Power Calculation for Chi-Square Test


Enter a value for any two varaibles:

  • Sample Size
  • Power
  • Degrees of Freedom

The remaining empty field will be calculated. You can perform multiple power/sample size calculations.

Sample size is the number of observations in a sample.

Power is the probability of accepting the alternative hyptothesis when it is in fact true.

Degrees of freedom is the number of parameters of the system that may vary independently. When a comparison is made between two samples, the degrees of freedom equals (c-1)\times(r-1)
where c is the number of columns and r is the number of rows. That means (v1 -1) \times (v2 -1)
where v1 is the number of categories for the first variable and v2 is the number of categories for the second variable.

Effect Size is the measure of strength of a phenomenon (effect). See the definition box on the right-hand-size.

Significance Level is the α value


Results

The highlighted field denotes which variable is calculated.

Effect size
The Effect size (w), is defined as:

w=\sqrt{\sum\limit_{i=1}^m\frac{(p0_{i}-p1_{i})^{2}}{p0_{i}}

where:
  • p0i = cell probability in ith cell under H0
  • p1i = cell probability in ith cell under H1

Cohen suggests that w values of 0.1, 0.3 and 0.5 represent small, medium and large effect sizes respectively.


Not sure if you are running the right test? Try the Statistical Decision Tree Wizard