Question

While performing a chi-squared test, a researcher obtains a two-sided p-value of .16. What was her Chi-squared statistic, using 1 degree of freedom. Show work and don't use software.

Answer 1

We know that the square of standard normal variate ( Z² ) follows chi-square distribution with one degrees of freedom.

The 2-tailed view:

"The two-tail probability beyond +/- z for the standard normal distribution equals the right-tail

probability above z-squared for the chi-squared distribution with df=1. For example, the two-tailed

standard normal probability of .05 that falls below -1.96 and above 1.96 equals the right-tail

chi-squared probability above (1.96)squared=3.84 when df=1.

Here p-value = 0.16

therefore p-value/2 = 016/2 = 0.08

Less than area from z test statistic value = 1 - 0.08 = 0.92

Let's use z table

z test statistic value = 1.41

Look the following image:

Therefore chi-square test statistic value = (1.41^2) = 1.9881

Note that if we use technology then we get the exact chi-square test statistic value as

chi-square test statistic = "=CHIINV(0.16,1)" = 1.974