) Is it worth doing?

e) Will it lead to other research problems?

f) Is it manageable in size?

3

g) If the problem is solved, will the result be reviewed well by scholars in

your field?

h) Are you, or will you become, competent to solve it?

i) What is the potential for making an original contribution to the literature

in the field?

Hypothesis: (Types source, Formulation)

Hypothesis is one of the concepts frequently used by scientist and other

researchers in their scientific writings and works.

Hypothesis is a proposed explanation for a phenomenon. It is simply defined as

the educated guess that is based upon observation of an event or phenomenon. It

is a possible explanation of an event.

That is, it provides an explanation as to why or how an observed event happen

or what makes it happen but which has not been proved. Therefore it is simply

based on intuition or reasoning. Most hypothesis can be supported or rejected

by experimentation or continued observation.

Types of Hypothesis

Types of hypothesis include: - Null hypothesis, alternate hypothesis and

scientific hypothesis. Null and alternate hypothesis are the two types of

hypothesis found in statistics hypothesis testing. One is often just the

contradiction of the other. Scientific hypothesis is not commonly known as an

educated guess, it is a scientific theory that has not yet been proven to be true.

Null hypothesis always predicts the absence of relation between two variable

e.g. “there is no relationship between education and income” while.

The alternate hypothesis states an actual expectation such as “Higher levels of

education increase the likelihood of earning a higher income”.

4

Sources of Hypothesis

Hypothesis can be derived from many sources:

a) Theory: Theory on the subject can act as source of hypothesis e.g. providing

employment opportunity is an indicator of social responsibility of a

government enterprises from the above many hypothesis can be deduced.

i. Public enterprise has greater social concern than the enterprises

ii. People’s perception of government enterprise is a social concern.

b) Observation: People’s behaviour is observed. In this method we use

observed behaviour to infer the attitudes.

c) Past experience: Here researcher goes by past experience to formulate the

hypothesis.

d) Case studies: Case studies published can be used as a source for hypothesis.

Formulating Hypothesis

Hypothesis can be explained as a statement that can be used to predict the

outcome of future observations. It stated that you predict will happen based on

changes in variables. Variables are things that change. A hypothesis is stated in

order to be tested by an experiment. It can come as answers or explanations to

the question you have raised since from the beginning. It can also be a statement

that explains or describe the way you think the observation you made are

brought about, that is the mechanism underlying the phenomenon.

Once you have identified your research question, it is time to formulate your

hypothesis. An experiment is carried out to test the validity of the hypothesis

formulated through acceptance or rejection. Hypothesis are form in order to be

discredited and when they are not rejected they become accepted.

5

Formulating a valid hypothesis takes practice but it is important to the success

of any experiment. The following steps need to be consider when formulating a

hypothesis.

1. Great your hypothesis in a form of a question. E.g. “Does smoothing

cause lung cancer?”

2. Formulate the hypothesis by making it a conditional statement e.g.

“smoking may cause lung cancer”.

3. Write a formalized hypothesis e.g. “It smoking cause lung cancer, then

individuals who smoke have a higher frequencies is consider as the most

useful.

4. Make sure that your hypothesis contains variable the researcher is always

in control of the independent variable in the experiment. The dependent

variables are mostly observed in the context of the experiment. For an

experiment to be valid, it must contain at least two variables.

5. Make sure that your hypothesis include subject group. A subject group

defines who or what the researcher is studying in our example the subject

group are the smokers.

6. Include a treatment or exposure in the experiment. A treatment is literally

what is being done to the subject group. In our example, the exposure is

smoke or smoking.

7. Prepare for an outcome measures, which is a measurement concerned

with how the treatment is going to be assessed. In our example the

outcome of smoking is the frequency of smoke developing cancer in

subject population.

8. Understanding your control group. Control group is a group similar to the

subject group but does not receive the treatment i.e. is a population that

the subject group is compared to. In our example, the control group is

non-smokers.

6

DATA COLLECTION (TYPES AND SOURCES)

Data (Singular Datum) is a numerical statement of fact in a specific field of

enquiry. Simply, data means numbers and these numbers are obtained from

research carried out in a specific area of investigation. For example a research

may be interested in finding out how many students are admitted into the

various departments in S.R.C.O.E Kano annually for the last five years (2008 –

2013). This will involve checking the records at student’s affairs and counting

numbers of students admitted into each department during the stated period. The

number counted for each department is then counted. This record forms your

data. The research may also involve distribution of questionnaires and getting

responses from the respondents. Example ministry of health is interested in

knowing how many people use treated nets in an area that is known to have a

higher prevalence rate of malaria in an attempt to popularize its use. The

researcher may have to cover the area with questionnaires, and use that to count

how many people use the nets, how many people use other methods of

prevention and how many people do not use any method. This also form a data

from which you can carry out further analysis. So also study may involve taking

measurement on blood pressure, parasite count, height weight, yield

temperature humidity etc. the measurements records from these parameters all

comprise data.

Therefore, data may be collected by two methods, counting or taking

measurements. Data collected from counting (e.g. number of students in

SRCOE) is taken in whole number (1,2,5,8,11 and so on) and is referred to as

DISCRETE or DISCONTINUOUS data. On the other hand data collected from

taking measurements (such as blood pressure is termed as Continuous data (2.3,

2.34, 2.345) depending on the accuracy of the measuring device. It is very

important to know the kind of data one is collecting whether Discrete or

7

Continuous because it is an important determinant of the kind of statistical test

to be used for data analysis.

Population Sample and Sampling Techniques

It is difficult to collect information from the whole population due to problems

associated with natural causes of variation in Biological materials as well as

limitation of resources and time. Consequently in an investigation, information

is collected from samples.

At the time of collecting data, sampling must be made randomly without bias or

proportionately as with allocation of treatments. The size of the sample, should

also be large enough to be a good representative of the whole population. This

is to enable the researcher collect adequate information he is after. Size of the

sample can be determined by the external of the variation you are seeking in

your experiment. It is important to decide on correct sample size before the start

of the experiment.

Population Sample and Sampling Techniques

Due to limitation of resources and time as well as variation in Biological

materials, it is difficult to collect information from the whole population during

research. Therefore during investigation, information or fact are collected from

a samples. By definition, sample in defined as the time representation of entire

population, when collecting information, sampling must be made randomly in

thought bias in the size of sample must be large enough to be a good

representation of the whole population. Sampling size must be determine before

the commencement of the experiment or investigation.

Sampling Techniques

This refers to the techniques of taking a portion of the population as a

representative of that population. The researcher has to decide on whether every

8

member of the population will be studied i.e. sample. In most areas, sampling is

done when the researcher wants to generalize the findings of his/her research to

the entire population: the following techniques are employed when sampling.

a) Simple random sampling

b) Systematic sampling

c) Stratified sampling

d) Cluster sampling

• Simple Random Sampling

This is a method of selecting a sample from a population so that all members of

the population have an equal chances of being selected. This indicates that no

member of the population has been omitted deliberately except by chance. This

is most applied when the population is homogenous. For example, suppose a

researcher wants to choose 10 students at random out of a population of 50

within a given class each students has one chance of being included in the

sample.

Sampling Techniques

For some members of the population to be selected and included in a study

sample, rules and methods, have to be established. This is in order to avoid bias

on the part of the researcher. A sample should be a true representative of the

population under investigation and to achieve that it has to be taken randomly.

Random sampling ensures that every member of the population has an equal

chance of being selected as a sample. The following techniques are employed

when sampling.

a. Random Sampling: Simple random sampling is best applied where the

distribution of the organisms is homogenous, that is they are evenly

distributed. In simple random sampling, every member has an equal chance

9

of being selected and included in the sample. Randomness can be achieved

through the use of random member tables.

Stratified Sampling: Stratified sampling is applied when you are dealing with

a heterogeneous population. It involves grouping men or mutually exclusive

groups before sampling. In stratified sampling, an individual’s first of all

identifies the strata of interest and divides the population into sub-group or

strata depending on the number and types of sub-group that exist in the

population and the objectives of the study. For example stratification may

include variables of the study. For example stratification may include variables

of gender i.e. male and female, income tribe, religion etc.

b. After the researcher has divide the population into strata sub-groups, he then

uses simple random sampling to select appropriate sample size from each

stratum or sub-group, according to desire characteristic of the variables such

as sex, location academic ability etc. The idea behind using stratified

sampling techniques is to examine each sub-group separately.

c. Systematic Sampling: Systematic sampling techniques is best applied to a

homogenous population. It involves selecting samples at regular intervals or

fixed distances that are equally spaced. This is a method of selecting a

sample at fixed intervals from a population that is systematically arrange or

in an Alphabetical order or in some natural sequence. It is employed when

all the population or subjects are put in order for example systematic

sampling can be used in selecting 100 people out of 300.

Cluster Sampling: In cluster sampling, the population or habitat or field, is

divided into smaller groups or clusters and some of these cluster are randomly

selected to form the sample. In each cluster selected, every member would be

taken to be part of the sample and included in the study. In cluster sampling,

each cluster chosen must be a representative of the population. When the

population to be sampled is vast and spread over a wide geographical areas a

10

cluster sampling is used. In this type of sampling, the population is first divided

into sample units or cluster. For example states within the country, local

government area, within the state etc. Therefore some of these clusters are

randomly selected to form the sample. In each cluster selected, every member

would be taken to be part of the sample and included in the study.

• Data Presentation

Raw data, that is data recorded directly from the laboratory or field in the record

book is unorganized and because of that it make it difficult to comprehend and

draw information from it. Therefore, raw data collected from experiment have

to be properly organized summarized and present. Presented and statistical

analysed for any meaningful interpretation to be made out of it.

The first step in organizing data is the preparation of an ordered array. His

explain arranging the data in an ascending order. An ordered array enables one

to determine quickly the value of the smallest measurements and that of the

highest as well as other facts or information that may be need from the given

data. Consider the following example.

Example 1.0: Number of pods produced per plant by certain species of legume

in Kadawa research station.

69 74 71 74 71 71

69 72 72 78 72 68

70 67 72 70 75 72

71 70 74 73 75 75

75 74 74 73 74 72

67 76 75 75 68 78

11

69 68 75 78 69 78

73 69 75 68 71 78

The fact that the above data is unorganized make it difficult to draw information

from it, and so an ordered array can be prepared as follows: -

Table 1.0

67 67 68 68 68 68

69 69 69 69 69 70

70 70 71 71 71 71

71 72 72 72 72 72

72 73 73 73 74 74

74 74 74 74 75 75

75 75 75 75 75 75

76 78 78 78 78 78

From this ordered array one can easily find out the minimum number of

pods/plant (67) or the maximum (78).

However an ordered array may not be adequate in offering all the information

that are needed from the data obtained. Therefore further summary may be

required and one way is by tabulating your data according to frequencies.

• The Frequency Distribution

Classifying data according to frequencies enables further summary as well as

facilitates the computation of various descriptive measures like the percentages,

12

average and so on. To get the frequency of number, the first step is to get the

range of the figures in the table and then you take a tally and record the score of

each number that is the frequency of occurrence of each number. In example

1.0, the range is from 67 to 78 and the frequencies are obtained as followed:

Table 1.2: A tally of frequency of occurrence number of pods/plant

No. of Pods/plant Tally Frequency

67

68

69

70

71

72

73

74

75

76

77

78

II

III

IIII

IIII

IIII I

III

III

IIII I

IIII III

I

0

IIII

2

4

5

4

6

4

3

6

8

1

0

5

TOTAL 48

This frequency can then be presented in a table which is referred to as frequency

distribution table.

Table 1.3: Frequency distribution of the number of pods produced plant

No. of Pod/Plant (x) Frequency (f) Relative frequency (%)

67

68

2

4

2/48 x 100 = 4.17%

4/48 x 100 = 8.33%

13

69

70

71

72

73

74

75

76

77

78

5

3

5

6

3

6

8

1

0

5

5/48 x 100 = 10.42%

3/48 x 100 = 6.25%

5/48 x 100 = 10.42%

6/48 x 100 = 12.50%

3/48 x 100 = 6.25%

6/48 x 100 = 12.50%

8/48 x 100 = 16.67%

1/48 x 100 = 2.08%

0/48 x 100 = 0.00%

5/48 x 100 = 10.42%

Total 48 100%

• Cumulative Frequency

This is usually derived from the frequency distribution table by summing up the

observed frequencies. It gives way of obtaining information regarding the

frequency or relative frequency of value with two or more contiguous

observation or group. From example 1.0 the following cumulative frequency

distribution can be obtained.

Table 1.4: Cumulative frequency of number of pods/plant

No. of Pods/Plant

(x)

Frequency (f) Cumulative

frequency

Cumulative relative

frequency

67

68

69

70

71

72

2

4

5

3

5

6

2

6

11

14

19

25

4.1

12.5

22.9

29.2

39.6

52.0

14

73

74

75

76

77

78

3

6

8

1

0

5

28

34

42

43

43

48

58.3

70.8

87.5

89.6

89.6

100.0

The frequency distribution for group data

Another method of summarising a data is by classifying it into groups or classes

from which the various descriptive measures can be easily calculated. To group

data the first step is to select a class interval such that each value is placed in

only one interval bearing in mind that there can be not less than 6 intervals and

not more than 15. There are two methods of classification; exclusive which is

best for describe data and inclusive which is ideal for continuous data.

Example 2.0 the weight of all NCE II research method and biometry students

are measured and the results is expressed to the nearest kilogram (kg) as

follows: 100, 95, 85, 75, 80, 78, 90, 93, 109, 104, 88, ...... (the dots represent

value not shown) assuming we have 100 such measurement. The measurement

can be seen to range from lowest value of 75kg to a higher value of 109kg. If

we collect together the value in groups such that each value is placed in only

one class interval a frequency distribution.

Table 2.0: Frequency distribution of weight of NCE II Research method

and Biometry students.

Class interval of weight of students (kg) Frequency (f)

75 – 79

80 – 84

2

2

15

85 – 89

90 – 94

95 – 99

100 – 104

105 – 109

7

11

28

30

20

Total 100

Histograms: This is a graph of frequency or relative frequency distribution

plotted in a form of rectangle or bars continuous data is best represented in the

form of histogram.

Bar-

chart:

This represent the frequency distribution of describe data and because the data

is discontinuous, bar and columns are form, and exclusive type of classification

is used.

Example: Let us assume we have 37 observations on number of flowers

produced per plant as follows: -

Table 3.0: Frequency distribution of number of flowers/plant

16

Class interval of no. of flowers/plant Frequency (f)

1 – 5

6 – 10

11 – 15

16 – 20

21 – 25

26 – 30

3

5

8

4

7

10

Total 37

A bar chart can be drawn from the above illustration

Line Graphs: These changes in one variable in relation to another variable. In

this case we have;

Y = vertical axis as dependent variable. Dependent variable is the one which is

not under the control of the experimenter, it changes in response to changes in

the independent variable.

X = horizontal axis, and is the independent variable, which ............

Example: Measurement on height of maize plant were taken and the data

presented in the table below:

Table 4.0: Height of maize plant at different number of days after planting.

Time in days x (Independent variable) Heights (cm) y (Dependent variable)

20

40

60

80

25

50

75

100

17

100 125

A line graphs of maize plants height could be drawn as follows:

Data may be organized and summarized through the following processes.

1. Organize the data by putting them in tables such as frequency tables, and

other forms of summary tables.

2. Illustrate the data using graphs such as histograms, bar charts line graphs etc.

3. Analyze the data using mathematical approach.

Once the data is summarized an appropriate statistical test can be carried out in

order to draw conclusion about the investigation.

Example: The number of flowers produced per plants by rose plants in garden

are as follows:

18

6 3 6 7 8 4 6 7 8 4

9 8 9 5 7 8 9 5 7 8

8 5 7 8 10 6 7 8 6 7

The data above can be organized by constructing

a) A frequency distribution table

b) Relative frequency distribution

MEASURES OF CENTRAL TENDENCY

They are also known as measures of location. There are three most commonly

used measures and these are; mean, median and mode. These measurement

provide a general idea of the position of the center of a distribution.

The Mean

The most common of the measures of central tendency is the average or in

mathematics term, the arithmetic mean or simply the mean. This is achieve by

adding up all the observations and dividing by the total number of

measurements obtain; thus:

Mean = Sum of observation

Total number of observation

The mean is donated by X (x-bar). The general formula for the calculation of

sample mean can be given as:

X = ∑𝑥

𝑛

Where X represents the variable

∑ = summation sign n = number of observation

∑𝑥 = x1 + x2, x3 ............... xn

19

Example 3.0: To compute the mean of the number pods produced plant of 48

plants represented in table 1.0, which is a set of unsummarised measurements,

we simply add them all up and divide by the total number.

X = ∑𝑥

𝑛 = 69 + 74 + 71 .................. 71 + 78

48

= 3477

48 = 72.438

X = 72.44

Median

To calculate the median, the data has to be arrange in an array, in an increasing

order of size. When this is done then the median is the value which divide a set

of values into two equal parts. When the numbers are odd, the median is the

central or middle value, but when they are even, then it became mean of the two

central figures. In others words median can be defined as:

n = 1

2

Therefore, if we have 15 observations, the median is the (15+1

2) = 8th ordered

observation. If we have 16 observation, then it the (15+1

2) = 8.5 ordered

observation and this implies that the value is half way between the 8th and the

9th observation. You therefore take the average of the 8th and 9th observation as

your median.

Example 4.0: Taking the data presented in table 1.0 for illustration, since the

value are already arranged in a sequence and it is an even number, the median is

therefore the:

𝑛+1

2 =

48+1

2 =

49

2 = 24.5th value

Therefore we take the two middle values which are 72 and 72.

20

The median therefore is 72+72

2 = 72

The Mode

It is defined as the most commonly occurring value in a data. Thus if all the

figures are different e.g. 5, 6, 11, 15, 8 then there is no mode. Alternatively it is

possible to get more than one mode e.g. 5, 5, 6, 8, 8, 9; here 5 and 8 are the

modes.

Example 5.0: The mode of the data presented in table 1.0 is 75. This is because

it occurs most frequently (8 times).

MEASURES OF DISPERSION

The observation making up a set of data are scattered about the mean. This

scatter or dispersion reveals the degree of variability present in a set of

measurements. If all values are the same, then there is in dispersion in the data.

If on the other hand, the value are not these then there is dispersion, and the

amount of dispersion depend on spread of the figures, that is how close together

or how scattered, they are:

The main measures of dispersion encountered in biological estimates include

the followings:

a) Mean deviation

b) Variance

c) Standard deviation

The Mean Deviation

Dispersion can also be assessed by calculating deviation from the mean since

the mean is a very useful measure of central tendency. The sum of the deviation

from the mean is always zero, so one has to ignore the negative sign, since it is

not used in Biology. The contributions an observation (x) to scatter is equivalent

to its distance from the mean, i.e. X – X. Deviation from the mean (MD) can be

calculated using this equation.

MD = ∑(X – X) Where X = observation

21

n X = mean

n = No. observation

Example 6.0: Let us select a range of 5 figures from the observation on number

of pods produced/plant in table 1.0. These are 67, 70, 75, 78, 68. To calculate

Mean Deviation (MD), we to first of all calculate the mean: as thus:

X = ∑X = 67 + 70 + 75 + 78 + 68 = 358

n 5 5 = 71.6

MD = (67 – 71.6) + (70 – 71.6) + (75 – 71.6) + (78 – 71.6) + (68 – 71.6)

5

= (-4.6) + (-1.6) + (3.4) + (6.4) + (-3.6)

5

Ignoring the minus signs

MD = 19.6 = 3.92

5

The Variance

As ready mentioned that the amount of variation in a given data depends on

how close or scattered the values are from the mean. The closer they are to the

mean the less the dispersion while the further they are from the mean, the

greater the variation. Therefore it is common to measure dispersion relative to

the scattered of the value about their mean. One measure through which this is

achieved is through the computation of the VARIANCE. Variance is the sum of

the squares (S2) of the deviations of the values from the means divided by the

size of the sample (n) minus 1. If it is a population, you divide by the size of

population (N). The procedure for the computation of variance is therefore, to

compute the mean, then subtract the mean from each of the values, square the

resulting differences, sum up the squared differences and divide by the size of

the sample or population. The variance of a sample can be represented as

follows:

22

𝑆2 = ∑(𝑥−𝑥)2

𝑛−1.........................................(1)

When you have a large data the computation of sum of squares from the above

equation can be tedious, and so an alternative formula, which may be less

familiar can be adopted. This is

𝑆2 = ∑𝑋2−(£𝑥)2

𝑛 (𝑛−1)......................................(2)

Example 7.0: Let us compute the variance of the sample discussed in example

6.0. we substitute the value in the first equation.

𝑆2 = (67 – 71.6)2 + (70 – 71.6)2 + (78 – 71.6)2 + (68 – 71.6)2

5 – 1

𝑆2 = (-4.6)2 + (-1.6)2 + (3.4)2 + (6.4)2 + (-3.6)2

4

𝑆2 = 89.2

4 = 22.3

The fact that n – 1 is used in the division instead of n as would have been

expected is due to a concept known as degree of freedom (df).

The Standard Deviation

This is the positive square root of the variance and therefore has the same unit

of the original measurement unlike the variance. Standard deviation of the

sample is given as:

𝑆 = √∑(𝑥−𝑥)2

𝑛−1

Or the alternative formula for a large data;

𝑆 = √∑𝑥2−(∑𝑥)2

𝑛(𝑛−1)

Example 8.0: To compute the standard deviation of the sample discussed in

example 7.0. Since the variance (S2) of the same sample has already been

calculate in example 7.0 and it is 22.3 it follows that the standard deviation (S)

is.

23

𝑆 = √22.3

ᵟ = 4.722

Mean, Variance and Standard Deviation for a Grouped Data

You may wish to compute the mean and variance from a frequency distribution

table. In this case you assume that all values falling in a particular class interval

are placed at the mid-point of the class interval. To determine the mid-point of a

class interval, the average of the lower and upper and limits of the class interval

is calculated and that taken as the mid-point (X). It is good to prepare a

worktable as follow for convenience and ease in calculation.

1. The Mean

To complete the mean, the mid-point (x) of each class is multiplied by its

corresponding frequency (f) and divided by the sum of the frequencies (∑f).

This is represented as follows:

X = ∑𝑓𝑥

∑𝑓 = ....................................... for group data

MD = ∑(𝑋−𝑋)𝑓

∑𝑓.................................. for group data

Variance for grouped data

𝑆2 = ∑(𝑥−𝑥)2𝑓

∑𝑓−1

Standard deviation for grouped data

𝑆 = √∑(𝑥−𝑥)2𝑓

∑𝑓−1

Example 8.0: Let us compute the mean, mean deviation, variance and standard

deviation of the weight of NCE II research Method and Biometry students

presented in the frequency distribution table (2.0). The work table is shown as

follows: -

Table 5.0: Workable for calculating the mean, mean deviation, variance and

standard deviation from frequency data of table 2.0.

24

Class

Interval

Frequency

(f)

Mid-

point (x)

fx x-x (x-x)2 (x-x)2 f

75 – 79

80 – 84

85 – 89

90 – 94

95 – 99

100 – 104

105 – 109

2 3

2 2

7 5

11 12

28 30

30 32

20 21

77

82

87

92

97

102

107

154

164

609

1012

2716

3060

2140

-21.5

-16.5

-11.5

-6.5

-1.5

3.5

8.5

462.3

272.3

32.3

42.3

2.3

12.3

72.3

924.6

544.6

926.1

465.3

64.4

369

1446

Total 100 9855 4740

1. X = ∑𝑓𝑥

∑𝑓 =

9853

100 = 98.5

2. MD = ∑(𝑥−𝑥)𝑓

∑𝑓 =

545.0

100 = 5.5

3. 𝑆2 = ∑(𝑥−𝑥)2𝑓

∑𝑓−1 =

4740

100−1 =

4740

99 = 47.88

4. ᵟ = √

∑(𝑥−𝑥)2𝑓

∑𝑓−1 = √47.88 = 6.92

MEASURES OF RELATIONSHIP

1. The Chi-Squared Test

The statistical tests discussed in the previous sections are used to analyse

differences between mean or to determine relation between two variable

collected from every member of the population. The tests described are

considered when the data collected is from continuous variables like height,

weight, blood pressure age, yield e.t.c alternatively referred to as quantitative

date but there are discrete date which cannot be measured but counter. In such, a

ratio is found out known as the chi-squared (with the symbol x2) to goodness of

fit. There are experiments that collect qualitative date, similarly such research

25

seeks to determine association between two factors such as seedling vigor and

leaf colour or eye colour and hair colour or flower pigmentation and seed

germination and so on. In this case a contingency table is formed and chi-

squared X2 is used to determine whether or not there is association between the

factors. The X2 – test is also used to compare two proportions or percentages. It

may be regarded as a non-parametric test as it does not require detailed

information about the population from which the samples are drawn.

Test of Goodness of Fit

In situation where the basis of a hypothesis, which specifies the frequency of

occurrence of an observation, it is tested, the test of goodness of fit is used. It is

therefore frequently used in genetic studies. It is used to test whether the

outcome of a breeding experiment in line with the predicted mendelian rations.

In testing goodness of fit, the X2 determines how close the observes frequencies

are to those expected on the basis of a hypothesis. It is calculated using the

following expression;

X2 = ∑(𝑂−𝐸)2

𝐸

The computed value is compared with the table value of X2 at n-1 degree of

freedom. Goodness of fit test may involve one – way classification in which the

frequencies fall into only two classes that are mutually exclusive and then is the

simplest test. Or the test may also involve more than two classes.

Example 9.0: Test of goodness of fit with two classes.

In a determination of sex ratio among a sample species of birds, it was

discovered that out of 5000 birds, 378 were male. Does this sample conform to

the one male: one female ratio, that is 1.1?

Solution

Sex Male Female Total

Observed no. of bird

Expected no. of bird

378

250

122

250

500

500

26

O – E

X2 = ∑(O-E)2 /E

128

65.5

-128

65.5

0

121.0

Therefore the calculated value (131.0) exceeded the table value at 500% and 1

d.f. (that is 3.481) and even at 1& on the same do (that is 6.635), the difference

is highly significant. We therefore conclude that this sample does not confirm to

the 1:1 ratio.

Example 10.0: Test of goodness of fit with more than two classes.

Suppose a cross-involving two cowpea varieties (smooth white and rough

brown) show the ratio of 9:3:3:1, if a sample of 550 or observations give the

following frequencies 305 smooth white (sw), 110 smoth brown (sb), 105 rough

white (rw) and 30 rough brawn (br). Test whether this agrees with the given

ratio.

Solution

If the given ratio applies, it follows that the expected frequencies in the four

groups will be.

psw = 9/16 x 550; psb = 3/16 x 550; psw 3/16 x 550; prb = 1/6 x 440

respectively, where p stands for probability. The sum of the expected

frequencies must be the same as that of the observed frequencies the next step is

to construct the table of observed and expected frequencies in the following

way.

Phenotype category 1

sw

9

2

sb

3

3

rw

3

4

rb

1

Total

Observed frequency (O)

Expected frequency (E)

305

309.42

110

103.14

105

103.14

30

34.38

550

500

27

O – E

X2 = ∑(O-E)2

E

-4.42

0.06

6.86

0.46

1.86

0.03

-4.38

0.56

1.11

28

PROJECT REPORTING

Once the research has been carried out and the data is analyzed the researchers

has to write the research report or project report. The project report essentially

consist of the following parts:

a) Preliminary part of the report

b) The main body of the report.

c) Reference section.

Preliminary Part of the Project Report

This section should contain all or some of the following items in the

following order.

i. Cover page

ii. Certification page

iii. Title page

iv. Approval page

v. Abstract

vi. Acknowledgement

vii. Table of content

viii. List of tables

ix. List of figures (if any)

x. List of appendices (if any)

The manner of presentation of the preliminary pages in the project report is as

follows:

1. Cover Page: The cover page is the first page of the report. It contain the title

page of the project, full names of the authors and the month and year of

completion of the report.

29

2. Titled Page: This page covers information on the title of the project the

student’s full name, the degree, diploma or certificate for which the project is

submitted as well as the month and the year of submission of the project.

3. Certification Page: This page shows a statement signed by the supervisor to

the effect that materials recorded in the project report resulted from the

research originally carried out by the student.

4. Approval Page: This page contains a statement signed by the examiner, the

head of Department and the students’ supervisor to the effect that the student

has satisfied the requirements for acceptance of the project for the award of

NCE.

5. Abstract: An abstract is a summary of the research report and should not be

lengthy, it should contain in summary from the objectives of the study,

characteristics of the subject, and the method used, the finding of the study

and the conclusion reached by the researcher.

6. Acknowledgement: In this section, the researcher express his/her gratitude

and indebtedness to individuals institutions or organization who provided

one form of assistance or the other during the execution of the work e.g

financial support, review and /or manuscript, and assistance in conducting

the research and/or prepares the manuscript.

7. Table of Content: Table of contents consists of the list of main topics in the

research report beginning with the abstract and end in with appendices, it

also contains the first page of each of the topics listed. The table of content

enables the reader to locate without difficulty any topic of interest to him in

the research report.

8. List of Figure: All figures (if any) in the project one also listed, showing

titles and indicating the pages where they appear.

Main Body of Project Report

The main body of project report is divided into six major section.

30

1. Introduction

2. Literature review

3. Research Methodology

4. Analysis and presentation of result

5. Discussion, conclusion and recommendation

6. Reference and appendices.

Section 1 to 5 above are ordinary referred to as chapter section six is

separated after the fifth chapter into reference and appendices respectively.

1.0 Chapter One: Introduction

The title of the first chapter of the project report is the introduction it is divided

into the following sub-headings

a. The background of the problem

b. The statement of the problem

c. The purpose of the study/objectives of the study.

d. The importance/significance of the study.

e. The statement of hypothesis

f. Definition of terms.

2.0 Chapter Two: Literature Review

This referred to as review of literature. In this, one tries to summarize the

related literature previously written about the topic she/he is writing on. It gives

a background on what is to be written about in the research. The review of

literature often from a critical analysis of what is written before the researcher

came out with his/her view.

3.0 Chapter Three: Research Methodology

The third chapter is the methodology it compresses the following sub-heading.

31

3.1 Research Design: The researcher explain the general approach adopted in

executing the study. i.e he/she has to specifically explain the type of the

design followed in the study.

3.2 Area of Study: This refers to the geographical location covered by the

study which is usually stated in terms of country, state, education,

political or administrative zone, local government etc.

3.3 Population: The researcher specify the number of persons or items from

whom data related to the study were collected.

3.4 Sampling & Sampling Procedure: Cleary one has to inform the reader

about the sample used, how it was obtained including the sampling

techniques used.

3.5 Instrument for Data Collection: This involves giving detailed description

of the instrument used in collecting the date how the instrument was

developed and the major features of the instrument.

3.6 Method of Data Collection: The researcher reports the statistical

techniques tools employed in analyzing the data.

4.0 Chapter Four: Result Analysis and Presentation

This chapter presents the data and statistical analysis without discussing the

implication of the result. These are usually presented in tables, figures and

chart. It is advisable to present the result according to the research question or

hypothesis to which they relate.

5.0 Chapter Five: Discussion, Conclusion and Recommendation

5.1 Discussion: The researcher tries to discuss the findings and relate to the

findings of previous works.

5.2 Conclusion: Should indicate to major findings from the study.

32

5.3 Recommendation: The researcher should suggest action which could be

taken in the light of findings in ordered to bring improvement in the system.

Reference Section

The last section of a researcher report in followed by the list of references

and then appendices (if any).

Reference consist of all documents, including journals article books,

website and unpublished works that are cited in the project.

Appendix: The researcher includes any information/materials that might

have been bulky to be put in the context of the report. These might

include questionnaire design and tables.

Important Information: In research, the researcher has to use an

objective language and avoid personal pronouns like I, me, ours, or any

other personal references eg. I selected ten student from any sample

(irony) is better put it thin why. Ten students were selected.

General Guidelines for Writing References in Project Report

1. Surnames of authors to be written first before the appreciate initials e.g

Abdullahi, I.I.

2. The date of the work cited should be written in bracket e.g immediately in

front of the last initial of the author e.g Abdullahi I.I (2011).

3. Ensure that the surname of authors are arranged alphabetically in line

with APA style.

4. When references are from journal article the name of the journal should

be under line, the volume of the journal as well as the number of the

pages from the journal should be indicated.

33

When references come from text book, the name of the publishing company of

the book should be stated.