CHS Stats - 10.2 Quiz: Independence

contingency table

shows observed frequencies, is measured rows x columns, the intersection of a row & column is called a cell

cell

the intersection of a row and column

marginal frequencies

the sum of each row & column

joint frequencies

another name for observed frequencies

sample size

the total of the marginal frequencies for the rows or the marginal frequencies for the columns; write at the bottom right of the contingency table & box

Finding an expected frequency

E_{r, c} = (sum of row r • sum of column c) / sample size

What is the test in this section called?

the Chi-Square Test for Independence

Chi-Square Test For Independence Conditions

1. Sample is random

2. Each expected frequency is greater than or equal to 5

Chi-Square Test for Independence Steps

1. H₀: The variables ______ and ______ are independent. (order doesn’t matter); H_a: The variables ______ and ______ are dependent.

2. ∝ =

3. Standardized Test Stat

4. P-Value

   • For steps 3 & 4, write down matrices for observed and expected frequencies, input into calculator, go to STAT → TESTS: C) x² test

     • input correct matrices for observed & expected

5. Decision: If P ≤ ∝, R H₀; If P > ∝, F to R H₀

6. Final Statement: Something along the lines of “Evidence suggests that the variables are (independent/dependent).

   • Could also say related/not related

df =

(# of rows - 1) • (# of columns - 1)