Stats Meth Bus - Ch. 11 (One/Two-way ANOVA, Levene Test, TUKEY)

c

count or # of independent populations

One-way ANOVA: Q1

Do these populations have the same mean?

One-way ANOVA: A1

• Do a One-way ANOVA Test to compare population means

• YES, if population means are the same (H₀ is not rejected)

• NO, if population means are different (H₀ is rejected)

One-Way ANOVA Test

let μ_j be the ACTUAL MEAN _ from population j; j = 1, . . ., c

H₀: μ₁ = μ₂ = . . . = μ_j (no significant difference between μ_j)

H₁: Not all μ_j are equal. (at least one significant difference between μ_j)

α = 0.05, F_STAT = (MSA / MSW), F_CRIT = α, df_A, df_W

Decision Rule: If F_STAT > F_CRIT, then reject H₀.

Decision:

• Case A: Since F_STAT > F_CRIT, we reject H₀. (DO TUKEY PROCEDURE)

• Case B: Since F_STAT <= F_CRIT, we cannot reject H₀. (STOP)

Levene Test

let σ² be Variance for _ at j; j = 1, . . ., c

H₀: σ₁² = σ₂² = . . . = σ_j² (no significant difference between σ_j²)

H₁: Not all σ_j² are equal. (at least one significant difference between σ_j²)

α = 0.05, F_STAT = F in Excel, F_CRIT = α, df_A, df_W

Decision Rule: If F_STAT > F_CRIT, then reject H₀.

Decision:

• Case A: Since F_STAT > F_CRIT, we reject H₀. (we did the wrong thing)

• Case B: Since F_STAT <= F_CRIT, we cannot reject H₀. (we did the right thing)

Tukey Procedure

1) Make all possible pairs of populations (j, j’); j ≠ j’

2) Estimate the distance μ_j for each pair

3) Construct Critical Range for each pair

4) Decision: If result from 2) > result from 3), then μ_j & μ_j’ are different

* if means are different, use sample mean to pick best population

What to do when n - c is not on the Q_STAT table

choose a value between the lower n - c and higher n - c that your n - c falls between

Business Analytics Process

1) Leven Test:

• YES, same variance, CONTINUE

• NO, different variance, STOP

2) One-way ANOVA Test:

• YES, same means, STOP

• NO, different means, CONTINUE

3) TUKEY Procedure:

• find which means are different and choose best location