Imagine that all of the facts are the same as the example above, except that variance (s2b) = 60 and within-group variance (s2w) = 21. What, if anything, changes? = s2b / s2w = 60/21 = 2.86 F We still look to the Anova table for column 2, row 60 (df1, df2). The threshold value, of course, is still 3.15. What’s the decision? Our value of 2.86 is equal to or greater F not than the threshold value, so we: (a) accept H0, (b) prove H0, or (c) fail to reject H0? It’s that last one: we fail to reject H0. Equivalently, the effect of hearing status is not significant. Have we proven the Null? No. What and Have in Common z, t, F and (Anova) are all fractions; and are variations on a z score. In all three cases, z, t, F t F the numerator measures the how different the means are. numerator: z t numerator: F numerator: s2b (ordinary s2 calculated using the as data) sample means In all three cases, the denominator measures sampling error. denominator (std of the mean): (= z σx̅ σ/√n) t denominator (std error of the diff betw means): (= a long thing we didn’t discuss) F denominator (within-group variance: s2w (ordinary s2 calculated the groups) within So, all three formulas have the same form: difference between (or the means = __________________________________ z, t, F sampling
Imagine that all of the facts are the same as the example above, except that variance (s2b) = 60 and within-group variance (s2w) = 21. What, if anything, changes? F = s2b / s2w = 60/21 = 2.86 We still look to the Anova table for column 2, row 60 (df1, df2). The threshold value, of course, is still 3.15. What’s the decision? Our F value of 2.86 is not equal to or greater than the threshold value, so we: (a) accept H0, (b) prove H0, or (c) fail to reject H0? It’s that last one: we fail to reject H0. Equivalently, the effect of hearing status is not significant. Have we proven the Null? No. What z, t, and F Have in Common z, t, and F (Anova) are all fractions; t and F are variations on a z score. In all three cases, the numerator measures the how different the means are. z numerator: t numerator: F numerator: s2b (ordinary s2 calculated using the sample means as data) In all three cases, the denominator measures sampling error. z denominator (std of the mean): σx̅ (= σ/√n) t denominator (std error of the diff betw means): (= a long thing we didn’t discuss) F denominator (within-group variance: s2w (ordinary s2 calculated within the groups) So, all three formulas have the same form: difference between (or the means z, t, F = __________________________________ sampling
AnovaLogic.docx