anova
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anova [2018/10/19 07:54] – [F and t value] hkimscil | anova [2020/05/20 15:14] – [Example] hkimscil | ||
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====== Post hoc test ====== | ====== Post hoc test ====== | ||
[[Post hoc test]] | [[Post hoc test]] | ||
+ | < | ||
+ | > adata | ||
+ | Brands | ||
+ | 1 | ||
+ | 2 | ||
+ | 3 | ||
+ | 4 | ||
+ | 5 | ||
+ | 6 | ||
+ | 7 | ||
+ | 8 | ||
+ | 9 | ||
+ | 10 Apollo 36.41900 | ||
+ | 11 Apollo 36.43000 | ||
+ | 12 Apollo 34.83600 | ||
+ | 13 Apollo 38.32800 | ||
+ | 14 Apollo 30.62300 | ||
+ | 15 Apollo 32.57500 | ||
+ | 16 Bridgestone 33.52300 | ||
+ | 17 Bridgestone 31.99500 | ||
+ | 18 Bridgestone 35.00600 | ||
+ | 19 Bridgestone 27.87900 | ||
+ | 20 Bridgestone 31.29700 | ||
+ | 21 Bridgestone 31.06200 | ||
+ | 22 Bridgestone 34.83800 | ||
+ | 23 Bridgestone 33.97600 | ||
+ | 24 Bridgestone 32.55200 | ||
+ | 25 Bridgestone 30.88100 | ||
+ | 26 Bridgestone 28.14400 | ||
+ | 27 Bridgestone 29.18400 | ||
+ | 28 Bridgestone 33.07500 | ||
+ | 29 Bridgestone 32.36500 | ||
+ | 30 Bridgestone 30.92500 | ||
+ | 31 CEAT 34.44565 | ||
+ | 32 CEAT 32.80658 | ||
+ | 33 CEAT 33.41499 | ||
+ | 34 CEAT 36.86118 | ||
+ | 35 CEAT 36.97277 | ||
+ | 36 CEAT 35.08145 | ||
+ | 37 CEAT 34.95412 | ||
+ | 38 CEAT 33.47516 | ||
+ | 39 CEAT 30.42748 | ||
+ | 40 CEAT 36.13392 | ||
+ | 41 CEAT 34.78336 | ||
+ | 42 CEAT 36.11675 | ||
+ | 43 CEAT 41.05000 | ||
+ | 44 CEAT 32.16845 | ||
+ | 45 CEAT 32.72624 | ||
+ | 46 Falken 39.59600 | ||
+ | 47 Falken 38.93700 | ||
+ | 48 Falken 36.12400 | ||
+ | 49 Falken 37.69500 | ||
+ | 50 Falken 36.58600 | ||
+ | 51 Falken 35.96700 | ||
+ | 52 Falken 36.73700 | ||
+ | 53 Falken 34.31000 | ||
+ | 54 Falken 40.25200 | ||
+ | 55 Falken 37.38200 | ||
+ | 56 Falken 40.66300 | ||
+ | 57 Falken 37.09500 | ||
+ | 58 Falken 38.00500 | ||
+ | 59 Falken 37.75600 | ||
+ | 60 Falken 37.26500 | ||
+ | > | ||
+ | </ | ||
+ | |||
+ | < | ||
+ | > summary(fmod.tire) | ||
+ | Df Sum Sq Mean Sq F value | ||
+ | Brands | ||
+ | Residuals | ||
+ | --- | ||
+ | Signif. codes: | ||
+ | > | ||
+ | </ | ||
+ | < | ||
+ | > TukeyHSD(fmod.tire) | ||
+ | Tukey multiple comparisons of means | ||
+ | 95% family-wise confidence level | ||
+ | |||
+ | Fit: aov(formula = Mileage ~ Brands, data = adata) | ||
+ | |||
+ | $Brands | ||
+ | diff lwr | ||
+ | Bridgestone-Apollo -3.01900000 -5.1288190 -0.909181 0.0020527 | ||
+ | CEAT-Apollo | ||
+ | Falken-Apollo | ||
+ | CEAT-Bridgestone | ||
+ | Falken-Bridgestone | ||
+ | Falken-CEAT | ||
+ | > | ||
+ | > tapply(adata$Mileage, | ||
+ | | ||
+ | | ||
+ | > | ||
+ | </ | ||
+ | |||
====== F and t value ====== | ====== F and t value ====== | ||
$$ F = t^{2}$$ | $$ F = t^{2}$$ | ||
Line 433: | Line 530: | ||
| | 41 | 21 | 15 | | | | 41 | 21 | 15 | | ||
| T | 180 | 240 | 270 | | | T | 180 | 240 | 270 | | ||
- | | n | 10 | 10 | 10 | | + | | n | 10 | 10 | 10 | |
- | | Mean | $\overline{X_1}$ = 18 | $\overline{X_2}$ = 24 | $\overline{X_3}$ = 27 | | + | | Mean | 18 | 24 | 27 | |
- | | Total | + | | Mean%%^%%2 |
- | | $\sum{(X_i)^2}$ | + | | b = $n*(mean)^2$ | 3240 | 5760 | 7290 | |
+ | | a = $\sum{(X_i)^2}$ | ||
+ | | a-b = Var.within | ||
+ | \begin{eqnarray*} | ||
+ | a & = & \sum (X_i)^2 = 17370 \\ | ||
+ | b & = & \overline{X_{total}} = 23 \\ | ||
+ | c & = & \overline{X}^2 = 529 \\ | ||
+ | d & = & N = 30 \\ | ||
+ | e & = & SS_{total} = \sum {(X_i)^2} = a - (d * c) = 1500 \\ | ||
+ | f & = & SS_{within} = 648 + 108+ 324 = 1080 \\ | ||
+ | g & = & SS_{between} = e - f = 420 | ||
+ | \end{eqnarray*} | ||
- | $\sum (X_i)^2 | + | \begin{eqnarray*} |
- | $\overline{X_{total}} | + | k & = & 3 \\ |
- | $\overline{X}^2 = 529 $ \\ | + | n & = & 10 \\ |
+ | N & = & 30 \\ | ||
+ | \end{eqnarray*} | ||
- | $ G = ? $ \\ | + | \begin{eqnarray*} |
- | $ G^2 = ? $ \\ | + | df_{between} & = & \\ |
- | $ \sum {(X_i)^2} = 17370 $ \\ | + | df_{within} & = & \\ |
- | \\ | + | df_{total} |
- | $ k = $ \\ | + | \end{eqnarray*} |
- | $ n = $ \\ | + | |
- | $ N = $ \\ | + | |
- | \\ | + | |
- | $ df_{total} = $ \\ | + | |
- | $ df_{between} = $ \\ | + | |
- | $ df_{within} = $ \\ | + | |
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anova.txt · Last modified: 2022/09/30 09:02 by hkimscil