Business Research Methods PPT -IV

Business Research Methods
Unit - IV
Dr. Ravindra
Associate Professor
Department of Commerce
Indira Gandhi University,
Meerpur, Rewari

Analysis of Variance (ANOVA)
Introduction
The analysis of variance frequently referred to by the
contraction ANOVA is a statistical technique specially
designed to test whether the means of more than two
quantitative populations are equal.
The analysis of variance technique, developed by R.A. Fisher
1920’s is capable of fruitful application to a diversity of
practical problems. Basically, it consists of classifying and
cross-classifying statistical results and testing whether the
means of a specified classification differ significantly. In this
way it is determined whether the given classification is
important in affecting the results. For example, the output of a
given process might be cross-classified by machines and
operators. From this cross-classification, it could be determined
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Dr. Ravindra, IGU, Meerpur

whether the mean qualities of the outputs of the various
machines differed significantly. Also it could
independently be determined whether the mean qualities
of the output of the various machines differed
significantly. Such a study would determine, for example,
whether uniformity in quality of output could be increased
by standardizing the procedures of the operators and
similarly whether it could be increased by standardizing
the machines. Analysis of variance thus enables us to
analyze the total variation of our data into components
which may be attributed to various ‘sources’ or ‘causes’
of variation.
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The reader should keep in mind that the analysis of variance
test discussed here is not intended to serve the ultimate
purpose of testing for the significance of the difference
between two sample variances; rather its purpose is to test for
the significance of the differences among sample means. They
do this via the mechanism of the F-test for testing for the
significance of the difference between two variances, but the
test is so designed that the variances being compared are
different only if the means under consideration are not
homogeneous. In this way, significant values of F indicate
that the means are significantly different from one another.
Total Variance = Variance Between Samples + Variance Within Samples
(SST) = (SSB) + (SSW)

Definitions
1. According to R. A. Fisher, “The separation of the variance
ascribable to one group of cases from the variance
ascribable to other group.”
2. According to Owen Davies, “The analysis of variance is
essentially a method of analyzing the variance to which a
response is subject, into its various components
corresponding to the sources of variation which can be
identified.”
Assumptions of Analysis of Variance
1. Variance of all component must be equal to the total variance.

2. Sample should be selected randomly.
3. Each population under study is normally distributed.
4. The value of F is always be positive, because it is calculated
from the square values.
5. The value of F is always greater then 1, because, largest
variance is divided by smaller variance.
Techniques of Analysis of Variance
Techniques of Analysis of Variance is divided into two part;
1. One-way classification.
2. Two-way classification

1. One-way Classification: In one way classification the data
are classified according to only one criterion. The null
hypothesis is;
Ho: µ1 = µ2 = µ3 . . . . . . . . .= µk
H1: µ1 = µ2 = µ3 . . . . . . . . .= µk. All the means are not
equal.
The calculation of total variance may be carried out in each
of the two types of classification by;
• Direct method
• Short-cut method
• Coding method.

• Direct Method: The steps in calculating the variance is;
(a) Variance Between samples
(i) Calculate the mean of each sample i.e. X1, X2, X3 etc.
(ii) Calculate the grand average X, pronounced ‘X double
bar’. Its value is obtained as follows:
X1 + X2 + X3 + . . .
X =
K
(iii) Take the difference between the means of the various
samples and the grand average. Square these deviations
and obtained the total which will give sum of squares

between the samples; and calculate Sum of Square
between samples (SSB).
SSB = n1 (X1 – X1)2 + n2 (X2 – X2)2 + n3 (X3 – X3)2 . . . +
nk (Xk – X)2

(iv) Divide the total obtained in step (iii) by the degree of
freedom and obtained variance between samples and
called it MSB. MSB = SSB ÷ (K – 1)
Degree of freedom = K – 1
K = the number of samples.
(b) Variance Within Sample
(i) Calculate mean value of each sample i.e. X1, X2, X3 etc.
(ii) Take the deviations of the various items in a sample
from the mean values of the respective samples and

these deviations and obtained the total which gives the sum of
square within the sample.
∑(X1 – X1)2 + ∑(X2 – X2)2 + ∑(X3 – X3)2 + . . . .∑(Xk -Xk)2
(iii) Divide the total obtained in step (iii) by the degrees of
freedom. The degree freedom is obtained by deduction from the
total number of items the number of samples i.e. v = N – K,
where K refers to number of samples and N refers to total
number of all the observations.
Calculate the ratio F as follow:
Between column variance Largest variance (V1)
F = or
Within column variance Smallest variance (V2)

Decision Criterion
Compare the calculated value of F with the table value of
F for the degrees of freedom at a certain critical level i.e.
5% or 1%. If the calculated value of F is greater than the
table value, it is concluded that the difference in sample
means is significant, i.e. it could not have arisen due to
fluctuations of simple sampling or, in other words, the
samples do not come from the sample population. On the
other hand, if the calculated value of F is less than the
table value, the difference is not significant and has arisen
due to fluctuation of simple sampling.

Table value can be calculated using V1 (degree of freedom of
largest variance) and V2 (degree of freedom of smallest variance).
Analysis of Variance Table
Analysis of Variance Table (ANOVA)
Sr.
No.
Source of
Variance
Degree of
freedom
Sum of
square
Variance F - ration
1. Between
samples
k – 1
∑[ n(X – X)2]
SSB
∑[ n(X – X)2]/ K - 1
MSB
F =
MSB/MSW
or
2 Within
samples
N – K ∑(X – Xk)2
SSW ∑(X – Xk)2 / N – K
MSW
F =
MSW/MSB
Total N – 1
∑(X – X)2
SST
∑(X – X)2 / N – 1
SST

Illustration: The following table gives the results of
experiments on four varieties of a crop in 5 blocks of
plots;
Prepare table of analysis of variance to test the
significance of difference between the yield of the four
variety.
Variety Block
1 2 3 4 5
A 32 34 33 35 37
B 34 33 36 37 35
C 31 34 35 32 36
D 29 26 30 28 29
Total 126 127 134 132 137

Solution: lets take the null hypothesis that all means are
equal at 5 % level of significance.
X1 (X1 –
X1)
(X1 –
X1)2
X2 (X2 –
X2)
(X2 –
X2)2
X3 (X3 –
X3)
(X3 –
X3)2
X4 (X4 –
X4)
(X4 –
X4)2
32 -2.2 4.84 34 -1 1 31 -2.6 6.76 29 0.6 0.36
34 -0.2 0.04 33 -2 4 34 0.4 0.16 26 -2.4 5.76
33 -1.2 1.44 36 1 1 35 1.4 1.96 30 1.6 2.56
35 -0.8 0.64 37 2 4 32 -1.6 2.56 28 -0.4 0.16
37 2.8 7.84 35 0 0 36 2.4 5.76 29 0.6 0.36
171 14.80 175 10 168 17.20 142 9.20

(i) Calculate the mean of the samples;
171 175 168 142
X1 = X2 = X3 = X4 =
5 5 5 5
= 34.2 = 35 = 33.6 = 28.4
(ii) Now calculate the combined mean;
34.2 + 35 + 33.6 + 28.4
X = = 32.8
4

Variance between samples (SSB)
SSB = n1 (X1 – X)2 + n2 (X2 – X)2 + n3 (X3 – X)2 . . . + nk
(Xk – X)2
SSB = 5 (34.2 – 32.8)2 + 5 (35 – 32.8)2 + 5 (33.6 – 32.8)2 +
5 (28.4 – 32.8)2
= 5(1.4)2 + 5(2.2)2 + 5(0.8)2 + 5(-4.4)2
= 9.80 + 24.20 + 3.20 + 96.80 = 134 134
Degree of freedom v = K – 1 = 4 – 1 = 3, MSB = = 44.67
3
SSW = ∑(X1 – X1)2 + ∑(X2 – X2)2 + ∑(X3 – X3)2 + . . . .∑(Xk -Xk)2

SSW = 14.80 + 10 + 17.20 + 9.20 = 51.20
Degree of freedom v = N – K = 20 – 4 = 16
MSW = SSW/ N – K = 51.20/ 16 = 3.2
Source of
Variance
Degree of
Freedom
Sum of
Square
Variance F- Ratio
Variance
between
samples
K – 1
3
SSB = 44.67 MSB =
SSB/K – 1
14.89
F- ration =
MSB/MSW
Variance
within
samples
N – K
16
SSW = 51.20 MSW =
SSW/N – K
3.2
= 14.89/ 3.2
F = 4.65
Total N – 1
19
F0.05 = V1/V2
3/16 = 3.24

The calculated value of F is 4.65 and the table value of
F0.05 with V1 = 3 and V2 = 16 is 3.24. Therefore, the
hypothesis is rejected, it means there is significance
difference among the productivity of four verities.
• Short-cut Method for One-way ANOVA
ANOVA can be performed by following the short-cut
method which is usually used in practice since the same
happens to be a very convenient method, particularly
when means of the samples and /or mean of the samples
means happen to be non-integer value. The various steps
involved in the short-cut method are as under:

(i) Take the total of the values of individual items in all the
samples i.e. work out; ∑X1 + ∑X2 + ∑X3 + ∑X4 + . .
(ii) Take the total of the square values of individual items in
all the samples i.e. ∑X12 + ∑X22 + ∑X32 + ∑X42 + . .
(iii) Calculate the correction factor using the following
formula; [∑X1 + ∑X2 + ∑X3 + ∑X4 + . . ]2 [T]2
C = =
N N
T = total of all items.

(iv) Calculate total sum of square by using the following
procedure; [T]2
SST = [∑X12 + ∑X22 + ∑X32 + ∑X42 + . .] –
N
(v) Calculate sum of square between samples (SSB) by using
the following procedure;
(∑X1)2 (∑X2)2 (∑X3)2 (∑Xk) 2 [T]2
+ + + -
n1 n2 n3 nk N

(vi) Calculate some of square within samples (SSW) by using
the following procedure;
Sum of Square Within Sample =
Total Sum of Square – Sum of Square Between Samples
SSW = SST – SSB
(vii) Prepare ANOVA table.
(viii) Calculate variance ratio i.e. F – ratio.
Largest Variance
F – ratio =
Smallest Variance

Illustration: The table below gives the yield of four
varieties of wheat in six blocks.
Test the significance of difference between the yield of the
four varieties.
Varity 1 2 3 4 5 6
A 12 16 15 17 20 25
B 14 12 20 22 18 23
C 11 14 18 15 21 18
D 7 11 15 12 19 16

Solution: Lets take the null hypothesis that there is no
significance difference among the yield of verities, at 5%
level of significance.
(i) Calculate the value of T = ∑X1 + ∑X2 + ∑X3 + ∑X4
105 + 109 + 97 + 80 = 391
(ii)Calculate the correction factor (T)2 / N
= (391)2 / 24 = 6370
(iii) Calculate total sum of square (SST).
SST = [∑X12 + ∑X22 + ∑X32 + ∑X42] - (T)2 / N
SST = [1939 + 2077 + 1631 + 1156] – 6370 = 433

A B C D
X1 X12
X2 X22
X3 X32
X4 X42
12 144 14 196 11 121 7 49
16 256 12 144 14 196 11 121
15 225 20 400 18 324 15 225
17 289 22 484 15 225 12 144
20 400 18 324 21 441 19 361
25 625 23 529 18 324 16 256
105 1939 109 2077 97 1631 80 1156
∑X1 ∑X12
∑X2 ∑X22
∑X3 ∑X32
∑X4 ∑X42

(iv) Calculate the value of SSB.
(∑X1)2 (∑X2)2 (∑X3)2 (∑Xk) 2 [T]2
SSB = + + + -
n1 n2 n3 nk N
(105)2 (109)2 (97)2 (80)2
= + + + - 6370
6 6 6 6
= 1837.5 + 1980.1 + 1568.1 +1066.6 – 6370
= 6452.3 – 6370 = 82.3

(v) Calculate sum of square within sample (SSW).
SSW = SST – SSB = 433 – 82.3 = 350.7
Analysis of Variance Table (ANOVA)
The calculated value is less than table value, therefore,
null hypothesis is accepted.
Source of
Variance
Degree of
freedom
Sum of square Mean sum of
square
F-ratio
Between
Samples
K – 1
4 – 1 = 3
SSB
82.3
MSB
27.4
F = MSB/ MSW
V = V1 / V2= 3/20
F = 27.4/ 17.53
= 1.563
F0.05 = 3.10
Within
Samples
N – K
24 – 4 =20
SSW
350.7
MSW
17.53
Total N – 1
24 – 1 = 23
SST
433

• Coding Method: In the above method, computational
time increases when numerical values of observations are
in more than one digit. Since F-test statistic is the ratio of
variances without unit of measurement, its value does not
change when an appropriate constant value is either
multiplied, divided, subtracted and added to each of the
observations in the sample data. This adjustment reduces
the digits of numerical values in the sample data and
hence reduces computational time to calculate F-value
without any change.
Illustration: Set up a table of Analysis of Variance for the
following data:

Test whether the varieties are different?
Solution: Let 200 be deducted from each sample value
and dividing the difference by 10, we get the following
table;
(i) Calculate the value of T = ∑X1 + ∑X2 + ∑X3 + ∑X4
Plot Variety
A B C D
1 200 230 250 300
2 190 270 300 270
3 240 150 145 180

T = 3 + 5 + 9.5 + 15 = 32.5
C = (32.5)2 / 12 = 88.02
SST = 17 + 83 + 155.25 + 153 – 88.02 = 320.23
A B C D
X1 X12
X2 X22
X3 X32
X4 X42
0 0 3 9 5 25 10 100
-1 1 7 49 10 100 7 49
4 16 -5 25 -5.5 30.25 -2 4
3 17 5 83 9.5 155.25 15 153

SSB = (3)2 /3 + (5)2 / 3 + (9.5)2 / 3 + (15)2 / 3 – 88.02
= 28.39
SSW = SST – SSB = 320.23 – 28.39 = 291.84
Source of
Variance
Degree of
freedom
Sum of
Square
Variance F-ratio
Between
samples
K – 1
4 – 1 = 3
SSB
28.39
SSB÷ K-1
MSB= 9.4
F = MSW/MSB
V1/V2= 8/3
Within
sample
N – K
12 – 4 = 8
SSW
291.84
MSW: SSW
÷N – K=
36.48
36.48/9.4
= 3.88
Total N – 1
12 -1 = 11
SST
320.23
F0.05 = 8.85

The calculated value 3.88 is less than the table with V1 = 8
and V2 = 3 is 8.85. Therefore, the null hypothesis is
accepted.
2. Analysis of Variance in Two Way Classification
We have studied that in one way classification the data are
classified according to one factor or the influence of one
factor on different sample group. But two way
classification refers to data according to two factors or
influence of two factors on sample groups. For example,
the production of a manufacturing concern can be studied
on the basis of workers as well as machines. A company
can analyze its sales according to salesmen and seasons.

In two way classification, the analysis of variance is
studied in following three parts;
(i) Sum of Square Between Column (SSC)
(ii) Sum of Square Between Rows (SSR)
(iii) Residual Variation (SSE)
SST = SSC + SSR + SSE
Following steps should be followed to calculate Variance
ratio (F) in the case of Two Way Classification.
(i) Coding method can be used to simplify the calculations.
(ii) Calculation of Correction Factor

(T)2
Correction Factor (c. f.) =
N
(iii) Total Sum of Squares (SST): It is obtained by subtracting
correction factor from the total of squared values of the
sample, i.e.
SST = [∑X12 + ∑X22 + ∑X32 + ∑X42] - (T)2 / N
(iv) Sum of Square Between Columns (SSC): The total of each
column is squared and divided by the number of items in the
respective column. The correction factor is subtracted from
the total of thus arrived values and SSC is obtained:

(∑Xc)2 (T)2
SSC = ∑ -
nc N
Where; (∑Xc)2 = Total of squared values in each column.
nc = Number of items in each column.
(v) Sum of Squares Between Rows (SSR): The total of the
sample values in each row is squared and divided by the
number of items in the respective row. From the total of
the of the values thus arrived correction factor is deducted

and remaining is known as sum of squares between rows or
SSR.
(∑Xr)2 (T)2
SSR = ∑ -
nr N
Where; (∑Xr)2 = Sum of the Squared Value of each row.
nr = No. of items in each row.
(vi) Sum of the Squares of the Residual (SSE): The sum of the
squares of the residual is obtained by deducting the sum of
squares between columns and sum of squares between rows

from the total sum of squares:
SSE = SST – SSC – SSR
(vii) Number of Degree of Freedom: It is calculated as follows:
No. of degrees of freedom between column = (c – 1).
No. of degree of freedom between rows = (r – 1).
No. of degree of freedom for residual = (c – 1) (r – 1).
Total No. of degree of freedom = N – 1 or cr – 1.
Where; r = refers to number of rows.
c = refers to number of columns.
N = refers to total number of items in the samples.

(viii) ANOVA Table: In a two way classification the
Analysis of Variance Table is prepared in the following
form:
ANOVA Table (Two way classification)
Source of
Variance
Degree of
freedom
Sum of Square Variance F-ratio
Between
Column
C – 1 SSC SSC÷ c – 1
MSC
F = MSC ÷MSE
Between Row r – 1 SSR SSR ÷ r – 1
MSR
F = MSR ÷ MSE
Residual (c – 1) (r – 1) SSE MSE = SSE
÷(c – 1)(r – 1)
Total N – 1 or
cr – 1
SST

Illustration: The following table gives the average
monthly sale of four salesmen in three different types of
territories:
Make an analysis of variance from the above facts and
give your comments:
Territory Salesmen Total
A B C D
X 5 4 4 7 20
Y 7 8 5 4 24
Z 9 6 6 7 28
Total 21 18 15 18 72

Solution:
Correction Factor = (T)2 / N = (72)2 / 12 = 432
Total Sum of Square (SST):
Data Square of data
Territ
ory
Salesmen Total
∑Xr
Territo
ry
Salesmen Total
A B C D A B C D
X 5 4 4 7 20 X 25 16 16 49 106
Y 7 8 5 4 24 Y 49 64 25 16 154
Z 9 6 6 7 28 Z 81 36 36 49 202
∑Xc 21 18 15 18 72 Total 155 116 77 114 462

SST = [∑X12 + ∑X22 + ∑X32 + ∑X42] - (T)2 / N
= 155 + 116 + 77 + 114 – 432
= 462 - 432 = 30
Number of degree of freedom = cr – 1 = (4 x 3) – 1 = 11
Sum of Square Between Column (SSC)
(∑Xc)2 (T)2
SSC = ∑ -
nc N
= (21)2 /3 + (18)2 /3 + (15)2 /3 + (18)2 /3 – 432

= 147 + 108 + 75 + 108 – 432 = 6
Number of degree of freedom = (c – 1) = 4 – 1 = 3
Sum of Square Between Row (SSR)
(∑Xr)2 (T)2
SSR = ∑ -
nr N
= (20)2 / 4 + (24)2 / 4 + (28)2 / 4 – 432
= 100 + 144 + 196 – 432 = 8
Number of degree of freedom = (r – 1) = 3 – 1 = 2

Sum of Squares of Residual (SSE)
SSE = SST – SSC – SSR
= 30 – 6 – 8 = 16
Number of degree of freedom = (c – 1) (r – 1)
= (4 – 1) (3 – 1) = 6
ANOVA Table
Source of
Variance
Degree of
Freedom
Sum of Square Variance F-ratio
Between Column C – 1 = 3 SSC = 6 MSC = 2 F-ratio = MSC ÷ MSE =
2/ 2.67 = 0.75
Between Row r - 1 = 2 SSR = 8 MSR = 4 F-ratio MSR ÷ MSE =
4/2.67 = 1.50
Residual (C-1) (r -1) = 6 SSE = 16 MSE = 2.67 V1/V2= 3/6 and 2/6
Total Cr – 1 = 11 SST = 30 F0.05 = 4.76 and 5.14

The calculated value of F is less than the table value,
therefore, the null hypothesis is accepted. There is no
significance difference between sales of territory and sales of
salesmen.
3. Analysis of Variance in Latin Square
It is an important design of experiment. It is mainly used in the
field of agriculture. In the area of agriculture various types of
investigations are made and conclusion are drawn from
various investigations. For example, an experiment regarding
the effect of use of five different types of fertilizers on
agricultural yield has to be considered. While carrying out

such an experiment, it should be noted that the fertility of land
in the land in the same agricultural field cannot be the same.
Therefore, it has to considered that the productivity is not only
affected by fertilizer but also by the basic fertility of original
land. To overcome this problem ‘Latin Squares’ are used.
Latin Square is defined as a square containing Chi-square cell
constructed in ‘n’ row and ‘n’ columns, each of the cell
containing one of ‘n’ specified numbers so that every number
appears once, and only once in each row and column. In the
words of Kaine and Keeping Latin Square is a technique of
controlling two sources of an error. In the area of agriculture

treatments are allocated into plots in such a way that a
treatment does not repeat in the same column or row.
Variance between the columns and variance within the
rows are kept apart from the error so that the variation in
the fertility of soil is controlled at right angles from two
directions.
Given following are the format of Latin Squares.
Generally in a standard Latin Square, the first row and
column are occupied by the serial order of alphabets.

Standard Latin Squares
3 × 3 4 × 4
Analysis of Variance: In Latin Squares the total sum of
squares are divided into following four parts.
(i) Between Column (SSC).
(ii) Between Row (SSR)
A B C
B C A
C A B
A B C D
B C D A
C D A B
D A B C

(iii) Between Treatment (SSTr).
(iv) Residual Variance (SSE).
or SST = SSC + SSR + SSTr + SSE
To calculate the value of F Ratio, we follow the same
procedure as discussed earlier in the slides. The procedure
is as follow;
(i) Calculate the correction factor = (T)2 /N
(ii) Calculate Total Sum of Square (SST)
SST = [∑X12 + ∑X22 + ∑X32 + ∑X42] - (T)2 / N

Degree of freedom = cr – 1 or (n)2 -1
(iii) Sum of Square Between Column (SSC)
(∑Xc)2 (T)2
SSC = ∑ -
nc N
Where; (∑Xc)2 = Sum of squares of original values in
each column.
nc = Number of items in each column.
Degree of freedom = n – 1 or c – 1

(iv) Sum of Square Between Rows (SSR)
(∑Xr)2 (T)2
SSR = ∑ -
nr N
Where; (∑Xr)2 = Sum of the squares of original values in each
row.
nr = Number of items in each row.
Degree of freedom = n – 1 or r -1
(v) Sum of Squares between Treatment (SSTr): To get the
SSTr, we get the total of the values alphabetically (∑Xt) and

then after the sum of the squares of their total is obtained
i.e. (∑Xt)2. It can be computed as follows;
(∑Xt)2 (T)2
SSTr = ∑ -
nt N
Degree of freedom = n – 1
(vi) Sum of the Square of the Residual (SSE)
SSE = SST – SSC – SSR – SSTr
Degree of freedom = (n – 1) (n – 2)
(vii) Analysis of Variance Table: It is prepared as follow:

ANOVA Table
(viii) Interpretation: The computed value of F is compared
with the table value and conclusion is made accordingly.
Source of
Variance
Degree of
freedom
Sum of
Squares
Variance F-ratio
Between
Column
c – 1 SSC MSC = SSC÷ c – 1 F1 = MSC ÷ MSE
Between Row r – 1 SSR MSR = SSR ÷ r – 1 F2 = MSR ÷
MSE
Between
Treatment
n – 1 SSTr MSTr = SSTr ÷ n -1 F3 = MSTr ÷
MSE
Residual (n – 1) (n – 2) SSE MSE = SSE ÷
(n – 1) (n – 2)

Illustration: The following is a Latin Square lay out of a
design when four varieties of seeds are being tested. Set
out the analysis of variance table and state your
conclusion:
C
25
B
23
A
20
D
20
A
19
D
19
C
21
B
18
B
19
A
14
D
17
C
20
D
17
C
20
B
21
A
15

Solution: It is 4 × 4 Latin square, let 19 be the common
factor which when deducted from each value, we get the
following table:
Rows Columns (Coded Data) Square
1 2 3 4 ∑Xr 1 2 3 4 Total
1 6 4 1 1 12 1 36 16 1 1 54
2 0 0 2 -1 1 2 0 0 4 1 5
3 0 -5 -2 1 -6 3 0 25 4 1 30
4 -2 1 2 -4 -3 4 4 1 4 16 25
∑Xc 4 0 3 -3 4 Total 40 42 13 19 114

(i) Correction Factor = (T)2 /N = (4)2 /16 = 1
(ii) Calculate SST.
SST = [∑X12 + ∑X22 + ∑X32 + ∑X42] - (T)2 / N
114 – 1 = 113
Degree of freedom = cr – 1 = 4 ×4 – 1 = 15
(iii) Calculate SSC
(∑Xc)2 (T)2
SSC = ∑ -
nc N
= (4)2 /4 + (0)2 / 4 + (3)2 / 4 + (-3)2 / 4 – 1
4 + 0 + 2.25 + 2.25 – 1 = 7.50

Degree of freedom = c – 1 = 4 – 1 = 3
(iv) Calculate SSR
(∑Xr)2 (T)2
SSR = ∑ -
nr N
= (12)2 / 4 + (1)2 / 4 + (-6)2 / 4 + (-3)2 / 4 – 1
= 36 + 0.25 + 9 + 2.25 – 1 = 47.50 – 1 = 46.50
Degree of freedom = r – 1 = 4 – 1 = 3
(v) Sum of Square Between Treatments (SSTr): To get
the sum of squares between treatment the values are to be

rearranged alphabetically as follows: Treatment
(vi) Calculate SSTr:
(∑Xt)2 (T)2
SSTr =∑ -
nt N
= (-8)2 / 4 + (5)2 / 4 + (10)2 / 4 + (-3)2 / 4 - 1
= 16 + 6.25 + 25 + 2.25 – 1 = 49.50 – 1 = 48. 50
Degree of freedom = n – 1 = 4 – 1 = 3
A B C D
1 1 4 6 1
2 0 -1 2 0
3 -5 0 1 -2
4 -4 2 1 -2
Total -8 5 10 -3

(vii) Calculate SSE.
SSE = SST – SSC – SSR – SSTr
= 113 – 7.50 – 46.50 – 48.50 = 113 – 102.50 = 10.50
Source of
Variance
Degree of
freedom
Sum of
square
Variance F-ration Table
Value
Due to Column c – 1 = 3 SSC =
7.50
MSC = 2.50 F1 = 2.50 / 1.75
= 1.429
V1/ V2
4.76
Due to Row r – 1 = 3 SSR =
46.50
MSR =
15.50
F2 = 15.50 / 1.75
= 8.857
4.76
Due to
Treatments
n – 1 = 3 SSTr =
48.50
MSTr =
16.17
F3 = 16.17 / 1.75
= 9.24
4.76
Residual (n – 1)(n
– 2 ) = 6
SSE =
10.50
MSE = 1.75 V1/ V2
for all is
Total 15 113 3/6

Conclusion:
1. The calculated value of F for column is less than the
table value, hence the effect at 5% level of significance
is not significant.
2. The calculated value of F for rows is 8.85 is greater than
the table value. Therefore, the effect at 5% level of
significance can be regarded significant.
3. The calculated value of F for treatment is 9.24 is greater
than the table value. Therefore, the effect at 5% level of
significance can be regarded significant.

The F- Test or The Variance Ratio Test
The F-test is named in honour of the great statistician R.A.
Fisher. The object of the F-test is to find out whether the
two independent estimates of population variance differ
significantly, or whether the two samples may be regarded
as drawn from the normal populations having the same
variance. For carrying out the test of significance, we
calculate the ratio F.
S12 ∑(X1 – X1)2 ∑(X2 – X2)2
F = , where S12 = , S22 =
S22 n1 – 1 n2 – 1

It should be noted that S12 is always the larger estimate of
variance i.e. S12 > S22.
Largest Estimate of Variance
F =
Smallest Estimate of Variance
V1 = n1 – 1 and V2 = n2 – 1
V1 = degree of freedom for sample having larger variance.
V2 = degree of freedom for sample having smaller
variance.
The calculated value of F is compared with the table value

for V1 and V2 at certain level of significance. If
calculated value of F is greater than the table value then
the F-ratio is considered significant and the null
hypothesis is rejected. On the other hand, if the calculated
value is less than the table value of F, the null hypothesis
is accepted and it is inferred that both the samples have
come from the population having same variance.
Since, F is based on the ratio of two variances, it is also
known as the Variance Ration Test.
Assumptions of F-test: The F-test is based on the
following assumptions;

1. Normality: The values in each group are normally
distributed.
2. Homogeneity: The variance within each group should be
equal for all groups.
3. Independence of Error: It state that the error should be
independent for each value.
Illustration: Two random samples were drawn from two
normal populations and their values are;
A 66 67 75 76 82 84 88 90 92 - -
B 64 66 74 78 82 85 87 92 93 95 97

Test whether the two populations have the same variance at
the 5% level of significance. (F = 3.36) at 5% level for V1 =
10 and V2 = 8.
Solution: Let us take the hypothesis that the two populations
have the same variance, Applying F-test.
S12 ∑(X1 – X1)2 ∑(X2 – X2)2
F = , where S12 = , S22 =
S22 n1 – 1 n2 – 1
∑X1 720 ∑X2 913
X1 = = = 80, X2 = = = 83
n1 9 n2 11

A
X1
(X1 – X1)
x1
x12
B
X2
(X2 – X2)
x2
x22
66 -14 196 64 -19 361
67 -13 169 66 -17 289
75 -5 25 74 -9 81
76 -4 16 78 -5 25
82 2 4 82 -1 1
84 4 16 85 2 4
88 8 64 87 4 16
90 10 100 92 9 81
92 12 144 93 10 100
95 12 144
97 14 196
∑X1 = 720 ∑x1 = 0 ∑x12 = 734 ∑X2 = 913 ∑x2 = 0 ∑x22 = 1289

734 1289
S12 = = 91.75, S22 = = 129.8
9 – 1 11 – 1
S12 129.8
F = = = 1.414
S22 91.75
For V1 = 10 and V2 = 8, F0.05 = 3.36
The calculated value of F is less than the table value. The
hypothesis is accepted. Hence, it may be concluded that
the two population have the same variance.

Research Report
Research Report
One of the reasons for carrying out research is to add to
the existing body of knowledge. Therefore, when
conducting research, you need to document your
processes and findings in a research report.
With a research report, it is easy to outline the findings of
your systematic investigation and any gaps needing
further inquiry. Knowing how to create a detailed research
report will prove useful when you need to conduct
research.

Research Report
What is a Research Report?
A research report is a well-crafted document that outlines the
processes, data, and findings of a systematic investigation. It
is an important document that serves as a first-hand account of
the research process, and it is typically considered as an
objective and accurate source of information.
In many ways, a research report can be considered as a
summary of the research process that clearly highlights
findings, recommendations, and other important details.
Reading a well-written research report should provide you
with all the information you need about the core areas of the
research process.

Research Report
Features of a Research Report
So how do you recognize a research report when you see one?
Here are some of the basic features that define a research
report.
• It is a detailed presentation of research processes and findings,
and it usually includes tables and graphs.
• It is written in a formal language.
• A research report is usually written in the third person.
• It is informative and based on first-hand verifiable
information.
• It is formally structured with headings, sections, and bullet
points.
• It always includes recommendations for future actions.

Research Report
Different Steps in Writing Report
Research reports are the product of slow, painstaking, accurate
inductive work. The usual steps involve in writing report are;
(i) Logical analysis of the subject matter; (ii) Preparation of
the final outline; (iii) Preparation of the rough draft; (iv)
Rewriting and polishing; (v) Preparation of the final
bibliography; and (vi) Writing the final draft. Though all
these steps are self explanatory, yet a brief mention of each
one of these will be appropriate for better understanding.
(i) Logical Analysis of the Subject Matter: It is the first step
which is primarily concerned with the development of a
subject . There are two ways in which to develop a subject (a)
logically and (b) chronologically. The logical development is

Research Report
made on the basis of mental connections and associations
between the one thing and another by means of analysis.
Logical treatment often consists in developing the material
from the simple possible to the most complex structures.
Chronological development is based on a connection or
sequence in time or occurrence. The directions for doing or
marking something usually follow the chronological order.
(ii) Preparation of the Final Outline: Outline are the
framework upon which long written works are constructed.
They are an aid to the logical organization of the material and
a reminder of the points to be stressed in the report.

Research Report
(iii) Preparation of the Rough Draft: The following are the
logical analysis of the subject and the preparation of the final
outline. Such a step is of utmost important for the researcher
now sits to write down what he has done in the context of his
research study. He will write down the procedure adopted by
him in collecting the material for his study along with various
limitations faced by him, the technique of analysis adopted by
him, the broad findings and generalization and the various
suggestions he wants to offer regarding the problem
concerned.
(iv) Rewriting and Polishing of the Rough Draft: Usually this
step requires more time than the writing of the rough draft.
The careful revision makes the difference between a mediocre

Research Report
and a good peace of writing. While rewriting and
polishing, one should check the report for weakness in
logical development or presentation. The researcher
should also (i) see whether or not the material, as it is
presented, has unity and cohesion (ii) the report stand
upright and firm and exhibit a definite pattern. In addition
the researcher should give due attention to the fact that in
his rough draft he has been consistent or not. He should
check the mechanics of writing – grammar, spelling and
usage.
(v) Preparation of the Final Bibliography: Next in order
comes the task of the preparation of the final bibliography.

Research Report
The bibliography, which is generally appended to the research
report, is a list of books in some way pertinent to the research
which has been done. It should contain all those works which
the researcher has consulted. The bibliography should be
arranged alphabetically and may be divided into two parts; the
first part may contain the names of books and pamphlets, and
the second part may contain the names of magazines and
newspaper articles. Generally, this pattern of bibliography is
considered convenient and satisfactory from the point of view
or reader, through it is not the only way of presenting
bibliography. The entries in bibliography should be made
adopting the following order;

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For Books and Pamphlets the Order May be as Under:
(i) Name of the author, last name first.
(ii) Title, underlined, in quotation marks.
(iii) Publisher, place, and date of publication.
(iv) Number of Volumes.
Example:
Kothari, C.R., Quantitative Techniques, Vikash Publishing
House Pvt. Ltd., New Delhi, 1978.
For Magazines and Newspapers the Order May be as Under:
(i) Name of the author, last name first.
(ii) Title of the article, in quotation marks.
(iii) Name of periodical, underlined to indicate italics.

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(iv) The volume number and issue number.
(v) The date of the issue.
(vi) The pagination.
Example;
Robert V. Roosa, “Coping with Short-term International
Money Flows”, The Banker, London, September, 1971, p.
995.
The above examples are just the samples for bibliography
entries and may be used, but one should also remember that
they are not the only acceptable forms. The only thing
important is that, whatever method one selects, it must remain
consistent.

Research Report
(vi) Write the Final Draft: This constitute the last step. The
final draft should be written in a concise and objective style
and in simple language, avoiding vague expressions such as
“it seems”, “there may be”, and the like ones. While writing
the final draft, the researcher must avoid abstract terminology
and technical jargon. Illustrations and examples based on
common experiences must be incorporated in the final draft as
they happen to be most effective in communicating the
research findings to others. A research report should not be
dull, but must enthuse people and maintain interest and must
show intellectual problem and must contribute to the solution
of a problem and must add to the knowledge of both the
researcher and the reader.

Research Report
Layout of the Research Report
Anybody, who is reading the research report, must
necessarily be conveyed enough about the study so that he
can place it in its general scientific context, judge the
adequacy of its methods and thus form an opinion of how
seriously the findings are to be taken. For this purpose
there is the need of proper layout of the report. The layout
of the report means as to what the research report should
contain. A comprehensive layout of the research report
should comprise (a) preliminary pages; (b) the main text;
and (c) the end matter. Let us deal with them separately.

Research Report
(a) Preliminary Pages: In its preliminary pages the report
should carry a title and date, followed by acknowledgement
in the form of “Preface’ or ‘Foreword’. Then there should be
a table of contents followed by list of tables and illustrations
so that the decision-maker or anybody interested in reading
the report can easily locate the required information in the
report.
(b) Main Text: The main text provides the complete outline of
the research report along with all detail. Title of the research
study is repeated at the top of the first page of the main text
and then follows the other details on pages numbered
consecutively, beginning with the second page. Each main
section of the report should begin on a new page.

Research Report
The main text of the report should have the following
sections: (i) Introduction; (ii) Statement of Finding and
Recommendations; (iii) The results; (iv) The implications
drawn from the results; and (v) The Summary.
(i) Introduction: The purpose of introduction is to introduce
the research project to the readers. It should contain a
clear statement of the objectives of research i.e. enough
background should be given to make clear to the reader
why the problem was considered worth investigating. A
brief summary of other relevant research may also be
stated so that the present study can be seen in that context.

Research Report
The hypothesis of the study, if any, and the definitions of the
major concepts employed in the study should be explicitly
stated in the introduction of the report.
The methodology adopted in conducting the study must be
fully explained. The scientific reader would like to know in
detail about such thing: How was the study carried out? What
was its basic design? If the study was an experimental one,
then what were the experimental manipulations? If the data
were collected by means of questionnaires or interviews, then
exactly what questions were asked? If the measurement were
based on observation, then what instructions were given to the
observers? Regarding the sample used in the study the reader
should be told: Who were the subjects? How many were
there? How are they selected? All these questions are crucial

Research Report
for estimating the probable limits of generalizability of the
findings. The statistical analysis adopted must also be
clearly stated. In addition to all this, the scope of the study
should be stated and the boundary lines be demarcated.
The various limitations, under which the research project
was completed, must also be narrated.
(ii) Statement of Findings and Recommendations: After
introduction, the research report must contain a statement
of findings and recommendations in non-technical
language so that it can be easily understood by all
concerned. If the findings happen to be extensive, at this
point they should be put in the summarized form.

Research Report
(iii) Results: A detail presentation of the findings of the
study, with supporting data in the form of tables and
charts together with a validation of results, is the next step
in writing the main text of the report. This generally
comprises the main body of the report, extending over
several chapters. The result section of the report should
contain statistical summaries and reduction of the data
rather than the raw data. All the results should be
presented in logical sequence and splitted into readily
identifiable sections. All relevant results must find a place
in the report.

Research Report
(iv) Implication of the Results: Toward the end of the main
text, the researcher should again put down the results of his
research clearly and precisely. He should, state the
implications that flow from the results of the study, for the
general reader is interested in the implications for
understanding the human behaviour. Such implications may
have three aspects as stated below;
a. A statement of the inferences drawn form the present study
which may be expected to apply in similar circumstances.
b. The conditions of the present study which may limit the
extent of legitimate generalization of the inferences drawn
from the study.
c. The relevant question that still remain unanswered or new
question raised by the study along with suggestions for the

Research Report
It is considered a good practice to finish the report with a
short conclusion which summarizes and recapitulates the
main points of the study. The conclusion drawn from the
study should clearly related to the hypotheses that were
stated in the introductory section. At the same time, a
forecast of the probable future of the subject and an
indication of the kind of research which needs to be done
in that particular field is useful and desirable.
(v) Summary: It has become customary to conclude the
research report with a very brief summary, resting in brief
the research problem, the methodology, the major findings
and the major conclusion drawn from the research results.

Research Report
(c) End Matter: At the end of the report, appendices should
be enlisted in respect of all technical data such as
questionnaire, sample information, mathematical
derivations and the like ones. Bibliography of sources
consulted should also be given. Index should invariably be
given at the end of the report. The value of index lies in
the fact that it works as a guide to the reader for the
contents in the report.
Types of Reports
The research report is classified based on 2 things; nature
of research and target audience.

Research Report
Nature of Research
(a) Qualitative Research Report: This is the type of report
written for qualitative research. It outlines the methods,
processes, and findings of a qualitative method of systematic
investigation. In educational research, a qualitative research
report provides an opportunity for one to apply his or her
knowledge and develop skills in planning and executing
qualitative research projects.
A qualitative research report is usually descriptive in nature.
Hence, in addition to presenting details of the research
process, you must also create a descriptive narrative of the
information.

Research Report
(b) Quantitative Research Report: A quantitative research
report is a type of research report that is written for
quantitative research. Quantitative research is a type of
systematic investigation that pays attention to numerical or
statistical values in a bid to find answers to research
questions.
In this type of research report, the researcher presents
quantitative data to support the research process and findings.
Unlike a qualitative research report that is mainly descriptive,
a quantitative research report works with numbers; that is, it is
numerical in nature.
Target Audience
Also, a research report can be said to be technical or popular
based on the target audience. If you're dealing with a general

Research Report
audience, you would need to present a popular research report,
and if you're dealing with a specialized audience, you would
submit a technical report.
(a)Technical Report: In the technical report the main emphasis
is on (i) the methods employed, (ii) assumptions made in the
course of the study, (iii) the detail presentation of the findings
including their limitation and supporting data.
A general outline of a technical report can be as follows:
(i) Summary of Results: A brief review of the main findings
just in two or three pages.
(ii) Nature of the Study: Description of the general objective
of study, formulation of the problem in operational terms,

Research Report
the working hypothesis, the type of analysis and data required,
etc.
(iii) Methods Employed: Specific method used in the study and
their limitations. For instance, in sampling studies we should
gives details of sample design viz, sample selection, etc.
(iv) Data: Discussion of data collected, their sources,
characteristics and limitations. If secondary data are used,
their suitability to the problem at hand be fully assessed. In
case of a survey, the manner in which data were collected
should be fully described.
(v) Analysis of Data and presentation of Finding: The analysis
of data and presentation of the findings of the study with
supporting data in the form of tables and charts be fully
narrated. This, in fact, happens to be the main body of the

Research Report
report usually extending over several chapters.
(vi) Conclusions: A detailed summary of the finding and the
policy implications drawn from the results be explained.
(vii) Bibliography: Bibliography of various sources
consulted be prepared and attached.
(viii) Technical Appendices: Appendices be given for all
technical matters relating to questionnaire, mathematical
derivations, elaboration on particular technique of analysis
and the like ones.
(ix) Index: Index must be prepared and be given invariably
in the report at the end.

Research Report
The order presented above only gives a general idea of the
nature of a technical report; the order of presentation may
not necessarily be the same in all the technical reports.
This, in other words, means that presentation may be vary
in different reports; even the different section outline
above will not always be the same, nor will all these
sections appear in any particular report.
It should be, however, be remembered that even in a
technical report, simple presentation and ready availability
of the findings remain an important consideration and as
such the liberal use of charts and diagrams is considered
desirable.

Research Report
(b) Popular Report: The popular report is one which gives
emphasis on simplicity and attractiveness. The simplification
should be sought through clear writing, minimization of
technical, particularly mathematical, details and liberal use of
charts and diagrams. Attractive layout along with large print,
many subheadings, even an occasional cartoon now an then is
another characteristics feature of the popular report. Beside, in
such a report emphasis is given on practical aspects and policy
implication.
We give below a general outline of a popular report.
(i) The Finding and Their Implication: Emphasis in the report
is given on the findings of most practical interest and on the

Research Report
implications of these findings.
(ii) Recommendations for Action: Recommendation for action
on the basis of the findings of the study is made in this section
of the report.
(iii) Objective of the Study: A general review of the problem
arise is presented along with the specific objectives of the
project under study.
(iv) Methods Employed: A brief and non-technical description
of the methods and techniques used, including a short review
of the data on which the study is based, is given in this part of
the report.
(v) Results: This section constitutes the main body of the report
wherein the results of the study are presented in clear and non-
technical terms with liberal use of all sorts of illustrations

Research Report
such as charts, diagrams and the like ones.
(vi) Technical Appendices: More detailed information on
methods used, forms, etc. is presented in the form of
appendices. But the appendices are often not detailed if
the report is entirely meant for general public.
There can be several variations of the from in which a
popular report can be prepared. The only important thing
about such a report is that it gives emphasis on simplicity
and policy implication from the operational point of view,
avoiding the technical details of all sorts to the extent
possible.

Research Report
Mechanics of Writing a Research Report
There are very definite and set rules which should be followed
in the actual preparation of the research report or paper. Once
the techniques are finally decided, they should be
scrupulously adhered to, and no deviation permitted. The
criteria of format should be decided as soon as the materials
for the research paper have been assembled. The following
points deserve mention so far as the mechanics of writing a
report are concerned:
(i) Size and physical design: The manuscript should be written
on unruled paper 81/2× 11in size. If it is to be written by
hand, then black or blue-black ink should be used. A margin

Research Report
of at least one and one-half inches should be allowed at the
left hand and of at least half an inch at the right hand of the
paper. There should also be one-inch margins, top and bottom.
The paper should be neat and legible. If the manuscript is to
be typed, then all typing should be double-spaced on one side
of the page only except for the insertion of the long
quotations.
(ii) Procedure: Various steps in writing the report should be
strictly adhered (All such steps have already been explained
earlier in this chapter).
(iii) Layout: Keeping in view the objective and nature of the
problem, the layout of the report should be thought of and
decided and accordingly adopted (The layout of the research

Research Report
report and various types of reports have been described in this
chapter earlier which should be taken as a guide for report-
writing in case of a particular problem).
(iv) Treatment of quotations: Quotations should be placed in
quotation marks and double spaced, forming an immediate
part of the text. But if a quotation is of a considerable length
(more than four or five type written lines) then it should be
single-spaced and indented at least half an inch to the right of
the normal text margin.
(v) The footnotes: Regarding footnotes one should keep in view
the followings:
• The footnotes serve two purposes viz., the identification of
materials used in quotations in the report and the notice of
materials not immediately necessary to the body of research

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text but still of supplemental value. In other words, footnotes are
meant for cross references, citation of authorities and sources,
acknowledgement and elucidation or explanation of a point of view.
It should always be kept in view that footnote is not an end nor a
means of the display of scholarship. The modern tendency is to make
the minimum use of footnotes for scholarship does not need to be
displayed.
• Footnotes are placed at the bottom of the page on which the reference
or quotation which they identify or supplement ends. Footnotes are
customarily separated from the textual material by a space of half an
inch and a line about one and a half inches long.
• Footnotes should be numbered consecutively, usually beginning with
1 in each chapter separately. The number should be put slightly
above the line, say at the end of a quotation. At the foot of the page,

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again, the footnote number should be indented and typed a
little above the line. Thus, consecutive numbers must be used
to correlate the reference in the text with its corresponding
note at the bottom of the page, except in case of statistical
tables and other numerical material, where symbols such as
the asterisk (*) or the like one may be used to prevent
confusion. Footnotes are always typed in single space though
they are divided from one another by double space.
(vi) Documentation style: Regarding documentation, the first
footnote reference to any given work should be complete in its
documentation, giving all the essential facts about the edition
used. Such documentary footnotes follow a general sequence.
The common order may be described as under:

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1. Regarding the single-volume reference
– Author’s name in normal order (and not beginning with the last name as in a
bibliography) followed by a comma;
– Title of work, underlined to indicate italics;
– Place and date of publication;
– Pagination references (The page number).
– Example
John Gassner, Masters of the Drama, New York: Dover Publications, Inc. 1954,
p. 315.
2. Regarding multivolumed reference
– Author’s name in the normal order;
– Title of work, underlined to indicate italics;
– Place and date of publication;
– Number of volume;
– Pagination references (The page number).

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3. Regarding works arranged alphabetically
For works arranged alphabetically such as encyclopedias and
dictionaries, no pagination reference is usually needed. In
such cases the order is illustrated as under:
Example1
“Salamanca,” Encyclopaedia Britannica, 14th Edition.
Example 2
“Mary Wollstonecraft Godwin,” Dictionary of national
biography.
But if there should be a detailed reference to a long
encyclopedia article, volume and pagination reference may be
found necessary.

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4. Regarding periodicals reference
– Name of the author in normal order;
– Title of article, in quotation marks;
– Name of periodical, underlined to indicate italics;
– Volume number;
– Date of issuance;
– Pagination.
5.Regarding anthologies and collections
reference: Quotations from anthologies or collections of
literary works must be acknowledged not only by author,
but also by the name of the collector.

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(vii) Regarding second-hand quotations reference:
In such cases the documentation should be handled as
follows:
– Original author and title;
– “quoted or cited in,”;
– Second author and work.
Example
J.F. Jones, Life in Ploynesia, p. 16, quoted in History of the Pacific
Ocean area, by R.B. Abel, p. 191
(viii) Case of multiple authorship:
If there are more than two authors or editors, then in the
documentation the name of only the first given and the
multiple authorship is indicated by “et al.” or “and others”.
Subsequent references to the same work need not be so
detailed as stated above. If the work is cited again without

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any other work intervening, it may be indicated
as ibid, followed by a comma and the page number. A single
page should be referred to as p., but more than one page be
referred to as pp. If there are several pages referred to at a
stretch, the practice is to use often the page number, for
example, pp. 190ff, which means page number 190 and the
following pages; but only for page 190 and the following page
‘190f’. Roman numerical is generally used to indicate the
number of the volume of a book. Op. cit. (opera citato, in the
work cited) or Loc. cit. (loco citato, in the place cited) are two
of the very convenient abbreviations used in the footnotes.
Op. cit. or Loc. cit. after the writer’s name would suggest that
the reference is to work by the writer which has been cited in
detail in an earlier footnote but intervened by some other
references.

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(ix) Punctuation and abbreviations in footnotes: The first item
after the number in the footnote is the author’s name, given in
the normal signature order. This is followed by a comma.
After the comma, the title of the book is given: the article
(such as “A”, “An”, “The” etc.) is omitted and only the first
word and proper nouns and adjectives are capitalized. The
title is followed by a comma. Information concerning the
edition is given next. This entry is followed by a comma. The
place of publication is then stated; it may be mentioned in an
abbreviated form, if the place happens to be a famous one
such as Lond. for London, N.Y. for New York, N.D. for New
Delhi and so on. This entry is followed by a comma. Then the
name of the publisher is mentioned and this entry is closed by
a comma. It is followed by the date of publication if the date

Research Report
is given on the title page. If the date appears in the copyright notice
on the reverse side of the title page or elsewhere in the volume, the
comma should be omitted and the date enclosed in square brackets [c
1978], [1978]. The entry is followed by a comma. Then follow the
volume and page references and are separated by a comma if both are
given. A period closes the complete documentary reference. But one
should remember that the documentation regarding
acknowledgements from magazine articles and periodical literature
follow a different form as stated earlier while explaining the entries
in the bibliography.
Certain English and Latin abbreviations are quite often used in
bibliographies and footnotes to eliminate tedious repetition. The
following is a partial list of the most common abbreviations
frequently used in report-writing (the researcher should learn to
recognise them as well as he should learn to use them):

Research Report
anon., anonymous
ante., before
art., article
aug., augmented
bk., book
bull., bulletin
cf., compare
ch., chapter
col., column
diss., dissertation
ed., editor, edition, edited.
ed. cit., edition cited
e.g., exempli gratia: for example
eng., enlarged
et.al., and others
et seq., et sequens: and the following
ex., example
f., ff., and the following
fig(s)., figure(s)
fn., footnote

Research Report
ibid., ibidem: in the same place (when two or more successive footnotes
refer to the
same work, it is not necessary to repeat complete reference for the second
footnote. Ibid. may be used. If different pages are referred to, pagination
must be shown).
id., idem: the same
ill., illus., or
illust(s). illustrated, illustration(s)
Intro., intro., introduction
l, or ll, line(s)
loc. cit., in the place cited; used as op.cit., (when new reference
loco citato: is made to the same pagination as cited in the previous note)
MS., MSS., Manuscript or Manuscripts
N.B., nota bene: note well
n.d., no date

Research Report
n.p., no place
no pub., no publisher
no(s)., number(s)
o.p., out of print
op. cit: in the work cited (If reference has been made to a work
opera citato and new reference is to be made, ibid., may be used, if
intervening
reference has been made to different works, op.cit. must be used. The
name of the author must precede.
p. or pp., page(s)
passim: here and there
post: after
rev., revised
tr., trans., translator, translated, translation
vid or vide: see, refer to
viz., namely

Research Report
viz., namely
vol. or vol(s)., volume(s)
vs., versus: against
(x) Use of statistics, charts and graphs: A judicious use of
statistics in research reports is often considered a virtue for it
contributes a great deal towards the clarification and
simplification of the material and research results. One may
well remember that a good picture is often worth more than
thousand words. Statistics are usually presented in the form of
tables, charts, bars and line-graphs and pictograms. Such
presentation should be self explanatory and complete in itself.
It should be suitable and appropriate looking to the problem at
hand. Finally, statistical presentation should be neat and
attractive.

Research Report
(xi) The final draft: Revising and rewriting the rough draft of the report
should be done with great care before writing the final draft. For the
purpose, the researcher should put to himself questions like: Are the
sentences written in the report clear? Are they grammatically correct?
Do they say what is meant’? Do the various points incorporated in
the report fit together logically? “Having at least one colleague read
the report just before the final revision is extremely helpful.
Sentences that seem crystal-clear to the writer may prove quite
confusing to other people; a connection that had seemed self evident
may strike others as a non-sequitur. A friendly critic, by pointing out
passages that seem unclear or illogical, and perhaps suggesting ways
of remedying the difficulties, can be an invaluable aid in achieving
the goal of adequate communication.
(xii) Bibliography: Bibliography should be prepared and appended to
the research report as discussed earlier.

Research Report
(xiii) Preparation of the index: At the end of the report, an
index should invariably be given, the value of which lies
in the fact that it acts as a good guide, to the reader. Index
may be prepared both as subject index and as author
index. The former gives the names of the subject-topics or
concepts along with the number of pages on which they
have appeared or discussed in the report, whereas the
latter gives the similar information regarding the names of
authors. The index should always be arranged
alphabetically. Some people prefer to prepare only one
index common for names of authors, subject-topics,
concepts and the like ones.

Research Report
Precautions for Writing Research Report
1. The research report should be long enough to cover the
subjects but short enough to maintain the interest.
2. The report should not be dull, it should sustain the reader’s
interest.
3. Abstract terminology and technical language should be
avoided in a research report.
4. The report must provide a readily availability of the findings.
5. The layout of the report must be in accordance with the
objectives of the research problem.

Research Report
6. The report should be original in nature.
7. Appendices should be properly listed in all respect in order to
avoid any confusions.
8. Bibliography of sources of consulted is a must and it should be
very carefully and chronologically arranged.
9. The report must be attractive in its appearance.
10. The objective of the study, the nature of the problem, the
methods employed and the analysis techniques adopted must
all be clearly stated in the beginning of the report in the form
of introduction.
11. The limitations related to the study must also be clearly
indicated in the research report.

Analysis of Variance (ANOVA) (Appendices)

Research Report
Thank You!

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