This document provides an overview of analysis of variance (ANOVA). It defines ANOVA as a statistical method used to analyze differences between two or more means. The document outlines the key terminology used in ANOVA such as grand mean, sample mean, null and alternative hypotheses, between and within group variability, F-test, F-critical value, and F-ratio. It also describes how ANOVA compares total variance between samples to variance within samples and uses the F-ratio to determine if means are significantly different based on the F-critical value. Examples of medical treatments are provided to illustrate how ANOVA can be used to determine if treatments are equally effective.

1. ANOVA
Shumail Ayub Qureshi
MPhil Zoology
Biostatistics

2. AGENDA
Introduction
Terminologies
Types of ANOVA
Important applications of ANOVA
Practical

3. INTRODUCTION
 ANOVA stands for Analysis of
Variances
 It is also known as Fisher Analysis of
variances and extension of t-tests.
 In 1918, Ronald fisher created
ANOVA.
 Statistical Method (online / manual)
 Analyzed the differences of means of
two or more groups.
 Compares the variations b/w the

4. INTRODUCTION
 Careful examination/difference b/w
two or more samples.
 Total variance=Variance b/w samples
or within samples.
 Categorical classification type test
describes on the basis of significance
difference.
 Formula=variance b/w
samples/variance within samples.

5. LETS CONSIDER EXAMPLE
3 medical treatment
Best treatment will take less time to cure .
If possible patient may be taking other
medicine , or they partially cure, having strong
immunity.
For making reliable decision ANOVA plays
important role here.
It check the impacts of two or more factors by
comparing means of different samples.
It will proves and disproves whether all the
medications treatments were equally effective
or not.

6. TERMINOLOGIES
 Grand mean
 Degree of freedom
 Sample mean
 Hypothesis
 Null hypothesis
 Alternate hypothesis
 Between groups variability
 Within groups variability
 F-test
 F-critical value
 F-Ratio

7. GRAND MEAN/SAMPLE
MEAN/HYPOTHESIS
 Sum of all the sample means is called grand
mean. μ =μ+μ+μ
 Individual mean is known as sample mean.μ
 Suggested statement , lets consider earlier
example possible hypothesis were,
medication will effect or medicines will not
effect.
 Null hypothesis(Ho), all samples means were
equal. μ =μ=μ=μ
 Alternate hypothesis(H1), samples means are
different rest of total samples. μ ≠μ

8. B/W GROUPS AND WITHIN GROUP
VARIABILITY
 2 samples b/w groups overlap and won’t different by
great margins(difference in mean) and sometimes differ
by great margins and won’t overlap.
 3 samples within group somewhere overlap and
somewhere non overlapped.

9. F-TEST/DEGREE OF FREEDOM
Means of different samples are significantly
different is called its F-ratio. Which is inversely
proportional to the similarity of mean.
F critical value is just like a ∝ value through
we check if calculated value is less than 0.05
so it would rely in H1 region and would
accepted while if greater than 0.05 then it will
rejected.
SS sum of square of all sample means. SSc
b/w variations, SS e within variations.
MS sum of mean square value divided by df.
(SS/df)
How much change can be acceptable. It is
equal to the sum of individual is called degree
freedom for each sample.
Presentation title 9

10. CONTINUED
F ratio >1 reject Ho
F ratio <1 accept Ho
F ratio =1 accept Ho
F critical >F stats=accept Ho
F critical <F stats=reject Ho
F critical=numerator df/denominator df
F stats=variance b/w/variance within
Numerator df=no of samples – 1
Denominator df=Σ(nj-1)=n-k
F table numerator upper, denominator lower.
Presentation title 10

11. THANK YOU
Regards,
Shumail Ayub Qureshi
MPhil zoology
1st semester