CHS Stats - 10.3 Quiz: Comparing Two Variances

F-Distribution

1. A family of curves determined by 2 different degrees of freedom

   • df_N = df of numerator

   • df_D = df of denominator

2. Positively (right) skewed… NOT symmetric

3. Total area under the curve = 1

4. All values of F ≥ 0

5. For all F-distributions, the mean value of F is approximately 1

How to find F by hand

1. Assign subscripts to the two categories: 1 goes with the greater var./st. dev., 2 goes with the smaller var./st.dev.

2. F = s₁² / s₂²

   • s₁² ≥ s₂² - F will always be at least 1!

What is the test in this section called?

the Hypothesis Test for Comparing Variances and Standard Deviations

Hypothesis Test for Comparing Variances and Standard Deviations Conditions

1. Samples are random

2. Samples are independent

3. Populations are normal

Hypothesis Test for Comparing Variances and Standard Deviations Steps

1. H₀: σ₁⁽²⁾ = σ₂⁽²⁾, H_a: σ₁⁽²⁾ </>/≠ σ₂⁽²⁾; can specifiy claim

2. ∝ =

3. Standardized Test Statistic: F = s₁² / s₂²

   • s₁² ≥ s₂² - F will always be at least 1!

4. P-Value: Fcdf(lower, upper, df_N, df_D)

   • df_N = n₁ - 1

   • df_D = n₂ - 1

   • For steps 3 & 4, use STAT → TESTS → E) 2-SampFTest if two-tailed or given a list

     • If given a list, be sure to put them in the right order! (The 1st one is the one with the greater s⁽²⁾)

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

6. Final Statement

   • Original four

   • Evidence suggests that the variances/standard deviations are/are not equal.

   • Evidence suggests that there is no/is a difference in the variances/standard deviations.

Pitt Rule of Thumb

If 2 • the smaller s ≥ the larger s, then assume the populations have equal variances.

• If given an s², must take the square root of it for this

• Doesn’t always work