This document provides an overview of hypothesis testing, analysis of variance (ANOVA), and how to properly quote references and include a bibliography. It discusses the key steps in hypothesis testing, including stating the null and alternative hypotheses, choosing a significance level, determining the sampling distribution, calculating probabilities, and deciding whether to reject or fail to reject the null hypothesis. It also outlines one-way and two-way ANOVA, explaining how to calculate variances between and within samples/groups and use an F-test statistic. Finally, it defines what a bibliography is, lists standard citation styles, and distinguishes between references cited in a work and a full bibliography.

1. TESTING OF HYPOTHESIS ANOVA AND
QUATING REFERENCES AND BIBLIOGRAPHY
presented by - Neetu pandey
Research
Scholer

2. Table of Contents
1-Introduction
2-Criteria of Hypothesis Construction
3-Hypothesis Testing
4-Steps in Hypothesis Testing
5-Establish Critical or Rejection Region
6-Errors in Hypothesis Testing
7-ANOVA(Introduction)
8-Basic Principal of ANOVA
11-Steps in One Way ANOVA
12- Steps in Two Way ANOVA
13-Quoting of Reference and Bibliography
14-What is Bibliography
15-Standard Citation styles used in Bibliography
16-References Citation in Text
17-References Vs Bibliography

3. Introduction
• A Hypothesis is the statement or an assumption about relationships
between variables.
Or
• A Hypothesis is a tentative explanation for certain behaviors,
phenomenon or events that have occurred or will occur.
Example: “Students who receive counseling will show a greater
increase in creativity than students not receiving counseling.”

4. Criteria for Hypothesis Construction
• It should be empirically testable, whether it is right or wrong.
• It should be specific and precise.
• The statements in the hypothesis should not be contradictory.
• It should specify variables between which the relationship is to
be established.
• It should describe one issue only.

5. Hypothesis Testing
Null Hypothesis (H0 ) Alternative Hypothesis(Ha )
 State the hypothesized value
of the parameter before
sampling.
 The assumption we wish to
test(or assumption we are
trying to reject)
 All possible alternative other than
the null hypothesis.
 E.g. µ ≠ 30
µ > 30
µ < 30

6. Steps in hypothesis testing
State H0 As well as Ha
Specify the level of significance
Decide the correct sampling distribution
Sample a random sample & workout an
appropriate value
Calculate the probability that sample result
would diverge as widely as it has form
expectations, if H0 were true
If this probability equal to as smaller than α
value in case of one tailed & α/2 in case of
two tailed test
Reject H0
Accept H0

8. One and two sided test
 Hypothesis tests can be one or two sided
 We reject the null hypothesis when
(a) Two tailed Tests :
Value of test statistics <lower critical value >upper critical value
Example: H0 : µ = µ0 Against Ha : µ ≠ µ0
(b) One tailed test:
(i) Right-tailed Test
value of test statistics > critical value
Example: H0 : µ = µ0 Against Ha : µ > µ0
(ii) Left tailed Test
value of test statistics < critical value
Example : H0 : µ = µ0 Against H1 : µ < µ0
 Other wise can not reject the null hypothesis as we do not have enough
statistical evidence against it.

9. ERROS IN HYPOTHESIS TESTING
TYPES OF ERROR
Types of decision H0 True H0 False
Reject H0 Type I error (α) Correct decision (1-β)
Accept H0 Correct decision ( 1-α) Type II error(β)

10. ANOVA
(ANALYSIS OF VARIANCE)

11. INTRODUCTION
 Developed by Sir Ronald A. Fisher in 1920’s.
 Analysis of variance is a technique of testing hypotheses about
the difference in several population mean.
 If there are more than two populations, the test for the equality
of means could be carried out by Analysis of variance (ANOVA)
technique.
 Main purpose of analysis of variance is to find the difference
among various population means based on the information
gathered from the samples of the respective population.

12. Basic principles of ANOVA
 The basic principles of ANOVA is to test for difference among the
means of the population by examining the amount of variation
within each of these samples, relative to the amount of variation
between the sample.
 The total variance in the joint sample is partitioned in two parts
(i) Between samples variance (due to different treatment)
(ii) within sample variance (due to the random unexplained
disturbance)
 We define the test statistics as:
FC = between samples variance
within samples variance
 Between samples variance is large when the effects of all the
treatments are different .In such a case the computed FC is large
and we are likely to reject the null hypothesis.

13. ANOVA
One way ANOVA Two way ANOVA
The one way
ANOVA only consider
only one factor and
then observe that the
for said factor to be
important is that
several possible
types of samples can
occur with in that
factor.
Two way ANOVA
technique is used when
the data are classified on
the basis two factor. This
test is appropriate when
we wish to compare
three or more population
means within a set of
quantitative data that is
categorized according to
two treatments (or
factors)

14. One way ANOVA
Steps:
1-State null & alternative hypotheses
Suppose if k samples are being analyze, then the null
and alternative hypotheses can be set as below:
 H0: μ1 = μ2= μ3=…….= μk
 H1: μ1 ≠ μ2 ≠ μ3 ≠ ……. ≠ μk
2-State Alpha
i.e 0.05
3-Calculate degrees of Freedom
K-1 & n-1
k= No of Samples, n= Total No of observations
4. State decision rule
If calculated value of F >table value of F, reject Ho

15. 1-Calculate variance between samples:
a) Calculate the mean of each sample.
b) Calculate the Grand average
c) Take the difference between means of various samples & grand
average.
d) Square these deviations & obtain total which will give sum of
squares between samples (SSC)
Sum of Square between the column =
e) Divide the total obtained in step 4 by the degrees of freedom to
calculate the mean sum of square between samples (MSC)
MSC(Mean Square)= SSC/k-1 (Where is k-1 is degree of
freedom)
k
2
n (x  x)
j1
 j j
5-Calculating Total Sum of Squares (SST) and Mean
Squares

16. 2-Calculating Variance within Samples
a) Calculate mean value of each sample
b) Take the deviations of the various items in a sample from the
mean values of the respective samples.
c) Square these deviations & obtain total which gives the sum of
square within the samples (SSE)
n k
SSE (Sum of Square with in column)= ∑ ∑ (Xij - Xi )2
i=1 j=1
d) Divide the total obtained in 3rd step by the degrees of
freedom to
calculate the mean sum of squares within samples (MSE).
MSE(Mean Square ) = SSE/n-k (Where is n-k is the
degree of freedom)

17.  Applying the F Test statistic : F is obtained by
dividing the treatment variance(MSC) by the error
variance(MSE).
 For a given level of significance α.
 Reject null hypothesis if calculated F > critical
F(table value).
 Otherwise do not reject null hypothesis.
F = MSC/MSE
Calculation of F statistic

18. Analysis of variance table for
One way ANOVA
Source of
Variation
Sum of
Squares
(SS)
Degree of
freedom(d
.f.)
Mean
Square(MS)
F-ratio
Between
sample or
categories
SS between (k-1) MS between =
SS between/(k-
1)
MS between/
MS withinWithin
samples or
categories
SS within (n-k) MS within =
SS within/ (n-k)
Total
∑(Xij - Xi )2
i= 1,2,………
j= 1,2,……..
n-1

19. Two Way ANOVA
Steps:
The various steps in involved as follows:
1-Take the total of observations in all the samples and call it T
2- Calculate the Correction Factor-
Correction Factor = ( T)2 / n
3- Sum of Square of deviations for total variance
( T)2
Total SS = ∑ X2ij ─
n
4- calculate the sum of sum of Square deviations for variance between
columns ;
( Tj)2 ( T)2
SS Between columns treatment = ∑ ─
nj n

20. 5- Calculate the Sum of Squares deviations for variance between the
rows:
( Ti)2 ( T)2
SS Between columns treatment = ∑ ─
ni n
6- Calculate the Sum of Squares of deviations for resuidal or error
variance can be obtained as :
SS for residual or error variance = Total SS – (SS between columns
+ SS
between rows )
7-Calculate degree of freedom can be worked out as :
d.f for total variance = (c . r – 1)
d.f for variance between columns = (c – 1 )
d.f for variance between columns = ( r – 1)
d.f for residual variance = ( c – 1) ( r – 1 )
Where c = Number of columns

21. Calculate the F- statistics
1- F- Statistics for columns as
MS between columns
F column =
MS Residual
2- F- Statistics for rows as
MS between rows
F rows =
MS Residual
 MS residual is always due to the fluctuations of sampling and hence
serves as the basis for the significance test.
 The calculated F- ratio concerning variation between columns is greater
than is table value, then difference among the columns mean is different.
Similarly the F-ratio concerning variation between rows can be
interpreted.

22. Table for Two – way ANOVA
Source of
variation
Sum of
Squares (SS)
Degree of
freedom (d.f.)
Mean square
(MS)
F-ratio
Between
columns
treatment
( Tj)2 ( Ti)2
∑ ─
nj n
(c – 1 ) SS between
columns
(c – 1 )
MS between
columns/ MS
residual
Between
rows
treatment
( Ti)2 ( Ti)2
∑ ─
ni n
( r – 1) SS between
columns
(r – 1 )
MS between
rows/ MS
residual
Residual or
error
Total SS – (SS
between
columns + SS
between rows)
( c – 1)( r – 1) SS Residual
( c – 1)( r – 1)
Total ( T)2
∑ X2ij ─
n
( c . r – 1)

23. Quoting of references and
bibliography

24. What is a Bibliography
 Bibliography a science of the transmission of literary documents.
 A bibliography is an orderly list of resources on a particular
subject.
• A bibliography provides the full reference information for all the
sources which you may have consulted in preparing a particular
project.
• The purpose of a bibliography is to allow the reader to trace the
sources used.

25. Standard citation styles used in
Bibliography
There are various formats used in the creation of a bibliography
such as
 American Psychological Association (APA),
 Modern Language Association of America (MLA)
 Chicago Manual of Style(CBE)

26. Elements in bibliography
 Author
 Title of document
 Date ( year of publication)
 Place of publication
 Edition
 Periodicity (volume/ issue/ part number)
 Series

27. Reference Citation in Text
 The detailed description of the document from which you have
obtained your information. Referencing is a way of demonstrating
that you have done that reading.
 The Surnames of the Authors and the year of publication (more than
one author et.al)
1-Direct Quotation : Direct quotes as evidence in your writing. It is
useful sometimes to use the original words of the author when those
exact words carry special significance.
2- Indirect quotation : when use own words to express the ideas or
opinions of other writers, the result is an in direct quote which must also
we referred. Indirect quotes are included in the text & quotation marks
are not used.

28. Reference Vs. Bibliography
 The terms References and Bibliography are often used same, but
there is a difference in meaning between them.
 References are the items you have read and specifically referred
to (or cited) in your work, and your list of sources at the end of the
assignment will be headed References.
 Bibliography is a list of everything you read -whether or not you
referred specifically to it .
 A bibliography can give a tutor an overview of which authors have
influenced your ideas and arguments even if you do not
specifically refer to them.
 Which style to follow depends on the field of research and
university guidelines The most important thing is to be consistent
with a particular referencing styles.

29. Thank You