Testing for independence
H0 : X and Y are independent
HA : X and Y are dependent
The following test statistic is used:
P-value
The p-values is interpreted in the same way as for other hypothesis tests — it describes the strength of evidence against the null hypothesis:
p-value | Interpretation |
---|---|
over 0.1 | no evidence against the null hypothesis (independence) |
between 0.05 and 0.1 | very weak evidence of dependence between the row and column variables |
between 0.01 and 0.05 | moderately strong evidence of dependence between the row and column variables |
under 0.01 | strong evidence of dependence between the row and column variables |
Warning about low estimated cell counts
The χ2 test statistic has only approximately a chi-squared distribution. The p-value found from it can be relied on if:
If the cell counts are small enought that these conditions do not hold, the p-value is less reliable. (But advanced statistical methods are required to do better!)