Example:
A researcher wants to find whether there is significant difference in mean heights of adults from four different ethnic backgrounds, at confidence level of 95% (or type I error : alpha = 0.05). The study revealed the mean heights to be 165 ± 10 cm, 168 ± 10 cm, 175 ± 11 cm, and 169 ± 11 cm. He conducted the study with a sample size of 30 in each group. How much statistical power the study had achieved to detect the significant difference between these four mean heights?
Solution:
Here
Confidence level = 95%, power = 80%, M1 = 165, SD1= 10, M2=168, SD2=10, M3=175, SD3=11, M4=169, SD4=11.
After putting these values, we get statistical power = 89.25 %.
How statistical power is calculated? (Exclusively for advanced users)
1. Calculation of statistical power gained in ANOVA is a complex process, though much easier than calculating sample size.
2. Based on given sample size in each group, degrees of freedom for numerator and denominator are calculated. Then using given confidence level and these degrees of freedom, F critical value is calculated. For example, if the number of groups are 4, and Sample size for each group is 30, then degrees of freedom for numerator (d1) will be k -1 = 4 -1 =3. Degrees of freedom for denominator (d2) will be N – k = 30 * 4 – 4 = 116 (k = number of groups, N = total sample size in all k groups). Now F critical value (x) for 95% confidence level, 3 and 116 degrees of freedom is calculated using inverse F distribution function. (It is the F table value for given alpha and degrees of freedom)
3. Non centrality parameter (lambda) is calculated using following equation.
4. Using the values of non-centrality parameter (λ), d1, d2 and x; power of the test is calculated using non central cumulative distribution function formula.
Where, I (q | a, c) is the regularized incomplete beta function.
@ Sachin Mumbare