Nonparametric Tests. February 2013. Nonparametric Tests. Nature of the distribution is not known, or known to be non-normal. Sometimes called distribution free statistics Everything up to this point we’ve assumed comes from data that IS normally distributed. Nonparametric Tests.
Nature of the distribution is not known, or known to be non-normal.
Sometimes called distribution free statistics
Everything up to this point we’ve assumed comes from data that IS normally distributed.
Probably the most commonly used and easiest to understand and one of the only nonparametric tests that reveals association between variables.
Uses categorical data which can be presented in tabular fashion, e.g., rows and columns.
The chi-square statistic compares the observed count in each cell of the table with what would be expected if there is no association between the rows and columns in the table.
Used to test the hypothesis of no association between two (or more) groups and compares observed to expected counts.
(Note: Expected counts = row total X column total / total number)
X2 = Sumi[(Observedi – Expectedi) 2 / Expectedi]
X2 =(13 – 43)2 /43 + (86-56)2 /56 + (80-50)2 / 50 + (35-65)2 / 65
= 900/43 + 900/56 + 900/50 +900/65
=20.93 +16.07 +18.00 +13.85
X2calculated = 68.85
X2table= 3.84 with 1 degree of freedom (d.f. = (rows -1) times (columns-1) and alpha =0.05
Therefore, we reject the hypothesis of no association and can state the p-value would be less than 0.05 (would need to look up in the table to obtain the actual p-value)