Chi-Squared Test
( O−E)²
Formula: χ² = ∑
E
E = Expected Number
O = Observed Number
Degrees of Freedom = Number of Classes – 1 (N-1)
Significance Level = 5% = 0.05
Null Hypothesis = There is no significant difference between the observed and expected
date at the 5% significance level, any difference is due to chance
If χ² > CV, difference is significant, reject null hypothesis
If χ² < CV, difference is due to chance, accept null hypothesis
Example
Category Observed (O) Expected (E) (O-E)² (O−E)²
E
Yellow, Round 169 162 49 0.30
Green, Round 54 54 0 0.00
Yellow, Bumpy 51 54 9 0.17
Green, Bumpy 14 18 16 0.88
χ² 1.35
Degrees of Freedom = 4 - 1 = 3
CV = 7.82
1.35 < 7.82
χ² < CV
Accept null hypothesis, difference is due to chance
( O−E)²
Formula: χ² = ∑
E
E = Expected Number
O = Observed Number
Degrees of Freedom = Number of Classes – 1 (N-1)
Significance Level = 5% = 0.05
Null Hypothesis = There is no significant difference between the observed and expected
date at the 5% significance level, any difference is due to chance
If χ² > CV, difference is significant, reject null hypothesis
If χ² < CV, difference is due to chance, accept null hypothesis
Example
Category Observed (O) Expected (E) (O-E)² (O−E)²
E
Yellow, Round 169 162 49 0.30
Green, Round 54 54 0 0.00
Yellow, Bumpy 51 54 9 0.17
Green, Bumpy 14 18 16 0.88
χ² 1.35
Degrees of Freedom = 4 - 1 = 3
CV = 7.82
1.35 < 7.82
χ² < CV
Accept null hypothesis, difference is due to chance
