THIS IS RESEARCH METHODOLOGY TOPIC

1. ANOVA
PRESENTED BY:
KAMAKSHI
PHD SCHOLAR

2. Content
 INTRODUCTION
 Basic Principle of ANOVA
 Assumptions in ANOVA
 ANOVA Techniques
 EXAMPLE OF ANOVA

3. INTRODUCTION
 ANOVA stands for Analysis of Variance.
 It was introduced by Sir R.A Fisher in 1920.
 It is a statistical method used to analyse the differences between the means
of two or more samples or treatments.
 ANOVA is used to test the differences among different groups of data for
homogeneity.
 The basic principle of ANOVA is to test for differences among the populations
by examining amount of variation within each of these samples relative to
amount of variation between the samples.
 ANOVA is an extension of T test as T-test is not suitable to test for significance
of differences among more than two sample means

4.  However, conducting multiple t-tests can lead to severe inflation of the Type I
error rate.
 ANOVA can be used to test differences among several means for significance
without increasing the Type I error rate.

5. Assumptions in ANOVA
 Population distribution is normal
 Samples are random and independent
 Homogeneity of sample variance

6. ANOVA TECHNIQUES
Two types:-
 One-way ANOVA
 Two-way ANOVA
 One-way ANOVA can only be used when investigating a single factor and a
single dependent variable.

7. The F-test in One-Way ANOVA

8. Basics
 It tests the null hypothesis
 H₀:There is no significant difference between the means of all groups.(all
groups are same)
 H₀=μ₁=,μ₂=,μ₃=….=μĸ
 Where μ=group mean ,K=no. of group
ALTERNATIVE HYPOTHESIS
 HΑ:There are at least two groups means that are statistically significantly
different from each other.
 HA:μ₁≠μ₂≠μ₃≠…≠μκ

9. One way ANOVA (single factor)

10. Cont.…

11. Cont.…

12. Cont.…

13. ANOVA TABLE (ONE-WAY)

14. EXAMPLE

15. CONT…
 STEP1: CALCULATE MEAN OF EACH SAMPLE.

16. CONT…
 STEP2: CALCULATE GRAND SAMPLE MEAN (mean of sample means)

17. CONT…
 STEP3: Calculate sum of square between the samples and sum of square
within the samples.

18. CONT…
 STEP4: Calculate sum of square (SS) for total variance.
 SS(total)= SS Between the samples+ SS within the samples.
 SS(total)= 8+24 =32

19. CONT…
 STEP5: Setting up ANOVA Table.

20. conclusion
 The above table shows that calculated value of F is less than the table value
of 4.26 at 5% level with d.f being v1 = 2 and v2 =9 .

21. F TABLE