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Chi Squared Test for
Independence
c
2
Hypothesis Testing
• Null Hypothesis, H o
– States that the two variables in question are
independent of each other.
• Alternative Hypothesis, H1
– States that the two variables in question are
dependent on each other
Chi-Squared Test
with GDC
• A researcher conjectures that watching football on the
weekends is related to gender. Her data gathered is in the
frequency distribution chart below. Construct a chi-squared
hypothesis test to determine if there is enough evidence to
support the researcher’s conjecture.
Watch Football on Weekend?
Gender
Female
Male
Yes
No
Chi-Squared Steps
• Step 1: Write the null and alternative
hypothesis
c
2
Chi-Squared Steps
c
2
• Step 2: Find the p-value
– P-value is the probability value of evidence against
the null hypothesis.
• Smaller the number the more chance that the two
numbers in question really are significantly different
• GDC: 2nd Matrix -- Edit – 2 x 2 – Enter Data
• P-Value: Stat – Tests -- c 2-Test -- Calculate
Chi-Squared Steps
c
2
• Step 3: Select an alpha level α
– Alpha level represents the chance of making a
mistake, the mistake that you reject the null
hypothesis when it is actually true
• Common Alpha levels are 1%, 5%, 10%
• Select α = .01 for this example
Chi-Squared Steps
c
2
• Step 4:
• A) Compare the p-value to the alpha level
– P – value > alpha level
2
c
• B) Compare the calc against the critical value
Chi-Squared Steps
c
2
• Step 5: Interpret the comparison
2
• A) If the p-value > alpha level or c calc < CV,
DO NOT reject the null hypothesis
B) If the p-value < alpha level or c >CV,
REJECT the null hypothesis and accept the
alternative hypothesis
2
calc