ANALYSIS OF VARIANCE (ANOVA)

SINHGAD COLLEGE OF PHARMACY, VADGAON(BK.), PUNE-41

SEMINAR ON

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Presented By –Atul D. Garkal

M.Pharm (pharmaceutics) Sem-I

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Content:-

1. INTRODUCTION

INTRODUCTION

ANALYSIS OF VARIANCE (ANOVA)

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The t-test is designed to test the hypothesis that 2 means could be from the same population of data.

But what if we want to compare more than 2 means at the same time then the ANOVA is used.

The Procedure that can compare all the mean simultaneously is known as the analysis of variance.

The basic purpose of analysis of variance is to test the homogeneity several means.

The term ANOVA was introduced by Prof. R. A. Fisher in 1920.

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How they differ?

ANOVA

One-Way ANOVA Two way ANOVA•One independent variable

•One dependent variable For Example, Only temperature as independent variable

•Two or more independent variables

•Two dependent variables

For Example, Both Temperature and Concentration asindependent variable

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Purpose of ANOVA Use one-way Analysis of Variance to test when the mean of a variable

(Dependent variable) differs among three or more groups. For example, compare whether systolic blood pressure differs

between a control group and two treatment groups One-way ANOVA compares three or more groups defined by a single

factor. For example, you might compare control, with drug treatment with

drug treatment plus antagonist. Or might compare control with five different treatments.

Some experiments involve more than one factor. These data need to be analyzed by two-way ANOVA or Factorial ANOVA.

For example, you might compare the effects of three different drugs administered at two times. There are two factors in that experiment: Drug treatment and time

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What Does ANOVA Do?

ANOVA involves the partitioning of variance of the dependent variable into different components:A. Between Group VariabilityB. Within Group Variability

More Specifically, The Analysis of Variance is a method for partitioning the Total Sum of Squares into two Additive and independent parts.

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Assumptions of ANOVA: I. All populations involved follow a normal distribution. II. All populations have the same variance (or standard

deviation). III. The samples are randomly selected and independent of one

another.

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The ANOVA Procedure:This is the ten step procedure for analysis of variance:

1.Description of data2.Assumption: Along with the assumptions, we represent the model for each design we discuss.3. Hypothesis4.Test statistic5.Distribution of test statistic6.Decision rule

7.Calculation of test statistic: The results of the arithmetic calculations will be summarized in a table called the analysis of variance (ANOVA) table. The entries in the table make it easy to evaluate the results of the analysis.8.Statistical decision9.Conclusion10.Determination of p value

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ONE WAY ANOVA

TWO WAY ANOVA

TYPES OF ANOVA

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One way ANOVA

This analysis is called “one-way” or “one-factor” because it has only one factor.

It statistical technique by which we can test if three or more means are equal.

It tests if the value of a single variable differs significantly among three or more levels of a factor.

The one-way Analysis of Variance (ANOVA) is used with one categorical independent variable and one continuous variable.

The independent variable can consist of any number of groups (levels).

WHAT IS THE ONE-WAY ANOVA?

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Advantages: Very simple: Reduce the experimental error to a great extent.We can reduce or increase some treatments.Suitable for laboratory experiment.Number of observations need not be the same in each group.Layout of the design and statistical analysis is simple.

Disadvantages: Design is not suitable if the experimental units are not

homogeneous. Design is not so much efficient and sensitive as compared to

others. Local control is completely neglected. Not suitable for field experiment.

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TWO WAY ANOVA

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Anova: Two-Factor Without Replication

This analysis tool is useful when data is classified on two different dimensions as in the Two-Factor case With Replication.

However, for this tool it is assumed that there is only a single observation for each pair (for example, each {fertilizer, temperature} pair in the preceding example).

Two Way Analysis of Variance Two Way Analysis of Variance is a way of studying the effects of two factors separately (their main effects) and (sometimes) together (their interaction effect).

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Three type of antibiotics were used in curing a disease. It was experimented on three groups of patients in three cities. Can you conclude that at 5% level of significance whether the average of

different varieties of antibiotics show any significant difference in curing the diseases.

Sr. No. A B C

1 20 18 25

2 21 20 28

3 23 17 22

4 16 25 28

5 20 15 32

Total 100 95 135

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Solution:-Null Hypothesis: H0 :µ1 = µ2

Here grand total = X = 100+95+135 = 330There fore i. T = Ʃ Ʃ Xij =330ii. Correction factor C = = =7260iii. Sum of the square of all values Ʃ Ʃ Xij =7590iv SS1= Ʃ Ʃ Xij - = 7590- 7260= 330v SSC = -

= -7260 =2000+1805+3645-7260 =190vi SSE =SST-SSC=330-190=140vii v1 =2, v2 =12.The table value of F at 5% level is 3.88F =8.14

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Since the calculated value of F is greater than the table value F , the

hypothesis in rejected which means the three different types of

antibiotics have different significant effects in curing the diseases.

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References:-

1. S. Subramananian : Biostatistatics : Career publications page 145-

155.

2. C. Kokare, S. Kokare: Research Methodology : Nirali Publcations

page 6.15-6.19

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