Chi Square is a non-parametric test of statistical significance for bivariate tabular analysis. A non-parametric test, like chi-square, is a rough estimate of confidence.
Typically, the hypothesis tested with chi square is whether or not two different samples (Coleoptera (beetles) and Diptera (flies) are different enough in some characteristic or aspect of their behavior that we can generalize from our samples that the populations from which our samples are drawn are also different in the behavior or characteristic. .
The figure below shows our raw data for insects trapped on pitcher plants at different times of the day.
Time Diptera (flies) Coleoptera (beetles).
Evening 40 20.
Late Evening 10 30.
From the above bivariate tabular analysis, we can hypothesized that insects trapped by the pitcher plants is dependent to the time of the day, hence more flies are trapped in the evening as opposed to beetles which are mostly trapped in late evening.
By converting the above data into percentages of each cell, we standardize the cell frequencies as if they were 100 subjects in each category of the independent variable. This is done by totaling each row and dividing each cell by its row total and then multiplying the fraction by a 100. This gives us the different times each category of insect is trapped by the pitcher plant in terms of percentages as below.
Time Diptera (flies) Coleoptera (beetles) N.
Evening 66.7% 33.3% 60.
Late Evening 25% 75% 40.
.
As seen above, the percentages are calculated by dividing each cell y its row total then multiplying by 100. For cell 1 we have,.
40 X 100 .
60 =66.7%.
From the table, twice as many Coleoptera (beetles) are trapped in late evening and opposed to less than half Diptera (flies) trapped in the evening. Also this help us to make predictions of what time this two category of insects feed, since they visit the pitcher plant leave prominently for nectar.