CHS Stats - 10.4 Quiz: Analysis of Variance

What does one-way ANOVA test stand for?

one-way analysis of variance test

What is the one-way ANOVA test used for?

to compare the means of 3 or more populations

What do H₀ and H_a look like?

• H₀: μ₁ = μ₂ = μ₃ = … = μ_k

• H_a: At least 1 population mean (or μ) differs.

One-Way ANOVA Test Conditions

1. Samples are random

2. Samples are independent

3. Populations are normal or approximately normal

4. Each population has the same variance

   • If not told, use the Pitt Rule of Thumb (If 2 • smaller s ≥ larger s, assume population variances are equal.)

What does “between” relate to? How is it shown on the calculator?

relates to treatments given to each sample (on the calculator, FACTOR or GROUP)

What does “within” relate to? How is it shown on the calculator?

relates to differences within the same sample, usually due to sampling error (on the calculator, ERROR)

F =

F = MS_B / MS_W = Mean Square Between (variance between) / Mean Square Within (variance within)

MS_B =

MS_B = SS_B / df_N = sum of squares between / (k-1)

• k = # of samples

df_N =

df_N = k - 1

• k = # of samples

MS_W =

MS_W = SS_W / df_D = sum of squares within / (N-k)

• N = sum of the sample sizes (∑n)

• k = # of samples

df_D =

df_D = N - k

• N = sum of sample sizes (∑n)

• k = # of samples

Running an ANOVA test

1. Type lists in calculator

2. STAT → TESTS → H) ANOVA

3. On main screen, ANOVA (L₁, L₂, L₃, …, L_k)

Decisions with final statements

1. If P ≤ ∝, R H₀… Evidence suggests that at least one population mean (μ) is different.

2. If P > ∝, F to R H₀… Evidence suggests that all population means (μ) are equal.