16FTests

# 16FTests - Statistical Techniques I EXST7005 The F...

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Statistical Techniques I EXST7005 The F distribution

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The F test This test can be used to either, test the equality of population variances - our present topic test the equality of population means (this will be discussed later under ANOVA) The F test is the ratio of two variances (the ratio of two chi square distributions) Given two populations Population 1 Population 2 Mean μ 1 μ 2 Variance σ 1 σ 2
The F test (continued) Two populations Draw a sample from each population Population 1 Population 2 Sample size n1 n2 d.f. γ 1 γ 2 Sample mean f8e5 Y1 f8e5 Y2 Sample variance S1 S2

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The F test (continued) To test the Hypothesis H0: σ 12 = σ 22 H1: σ 12 σ 22 (one sided also possible) use F = σ 12 / σ 22 which has an expected value of 1 under the null hypothesis, but in practice there will be some variability so we need to define some reasonable limits and this will require another statistical distribution.
The F distribution 1) The F distribution is another family of distributions, each specified by a PAIR of degree of freedom, γ 1 and γ 2. γ 1 is the d. f. for the numerator γ 1 is the d. f. for the denominator Note: the two samples do not have to be of the same size and usually are not of the same size. 2) The F distribution is an asymmetrical distribution with values ranging from 0 to , so [ F ].

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The F distribution (continued) 3) There is a different F distribution for every possible pair of degrees of freedom. 4) In general, an F value with γ 1 and γ 2 d.f. is n the same as an F value with γ 2 and γ 1 d.f., so order is important. i.e. F γ 1, γ 2 F γ 2, γ 1 usually 5) The expected value of any F distribution is 1 i the null hypothesis is true.
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 F distribution with 1, 5 d.f. F distribution with 5, 10 d.f. F distribution with 100, 100 d.f. The F distribution

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The F tables 1) The numerator d.f. ( γ 1) are given along the to of the page, and the denominator d.f. ( γ 2) are given along the left side of the page. Some tables give only one F value at each intersection of γ 1 and γ 2. The whole page would be for a single α value and usually severa pages would be given.
The F tables (continued) Our tables will give four values at the intersectio of each γ 1 and γ 2, each for a different α value. These

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## This note was uploaded on 12/29/2011 for the course EXST 7087 taught by Professor Wang,j during the Fall '08 term at LSU.

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16FTests - Statistical Techniques I EXST7005 The F...

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