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Tests for Descriptive Stats—319 sample means (between groups) should be the same as the variability within any subgroup (within group). Denote the i-th observation in group g as x g, i , where i = 1, …, n g for groups g = 1, 2, …G . The between and within sums of squares are defined as: G SS B = Σ n g( x g − x ) g=1 ng G SS B = Σ Σ 2 ( x ig − x g ) (11.11) 2 (11.12) g=1 i =1 where x g is the sample mean within group g and x is the overall sample mean. The Fstatistic for the equality of means is computed as: SS B ⁄ ( G − 1 ) F = ----------------------------------SS W ⁄ ( N − G ) (11.13) where N is the total number of observations. The F-statistic has an F-distribution with G − 1 numerator degrees of freedom and N − G denominator degrees of freedom under the null hypothesis of independent and identical normal distribution, with equal means and variances in each subgroup. For tests with only two subgroups ( G = 2 ) , EViews also reports the t-statistic, which is simply the square root of the F-statistic with one numerator degree of freedom. The top portion of the output contains the ANOVA results: Test for Equality of Means of LWAGE Categorized by values of MARRIED and UNION Date: 02/24/04 Time: 12:09 Sample: 1 1000 Included observations: 1000 Method df Value Probability (3, 996) 43.40185 0.0000 df Sum of Sq. Mean Sq. Between Within 3 996 36.66990 280.5043 12.22330 0.281631 Total 999 317.1742 0.317492 Anova F-statistic Analysis of Variance Source of Variation
