Ans. Introduction of ANOVA:
The t-test have one very serious limitation- they are
restricted to tests of the significance of the difference between only two
groups. There are many times when we like to see if there are significant
differences among three, four, or even more groups. For example we may want to
investigate which of three teaching methods is best for teaching ninth class
algebra. In such case, we cannot use t-test because more than two groups are
involved.
To deal with such type of cases one of the most useful
techniques in statistics is analysis of variance. This technique was developed
by a British statistician Ronald A. Fisher.
Logic of ANOVA
Let us take a hypothetical data given in the table.
Hypothetical
data from an experiment examining learning performance under three temperature
condition.
There are
three separate samples, with n = 5 in each sample. The dependent variable is
the number of problems solved correctly.
These data
represent results of an dependent experiment comparing learning performance
under three temperature conditions. The scores are variable and we want to
measure the amount of variability to explain where it comes from. To compare
the total variability, we will combine all the score from all the separate
samples into one group and then obtain one general measure of variability for
the complete experiment. Once we have measured the total variability, we can
being to break it into separate components.
The word
analysis means breaking into smaller parts. Because we are going to analyze the
variability, the process is called analysis of variance ANOVA.
There are two fundamental sorts of ANOVA: single direction (or unidirectional) and two-way. There additionally varieties of ANOVA. For instance, MANOVA (multivariate ANOVA) contrasts from ANOVA as the previous tests for various ward factors at the same time while the last evaluates just a single ward variable at a time.
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