The data
## 1 2 3 4
##
## 1 Fibrous roots 1 1 1 1
## Mixture 1 1 1 1
## Taproots 1 1 1 1
## 2 Fibrous roots 1 1 1 1
## Mixture 1 1 1 1
## Taproots 1 1 1 1
## 3 Fibrous roots 1 1 1 1
## Mixture 1 1 1 1
## Taproots 1 1 1 1
There are no missing values.

The variety differs greatly between blocks. Not clear if this is the
result of the mechanical treatment or differences between the plots.

There is a strong positive linear correlation between bruto yield,
netto yield and yield of potato’s larger than 60mm.
The results
Bruto yield

Netto yield

Product tare

Yield under 35mm

Yield between 35 and 60mm

Yield above 60mm

Bruto yield (kg/ha)

##
## Grubbs test for one outlier
##
## data: yield.aardappel$bruto_yield
## G = 2.88375, U = 0.75561, p-value = 0.03923
## alternative hypothesis: highest value 72756.3333333333 is an outlier
There is an outlier in bruto yield.
##
## Shapiro-Wilk normality test
##
## data: model$residuals
## W = 0.9736, p-value = 0.5317
##
##
## Call:
## lm(formula = var ~ treatment + block/subplot, data = yield.aardappel)
##
## Coefficients:
## (Intercept) treatmentMixture treatmentTaproots block2
## 62023.2 412.8 -2534.9 2400.2
## block3 block4 block1:subplot2 block2:subplot2
## 5623.0 688.6 -3368.9 -1621.0
## block3:subplot2 block4:subplot2 block1:subplot3 block2:subplot3
## -2314.1 1855.7 -2559.6 -1523.3
## block3:subplot3 block4:subplot3
## -5111.7 1596.6
##
## Analysis of Variance Table
##
## Response: var
## Df Sum Sq Mean Sq F value Pr(>F)
## treatment 2 61140293 30570147 3.4954 0.048059 *
## block 3 128394394 42798131 4.8936 0.009365 **
## block:subplot 8 68884626 8610578 0.9845 0.473842
## Residuals 22 192406430 8745747
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## $emmeans
## treatment emmean SE df lower.CL upper.CL
## Fibrous roots 63114 854 22 61344 64884
## Mixture 63527 854 22 61756 65297
## Taproots 60579 854 22 58809 62350
##
## Results are averaged over the levels of: subplot, block
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Fibrous roots - Mixture -413 1207 22 -0.342 0.9378
## Fibrous roots - Taproots 2535 1207 22 2.100 0.1130
## Mixture - Taproots 2948 1207 22 2.442 0.0578
##
## Results are averaged over the levels of: subplot, block
## P value adjustment: tukey method for comparing a family of 3 estimates


There is an effect of cover crop treatment on bruto yield. The bruto
yield is significantly higher with mixture compared to a treatment with
taproots. There is weak evidence that the bruto yield is also higher
with treatment of fibrouw roots compared to taproots.
Netto yield (kg/ha)

##
## Grubbs test for one outlier
##
## data: yield.aardappel$netto_yield
## G = 3.08206, U = 0.72084, p-value = 0.01666
## alternative hypothesis: highest value 71761.5 is an outlier
There is an outlier in netto yield.
##
## Shapiro-Wilk normality test
##
## data: model$residuals
## W = 0.98076, p-value = 0.7706
##
##
## Call:
## lm(formula = var ~ treatment + block/subplot, data = yield.aardappel)
##
## Coefficients:
## (Intercept) treatmentMixture treatmentTaproots block2
## 61304.18 -13.17 -2613.96 2114.11
## block3 block4 block1:subplot2 block2:subplot2
## 5498.42 -151.53 -3519.44 -1014.81
## block3:subplot2 block4:subplot2 block1:subplot3 block2:subplot3
## -2392.11 1452.92 -2481.42 -1105.83
## block3:subplot3 block4:subplot3
## -5944.78 799.19
##
## Analysis of Variance Table
##
## Response: var
## Df Sum Sq Mean Sq F value Pr(>F)
## treatment 2 54388132 27194066 3.3611 0.05324 .
## block 3 106908304 35636101 4.4045 0.01429 *
## block:subplot 8 78743453 9842932 1.2165 0.33500
## Residuals 22 178000298 8090923
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## $emmeans
## treatment emmean SE df lower.CL upper.CL
## Fibrous roots 61986 821 22 60283 63688
## Mixture 61972 821 22 60270 63675
## Taproots 59372 821 22 57669 61075
##
## Results are averaged over the levels of: subplot, block
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Fibrous roots - Mixture 13.2 1161 22 0.011 0.9999
## Fibrous roots - Taproots 2614.0 1161 22 2.251 0.0846
## Mixture - Taproots 2600.8 1161 22 2.240 0.0865
##
## Results are averaged over the levels of: subplot, block
## P value adjustment: tukey method for comparing a family of 3 estimates


There is weak evidence of differences in cover crop treatment groups.
The netto yield is higher of mixture and fibrous roots compared to a
treatment with taproots.
Product tare (kg/ha)

##
## Grubbs test for one outlier
##
## data: yield.aardappel$yield_loss
## G = 3.0712, U = 0.7228, p-value = 0.0175
## alternative hypothesis: highest value 3824 is an outlier
There is an outlier in product tare.
##
## Shapiro-Wilk normality test
##
## data: model$residuals
## W = 0.94211, p-value = 0.0591
##
##
## Call:
## lm(formula = var ~ treatment + block/subplot, data = yield.aardappel)
##
## Coefficients:
## (Intercept) treatmentMixture treatmentTaproots block2
## 719.06 425.94 79.03 286.11
## block3 block4 block1:subplot2 block2:subplot2
## 124.56 840.14 150.50 -606.22
## block3:subplot2 block4:subplot2 block1:subplot3 block2:subplot3
## 78.06 402.81 -78.19 -417.42
## block3:subplot3 block4:subplot3
## 833.11 797.42
##
## Analysis of Variance Table
##
## Response: var
## Df Sum Sq Mean Sq F value Pr(>F)
## treatment 2 1232043 616022 1.3429 0.281651
## block 3 9493409 3164470 6.8987 0.001909 **
## block:subplot 8 2882575 360322 0.7855 0.620319
## Residuals 22 10091578 458708
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## $emmeans
## treatment emmean SE df lower.CL upper.CL
## Fibrous roots 1128 196 22 723 1534
## Mixture 1554 196 22 1149 1960
## Taproots 1207 196 22 802 1613
##
## Results are averaged over the levels of: subplot, block
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Fibrous roots - Mixture -426 276 22 -1.540 0.2921
## Fibrous roots - Taproots -79 276 22 -0.286 0.9560
## Mixture - Taproots 347 276 22 1.255 0.4349
##
## Results are averaged over the levels of: subplot, block
## P value adjustment: tukey method for comparing a family of 3 estimates


There are no significant differences between cover crop treatment
groups.
Yield of potato’s under 35 mm (kg/ha)

##
## Shapiro-Wilk normality test
##
## data: model$residuals
## W = 0.97553, p-value = 0.594
##
##
## Call:
## lm(formula = var ~ treatment + block/subplot, data = yield.aardappel)
##
## Coefficients:
## (Intercept) treatmentMixture treatmentTaproots block2
## 1134.85 -74.72 13.17 -49.56
## block3 block4 block1:subplot2 block2:subplot2
## -14.17 68.78 -83.58 45.33
## block3:subplot2 block4:subplot2 block1:subplot3 block2:subplot3
## -292.39 -196.44 -246.11 -41.03
## block3:subplot3 block4:subplot3
## -106.28 -105.36
##
## Analysis of Variance Table
##
## Response: var
## Df Sum Sq Mean Sq F value Pr(>F)
## treatment 2 53916 26958 0.5492 0.5851
## block 3 77906 25969 0.5290 0.6670
## block:subplot 8 294580 36822 0.7501 0.6482
## Residuals 22 1079938 49088

## $emmeans
## treatment emmean SE df lower.CL upper.CL
## Fibrous roots 1051 64 22 918 1183
## Mixture 976 64 22 843 1109
## Taproots 1064 64 22 931 1196
##
## Results are averaged over the levels of: subplot, block
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Fibrous roots - Mixture 74.7 90.5 22 0.826 0.6912
## Fibrous roots - Taproots -13.2 90.5 22 -0.146 0.9884
## Mixture - Taproots -87.9 90.5 22 -0.972 0.6020
##
## Results are averaged over the levels of: subplot, block
## P value adjustment: tukey method for comparing a family of 3 estimates


There are no significant differences between the cover crop treatment
groups.
Yield of potato’s between 35 and 60 mm (kg/ha)

##
## Shapiro-Wilk normality test
##
## data: model$residuals
## W = 0.98004, p-value = 0.7467
##
##
## Call:
## lm(formula = var ~ treatment + block/subplot, data = yield.aardappel)
##
## Coefficients:
## (Intercept) treatmentMixture treatmentTaproots block2
## 21115.9 -2864.6 -2364.4 1019.6
## block3 block4 block1:subplot2 block2:subplot2
## 1058.9 228.6 -158.3 -199.2
## block3:subplot2 block4:subplot2 block1:subplot3 block2:subplot3
## -923.4 1434.0 -2292.6 -973.7
## block3:subplot3 block4:subplot3
## -1160.6 -800.3
##
## Analysis of Variance Table
##
## Response: var
## Df Sum Sq Mean Sq F value Pr(>F)
## treatment 2 56185784 28092892 8.2279 0.002148 **
## block 3 11645433 3881811 1.1369 0.355982
## block:subplot 8 21369002 2671125 0.7823 0.622822
## Residuals 22 75115969 3414362
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## $emmeans
## treatment emmean SE df lower.CL upper.CL
## Fibrous roots 21270 533 22 20164 22376
## Mixture 18405 533 22 17299 19511
## Taproots 18905 533 22 17799 20012
##
## Results are averaged over the levels of: subplot, block
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Fibrous roots - Mixture 2865 754 22 3.797 0.0027
## Fibrous roots - Taproots 2364 754 22 3.134 0.0129
## Mixture - Taproots -500 754 22 -0.663 0.7870
##
## Results are averaged over the levels of: subplot, block
## P value adjustment: tukey method for comparing a family of 3 estimates


There is strong evidence of differences between cover crop treatment
groups. The yield of potato’s between 35 and 60 mm is significantly
higher with treatment fibrous roots than with a treatment of mixture or
taproots.
Yield of potato’s above 60 mm (kg/ha)

##
## Shapiro-Wilk normality test
##
## data: model$residuals
## W = 0.94457, p-value = 0.07057
##
##
## Call:
## lm(formula = var ~ treatment + block/subplot, data = yield.aardappel)
##
## Coefficients:
## (Intercept) treatmentMixture treatmentTaproots block2
## 39053.44 2926.11 -262.69 1144.11
## block3 block4 block1:subplot2 block2:subplot2
## 4453.64 -448.92 -3277.58 -860.92
## block3:subplot2 block4:subplot2 block1:subplot3 block2:subplot3
## -1176.33 215.33 57.31 -91.11
## block3:subplot3 block4:subplot3
## -4677.94 1704.86
##
## Analysis of Variance Table
##
## Response: var
## Df Sum Sq Mean Sq F value Pr(>F)
## treatment 2 75198270 37599135 3.4935 0.04813 *
## block 3 59731263 19910421 1.8500 0.16764
## block:subplot 8 63909217 7988652 0.7423 0.65446
## Residuals 22 236774195 10762463
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## $emmeans
## treatment emmean SE df lower.CL upper.CL
## Fibrous roots 39665 947 22 37701 41629
## Mixture 42591 947 22 40627 44555
## Taproots 39402 947 22 37438 41366
##
## Results are averaged over the levels of: subplot, block
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Fibrous roots - Mixture -2926 1339 22 -2.185 0.0962
## Fibrous roots - Taproots 263 1339 22 0.196 0.9790
## Mixture - Taproots 3189 1339 22 2.381 0.0654
##
## Results are averaged over the levels of: subplot, block
## P value adjustment: tukey method for comparing a family of 3 estimates


There is a significant difference between cover crop treatment
groups. There is weak evidence that mixture results in a higher yield of
potato’s larger than 60 mm compared to treatment fibrous roots.