Question

Below is table of observed count data that you would like to use to run a Chi Square Test of Independence. Based on data presented would you violate any assumptions? How do you know?

	Condition 1	Condition 2
Condition A	24	5
Condition B	6	7

Answer 1

Step-: State the hypothesis:

H0: Two categories variables are independent.

H1: Two categories variables are not independent.


Step-2: Observed Frequencies:

	Condition 1	Condition 2	Total
Condition A1	24	5	29
Condition A2	6	7	13
Total	30	12	42

Step-3:Expected Frequencies:

Fe11 = (29 x 30 ) / 42 = 20.7143

Fe12 = (29   x 12 ) / 42 = 8.2857

Fe21 = ( 13 x 30 ) / 42 = 9.2857

Fe22 = ( 13 x 12 ) / 42 = 3.7143

	Condition 1	Condition 2	Total
Condition A1	20.7143	8.2857	29
Condition A2	9.2857	3.7143	13
Total	30	12	42

Step-4: Compute Chi-square:

χ2 = ∑ [ (Oi - Ei)² / Ei ]

= (24 - 20.7143)² / 20.7143 + (5 - 8.2857)² / 8.2857 + (6 - 9.2857)² / 9.2857 + (7 - 3.7143)² / 3.7143

= 0.5212 + 1.303 + 1.1626 + 2.9066

= 5.8934

χ2 = 5.8934       -------------------------(Calculated value)

Step-5: Compute the degrees of freedom (df):
df= (2 - 1)⋅(5 - 1)

df = 4
Level of significance = 0.05

χ2 = 3.841     -------------------------(Tabulated value)

Step-6: Decision:

Calculated value > Tabulated value

5.8934   > 3.841

P value = 1 – (0.05/2)

             = 1 – 0.025

P value = 0.975

Critical value = 1.96

Step-7: Conclusion:

Null hypothesis is rejected.

Alternative hypothesis is accepted.

H1: Two categories variables are not independent.