# What is Anova (Analysis of Variance) one of the IATF requirement its importance and when to use it

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We are going to learn about how to compare more than two Means(X bar), or how to do hypothesis testing when we have more than two groups. TO calculate this we have to do one test that is called ANOVA. It is either one way ANOVA or Two way anova.

We all know about T test and how we can use it to compare the Means (X bar) of samples.
Now you will think why we need anything else?

As we know whenever we need to compare means, we'll use a t-test! But t test having its limitations .because we can only use T test while comparing two means but if we need to compare more than two means we cannot use T test at that time. It is the limitations of T test.

So we required a method which is advanced than t-tests. As we know t-test can be used to compare two independent means.

But the t-test has some limitations. t-test is limited to one independent variable and with two groups.

So if we need to compare multiple independent variables, it means we can’t use t test in that scenario.

But then again, if we want to compare three means, a general question is raised why not just use three t tests?
Ans. We cannot use multiple t tests because using multiple tests on the same data causes the Alpha level will increase it means that we are more chances to make Type I errors, or to find erroneously statistically significant results where no result truly exists.

So let us understand this with simple example about product inspection. As per standard cycle time it is recommended that inspect 20 parts per hours for effective inspection to meet best quality level.

Well, what if we wanted to compare people who do inspect 20 parts per hours with a control group that does not inspect part at all? But while we are at it, why not add another group that inspect part 40 parts per hours, doubling the recommended quantity.

Will that double the quality and productivity?
Now, here we can use our T tests. We have three groups: A, B, and C, so we could run one T test comparing group A and B.
Then we could run a second T test comparing groups B and C,
Then we would run a third T test comparing groups A and C. But with our alpha level set at .05, that means that each comparison has a 5% error rate and total error rate will increase and could not take judgement based on test conducted.

The point is that this same logic applies with hypothesis testing. Every T test has a p = .05 it means probability of error Type I error, of erroneously finding a difference where none exists. Simply when we are conducting any single t-test, you have a five percent chance of being wrong. But if we keep running t tests again and again on the same data, it will leads to a Type I error.
And also we don’t want to run t test again and again on large group data.

In that case we have to move towards another test method which is called analysis of variance. Analysis of variance is abbreviated as ANOVA. It help to analyses the variances of the groups to assess differences in means(X bar) between the groups. ANOVA is basically an extension of regression, named as (GLM) general linear model. The ANOVA model can be used with one independent variable with any number of conditions or levels. The general linear model can be used with both independent groups or related groups, called the repeated measures ANOVA. General linear model can be used with multiple independent variables or multiple dependent variables, called a MANOVA.

If we talk about general linear model is basically it is a special form of regression, so in reality, everything that we are doing with hypothesis testing from Z tests, to t-tests, to correlation, to ANOVA, is actually all regression. These all are under the regression. Means regression is a big umbrella.
So how would the ANOVA work with our now familiar hypnosis example of hypothesis testing? Using our research question of "Is recall better under hypnosis or without?", we would begin with an existing memory test.
With the help of ANOVA we can calculate the significant relation between groups and we can take a decision based on significant level.

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