analysis of variance

Analysis of Variance

Analysis of variance (ANOVA) is a statistical technique that can be used to evaluate whether there are differences between the average value, or mean, across several population groups. With this model, the response variable is continuous in nature, whereas the predictor variables are categorical. For example, in a clinical trial of hypertensive patients, ANOVA methods could be used to compare the effectiveness of three different drugs in lowering blood pressure.

Alternatively, ANOVA could be used to determine whether infant birth weight is significantly different among mothers who smoked during pregnancy relative to those who did not. In the simplest case, where two population means are being compared, ANOVA is equivalent to the independent two-sample t-test.

The analysis of variance is the process of resolving the total variation into its separate components that measure different sources of variance. If we have to test the equality of means between more than two populations, analysis of variance is used.

To test the equality of two means of a population we use t-test. But if we have more than two populations, t-test is applied pairwise on all the populations. This pairwise comparison is practically impossible and time consuming so, we use analysis of variance.

In analysis of variance all the populations of interest must have a normal distribution. We assume that all the normal populations have equal variances. The populations from which the samples are taken are considered as independent.

There are three methods of analysis of variance. Complete randomize design is used when on the variable is involved. When two variables are involved then Randomization complete block design is used. Latin square design is a very effective method for three variables. An analysis of the variation between all of the variables used in an experiment and Analysis of variance is used in finance in several different ways, such as to forecasting the movements of security prices by first determining which factors influence stock fluctuations. This analysis can provide valuable insight into the behavior of a security or market index under various conditions.

The easiest way to understand ANOVA is through a concept known as value splitting. ANOVA splits the observed data values into components that are attributable to the different levels of the factors. Value splitting is best explained by example:

The simplest example of value splitting is when we just have one level of one factor.

Suppose we have a turning operation in a machine shop where we are turning pins to a diameter of .125 +/- .005 inches. Throughout the course of a day we take five samples of pins and obtain the following measurements: .125, .127, .124, .126, .128. We can split these data values into a common value (mean) and residuals (what's left over) as follows:

=       .125       .127      .124      .126        .128

+       .126       .126      .126      .126        .126

       -.001       .001      -.002     .000        .002

From these tables, also called overlays, we can easily calculate the location and spread of the data as follows:
Mean = 0.126 Standard Deviation = 0.0016