          What is it: ANalysis Of VAriance (ANOVA), is an experimental design technique that looks at a number of variables at the same time. It is used to help determine which of the variables under study have a statistically significant impact on the process output. It uses a calculation procedure to allocate the amount of variation in a process and determine if it is significant or is caused by random noise. It subdivides the total variation of a data set into meaningful component parts associated with specific sources of variation in order to test a hypothesis on the parameters of the model or to estimate variance components. In practice, there are several types of ANOVA depending on the number of treatments and the way they are applied to the subjects in the experiment:

• One-way (or one-factor) ANOVA: Tests the hypothesis that means from two or more samples are equal (drawn from populations with the same mean). Student's t-test is actually a particular application of one-way ANOVA (two groups compared) and results in the same conclusions. One-way ANOVA is used to test for differences among two or more independent groups. Typically, however, the One-way ANOVA is used to test for differences among at least three groups, since the two-group case can be covered by a T-test. When there are only two means to compare, the T-test and the F-test are equivalent; the relation between ANOVA and t is given by F = t2.
• Two-way (or two-factor) ANOVA: Simultaneously tests the hypothesis that the means of two variables ("factors") from two or more groups are equal (drawn from populations with the same mean), e.g. the difference between a control and an experimental variable. Does not include more than one sampling per group. This test allows comments to be made about the interaction between factors as well as between groups.
• Repeated measures ANOVA: Used when members of a random sample are measured under different conditions. As the sample is exposed to each condition, the measurement of the dependent variable is repeated. Using standard ANOVA is not appropriate because it fails to take into account correlation between the repeated measures, violating the assumption of independence.

Why use it: To analyze the impact on the output of predetermined changes in the levels of process or product variables. ANOVA can compare two or more groups as opposed to other models when needed.

Where to use it:

• A standard 2-factor ANOVA format is used for analyzing measurement systems.
• ANOVAs provide information on interactions between samples and appraisers.
• With an ANOVA, we can vary the number of samples, appraisers, trials, and even the number of measurement devices to get a more accurate picture of the variation in the measurement system.
• ANOVAs allow us to get an accurate estimate of variances.
• ANOVA techniques are the preferred method for analyzing measurements for destructive testing.

When to use it: To help determine whether the variables being experimented on have a statistically significant impact on the process output.

How to use it: There are three conceptual classes of such models:

• Fixed-effects models assumes that the data came from normal populations which may differ only in their means. (Model 1) The fixed-effects model of analysis of variance applies to situations in which the experimenter applies several treatments to the subjects of the experiment to see if the response variable values change. This allows the experimenter to estimate the ranges of response variable values that the treatment would generate in the population as a whole.
• Random effects models assume that the data describe a hierarchy of different populations whose differences are constrained by the hierarchy. (Model 2) Random effects models are used when the treatments are not fixed. This occurs when the various treatments (also known as factor levels) are sampled from a larger population. Because the treatments themselves are random variables, some assumptions and the method of contrasting the treatments differ from ANOVA model 1.
• Mixed-effect models describe situations where both fixed and random effects are present. (Model 3)

Important Notes: ANOVA is a parametric test which assumes that the data analyzed:

1. Be continuous, interval data comprising a whole population or sampled randomly from a population.
2. Independence of cases
3. Has a normal distribution. Moderate departure from the normal distribution does not unduly disturb the outcome of ANOVA, especially as sample sizes increase. Highly skewed datasets result in inaccurate conclusions.
4. The groups are independent of each other.
5. The variances in the two groups should be similar.
6. For two-way ANOVA, the sample size the groups is equal (for one-way ANOVA, sample sizes need not be equal, but should not differ hugely between the groups).

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