> tapply(count,site,mean) 1 2 3 4 5 6 33.80 68.72 50.64 9.24 10.00 12.64 > tapply(count,site,md) Error in tapply(count, site, md) : object 'md' not found > tapply(count,site,min) 1 2 3 4 5 6 0 0 0 0 0 0 > tapply(count,site,max) 1 2 3 4 5 6 233 466 407 82 94 95 > > crab.mod <- lm(count~site) > summary.lm(crab.mod) Call: lm(formula = count ~ site) Residuals: Min 1Q Median 3Q Max -68.72 -33.80 -9.24 0.37 397.28 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 33.80 14.38 2.350 0.0201 * site2 34.92 20.34 1.717 0.0881 . site3 16.84 20.34 0.828 0.4090 site4 -24.56 20.34 -1.208 0.2292 site5 -23.80 20.34 -1.170 0.2438 site6 -21.16 20.34 -1.040 0.2999 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 71.9 on 144 degrees of freedom Multiple R-squared: 0.0934, Adjusted R-squared: 0.06192 F-statistic: 2.967 on 5 and 144 DF, p-value: 0.01401 > anova(crab.mod) Analysis of Variance Table Response: count Df Sum Sq Mean Sq F value Pr(>F) site 5 76695 15339.0 2.9669 0.01401 * Residuals 144 744493 5170.1 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > ehat <- residuals(crab.mod) > ybar <- predict(crab.mod) > > qqnorm(ehat) > qqline(ehat) > > plot(ybar,ehat,main="Residuals vs Site Mean") > > ehat1 <- ehat[site==1] > ehat2 <- ehat[site==2] > ehat3 <- ehat[site==3] > ehat4 <- ehat[site==4] > ehat5 <- ehat[site==5] > ehat6 <- ehat[site==6] > > levene1 <- abs(ehat1-median(ehat1)) > levene2 <- abs(ehat2-median(ehat2)) > levene3 <- abs(ehat3-median(ehat3)) > levene4 <- abs(ehat4-median(ehat4)) > levene5 <- abs(ehat5-median(ehat5)) > levene6 <- abs(ehat6-median(ehat6)) > > levene <- c(levene1,levene2,levene3,levene4,levene5,levene6) > levene 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 17 17 5 14 0 17 17 10 6 6 56 16 17 48 4 27 3 10 31 87 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 216 64 5 8 15 405 456 4 4 2 10 7 9 6 45 132 0 8 135 4 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 6 5 114 14 194 10 10 46 10 2 5 5 1 8 0 4 4 1 1 31 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 402 5 5 13 1 9 5 19 47 309 240 102 0 1 3 2 2 2 2 0 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 0 3 2 0 1 2 10 1 28 2 1 26 0 19 6 80 10 8 0 2 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 2 1 1 0 0 1 0 27 0 0 2 11 2 17 1 1 24 28 3 2 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 92 1 7 1 2 4 4 4 2 1 4 4 0 4 1 0 18 4 60 0 141 142 143 144 145 146 147 148 149 150 0 39 1 12 15 91 2 18 4 4 > > crab.lev <- lm(levene~site) > > anova(crab.lev) Analysis of Variance Table Response: levene Df Sum Sq Mean Sq F value Pr(>F) site 5 71146 14229 2.9278 0.01508 * Residuals 144 699845 4860 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1