OMIS 2050 - Class 4: Categorical Data Inference

What is the parameter between 2 population proportions?

p̂₁ - p̂₂

What are the p̂₁ - p̂₂ normal distribution conditions?

• n₁p̂₁

• n₂p̂₂

• n₁(1- p̂₁)

• n₂(1-p̂₂)

… ≥ 5

What is the z hypothesis test formula?

z=\frac{\left(\hat{p}_1-\hat{p}_2\right)}{\sqrt{\hat{p}\left(1-\hat{p}\right)\left(\frac{1}{n_1+n_2}\right)}}

What is the p̂ formula?

\frac{x_1+x_2}{n_1+n_2}

What is the z_crit Excel formula?

=NORM.S.INV

What is the CI formula?

\left(\hat{p}_1-\hat{p}_2\right)\pm z_{\frac{\alpha}{2}}\sqrt{\frac{\hat{p}_1\left(1-\hat{p}_1\right)}{n_1}+\frac{\hat{p}_2\left(1-\hat{p}_2\right)}{n_2}}

What is the chi-square independence test?

// chi-square contingency table test // chi-square association test

2 nominal variable independence

What is the chi-square independence test H₀?

independent

What is the chi-square independence test H₁?

dependent

What is the expected value formula?

\frac{row\sum\cdot column\sum}{total}

What is the chi-square independence test formula?

x^2=\sum\frac{\left(f_{i}-e_{i}\right)^2}{e_{i}}

What is the chi-square independence test expected value required condition?

rule of 5

What is the rule of 5?

E_i ≥ 5

IF E_i < 5, combine row/column & change d.f

What is the chi-square independence test freedom degree formula?

\left(rows-1\right)\left(columns-1\right)

What is the relationship between the chi-square curve & freedom degrees?

as freedom degrees increase, chi-square curve approaches normal distribution

What is the chi-square independence test critical value Excel formula?

=CHISQ.INV.RT(α,d.f)

What is the chi-square independence test rejection region?

x² > x²_crit

What are some chi-square independence test use examples?

• age & preference

• customer churn & service

• conversion rate & landing page

What is a contingency table?

// cross-tabulation table // 2-way table

arranged data

What are contingency table use examples?

• joint

• marginal

• conditional

… probability

What is the chi-square independence test process?

1. contingency table

2. e_i

3. rule of 5

4. x²