Question

For each of the following situations give the degrees of freedom and an appropriate bound on the P-value (give the exact value if you have software available) for the χ² statistic for testing the null hypothesis of no association between the row and column variables.

(a) A 2 by 2 table with χ² = 0.91.

df =
P-value =

(b) A 4 by 4 table with χ² = 18.5.

df =
P-value =

(c) A 2 by 8 table with χ² = 22.27.

df =
P-value =

(d) A 5 by 3 table with χ² = 12.89.

df =
P-value =

Answer 1

SOLUTION:

From given data,

For each of the following situations give the degrees of freedom and an appropriate bound on the P-value (give the exact value if you have software available) for the χ² statistic for testing the null hypothesis of no association between the row and column variables.

We know the formula for

degrees of freedom =(r-1)(c-1)

(a) A 2 by 2 table with χ² = 0.91.

For 2 by 2 table

r = 2 and c = 2 Then

degrees of freedom =(2-1)(2-1) = 1*1 = 1

χ² = 0.91

df = 1

The P-Value = 0.34011

(b) A 4 by 4 table with χ² = 18.5.

For 4 by 4 table

r = 4 and c = 4 Then

degrees of freedom =(4-1)(4-1) = 3*3 = 9

χ² = 18.5

df = 9

The P-Value = 0.02979

(c) A 2 by 8 table with χ² = 22.27.

For 2 by 8 table

r = 2 and c = 8 Then

degrees of freedom =(2-1)(8-1) = 1*7 = 7

χ² = 22.27

df = 7

The P-Value = 0.00228

(d) A 5 by 3 table with χ² = 12.89.

For 5 by 3 table

r = 5 and c = 3 Then

degrees of freedom =(5-1)(3-1) = 4*2 = 8

χ² = 12.89

df = 8

The P-Value = 0.11569