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ANALYSIS OF VARIANCE
When comparing the means of two groups or levels of a variable (e.g., above-average / below average) the
appropriate test is the t-test or t-ratio.
Most research involves looking for differences in the
means of 3 or more groups or levels of a variable (e.g.,
Low / Medium / High).
(i.e., we could compare mean scores on an abortion index for Protestants and Catholics using a t-test. But what about differences in average scores across more than 2 religious groups (Protestants, Catholics, Moslems, Jews)???
One possibility would be to do a series of t-tests for each
religious pairing (e.g., Protestants vs. Catholics;
Protestants vs. Jews; Protestants vs. Moslems; Catholics
vs. Jews; Catholics vs. Moslems; Jews vs. Moslems). But
a series of t-tests like this is tedious, hard to interpret,
and likely to produce “false” test results!
The more statistical tests you conduct on a hypothesis,
in this case 6 t-tests for each religious pairing, the more
likely you are to get a false finding!
So what we need, and what ANOVA provides, is a single
statistical test we can conduct when we want to compare the means of 3 or more groups or levels of a variable.
MEDIAN TEST
We use the t-ratio or ANOVA when testing hypotheses that involve variables measured at the interval or ratio level. We use Chi-square for testing hypotheses that involve variables measured at the nominal or ordinal level.
The Median test is used specifically to test hypotheses
where both variables are measured at the ordinal level.
Ordinal measurement provides us with enough information that we can rank respondents or cases in terms of having more or less of the phenomenon being measured…we just don’t know how much more or less!
MORE ON THE MEDIAN
TEST…
Whenever you are interested in testing for significant
differences in the medians of two groups or two levels of
a variable, you should use the Median test.
The Median test is a special case of the chi-
square statistic. It involves performing a chi- square test on a created variable that measures whether scores fall above or below the median of the two groups or levels of a variable.
