Treatments

Main crop and green manure

Treatment Year2019 Year2020&2021 Year2022
Main Spring wheat Spring Barley Potato
Mixture annual mixture Peronnial mixture (until end of 2021) -
Fibrous roots sudan grass Tall fescue & english ryegrass (until end of 2021) -
Taproots fodder radish Lucerne (until end of 2021) -

Mechanical treatment

Mechanical treatment
SS Subsoiling
SB Small boreholes
LB Large boreholes
Ref Untreated

The experimental design

The field is divided into four blocks. Every block is divided into three subplots. Every treatment occurs once in each subplot. We make the assumption that the treatments are divided randomly in each subplot. The mechanical treatments are divided over the blocks. The mechanical treatment will not be analysed, since we can not know if the variety between the mechanical treatments is explained by the treatment or by differences between the fields.

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.

Remark

The assumption was made that the treatments were randomized in the subplots, but in reality they were not. As we can see, there are some differences between the subplots and that can be of influence to the results.

Mechanical treatment Cover crop treatment Gross yield [kg/ha] Net yield [kg/ha] Product tare [kg/ha] <35 mm [kg/ha] 35-60 mm [kg/ha] >60 mm[kg/ha]
LB Fibrous roots 64454.78 63568.83 885.9444 1011.0000 22089.89 40467.94
LB Mixture 65631.33 64001.33 1630.0000 942.7222 19276.17 43782.44
LB Taproots 63304.67 61873.61 1431.0556 948.1111 17845.50 43080.00
Ref Fibrous roots 62674.25 60602.97 2071.2778 1105.2222 20928.00 38569.75
Ref Mixture 64049.83 61590.64 2459.1944 944.6389 18432.83 42213.17
Ref Taproots 62741.67 60889.33 1852.3333 1197.6667 20077.39 39614.28
SB Fibrous roots 64406.56 63583.33 823.2222 1168.5000 22788.00 39626.83
SB Mixture 62846.61 61951.33 895.2778 950.6944 18303.97 42696.67
SB Taproots 60750.81 59972.44 778.3611 1079.4444 18912.44 39980.56
SS Fibrous roots 60920.47 60187.17 733.3056 917.7778 19273.44 39995.94
SS Mixture 61579.33 60346.31 1233.0278 1065.5833 17608.08 41672.64
SS Taproots 55519.22 54751.08 768.1389 1029.9444 18786.25 34934.89