The same approach used to calculate a confidence interval for the effect size of a t test (see Confidence Intervals for Power and Effect Size of t Test) can be employed to create a confidence interval for a noncentrality parameter, and in turn Cohen’s effect size and statistical power, for a chi-square goodness of fit or independence test.

**Example 1**: Find the 95% confidence interval for the effect size *w* and power of a chi-square test of independence for a 3 × 3 contingency table with sample size 500 when *χ*^{2} = 30.

**Figure 1 – Confidence intervals for effect size and power**

We see from Figure 1 that the 95% confidence interval for the noncentrality parameter is (9.98, 51.81). The corresponding confidence interval for the effect size *w* of .24 is (.14, .32) and the confidence interval for power of 99.7% is (71.5%, 99.99%).

Using calculator for the noncentral chi-square distribuition

http://keisan.casio.com/exec/system/1180573184

for your above example I have recieved values 14.79 and 58.80 for the lower and upper limits for lambda which differ from yours.

What you have calculated is not the lower and upper limits for lambda, but the lower and upper limits for x. In fact NCHISQ_INV(.025,4,30) = 14.79 and NCHISQ_INV(.975,4,30) = 58.80, the same as the values you have shown.

Charles

I cannot understand where is this procedure in Real Statistics. In the list of Data Analysis Tools there is only Staistical Power and Sample Size. I mark it and then mark Chi-Square test and in the menu there are only Size Effect, Sample size, df, alpha and Sum Count (BTW, what is this?). However, there is no option for the CI calculation and no table like your Fig. 1

Nikita,

I have not implemented this capability yet in the Real Statistics software. You can calculate it yourself as described on the referenced webpage.

Sum Count = the number of terms used from the theoretically infinite sum required to calculate the noncentral chi-square distribution value. You don’t really need to worry about this and simply use the default.

Charles

What is “x” in this your reply?

Nikita,

x was simply my way of referencing the noncentral chi-square statistic value. The main thing is that NCHISQ_INV(.025,4,30) = 14.79 and NCHISQ_INV(.975,4,30) = 58.80.

Charles

Dear Dr. Ziontz,

please, help me to understand is it possible and how to calculate confidence interval for the effect size w using RealStatistics

Thank you in advance, best regards, Nikita

Yes

Yes, you use the NVHISQ_NCP, as shown in Figure 1 of the referenced webpage.

Charles