Percentage deviation and standardized residual are both measures of the degree to which an observed chi-square cell frequency differs from the value that would be expected on the basis of the null hypothesis._Q

---

For each cell, percentage deviation is calculated as_Q

xxx

observed — expected expected

x 100

Thus, a percentage deviation of +15% within a cell indicates that the observed frequency is 15% greater than the expected, while a percentage deviation of -15% indicates that the observed frequency is 15% smaller than the expected.

In the special case of df=1, the calculation of percentage deviation incorporates a correction for continuity:_Q

xxx

|observed — expected| —0.5 expected

x 100

The resulting value is then given a positive sign if observed>expected and a negative sign if observed<expected._Q

---

The standardized residual for a cell in a chi-square table is a version of the standard normal deviate, z, calculated as_Q

xxx

z =

observed — expected sqrt[expected]

In the special case of df=1, the calculation of the standardized residual incorporates a correction for continuity:_Q

xxx

z =

|observed — expected| —0.5 sqrt[expected]

The resulting value of z is then given a positive sign if observed>expected and a negative sign if observed<expected.

The chi-square value that results from a chi-square analysis is equal to the sum of the the squares of the standardized residuals.

Assuming the null hypothesis to be true, and providing that the expected value for a cell is at least 5, values of the standardized residual belong to a normally distributed sampling distribution with a mean of zero and a standard deviation of ±1.0.

---