Results

Row number in the field as well as the interaction was significant.

In the subsoiling treatment the tall fescue had a significantly different nitrate concentration compared to fodder radish.

                
                 Fodder radish Black oats Tall fescue
  Ref                        5          5           5
  Compost                    0          0           0
  LB                         5          5           5
  LB extensive               0          0           0
  LB Sand                    0          0           0
  SB                         5          5           5
  SS                         5          5           5
  SS Caterpillar             0          0           0


Call:
lm(formula = log(no3_meting_gw_mg_no3_l) ~ ondgr_bw + gr_bem + 
    gw_cm_mv + row + ondgr_bw:gr_bem, data = dataset)

Coefficients:
                 (Intercept)                    ondgr_bwLB  
                    4.196627                     -0.067684  
                  ondgr_bwSB                    ondgr_bwSS  
                    0.152362                     -0.444440  
            gr_bemBlack oats             gr_bemTall fescue  
                   -0.001153                     -0.053665  
                    gw_cm_mv                           row  
                    0.012799                     -0.100482  
 ondgr_bwLB:gr_bemBlack oats   ondgr_bwSB:gr_bemBlack oats  
                    0.050864                     -0.158842  
 ondgr_bwSS:gr_bemBlack oats  ondgr_bwLB:gr_bemTall fescue  
                    0.550133                     -0.107335  
ondgr_bwSB:gr_bemTall fescue  ondgr_bwSS:gr_bemTall fescue  
                   -0.094661                      0.884476  

    studentized Breusch-Pagan test

data:  md
BP = 18.594, df = 13, p-value = 0.1362
Analysis of Variance Table

Response: log(no3_meting_gw_mg_no3_l)
                Df Sum Sq Mean Sq F value    Pr(>F)    
ondgr_bw         3 0.3726  0.1242  1.0518   0.37876    
gr_bem           2 0.6385  0.3193  2.7040   0.07757 .  
gw_cm_mv         1 3.4130  3.4130 28.9062 2.461e-06 ***
row              1 0.6901  0.6901  5.8447   0.01964 *  
ondgr_bw:gr_bem  6 1.6815  0.2802  2.3735   0.04421 *  
Residuals       46 5.4313  0.1181                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


    Shapiro-Wilk normality test

data:  resid(md)
W = 0.98889, p-value = 0.8615
$emmeans
 gr_bem        response    SE df lower.CL upper.CL
 Fodder radish      118  9.33 46      101      139
 Black oats         132 10.69 46      112      156
 Tall fescue        133 10.47 46      114      156

Results are averaged over the levels of: ondgr_bw 
Confidence level used: 0.95 
Intervals are back-transformed from the log scale 

$contrasts
 contrast                    ratio     SE df null t.ratio p.value
 Fodder radish / Black oats  0.896 0.1037 46    1  -0.946  0.6145
 Fodder radish / Tall fescue 0.890 0.0988 46    1  -1.054  0.5474
 Black oats / Tall fescue    0.992 0.1147 46    1  -0.066  0.9976

Results are averaged over the levels of: ondgr_bw 
P value adjustment: tukey method for comparing a family of 3 estimates 
Tests are performed on the log scale 
$emmeans
 ondgr_bw response   SE df lower.CL upper.CL
 Ref           127 11.4 46    106.3      152
 LB            117 10.4 46     97.5      140
 SB            136 12.1 46    113.9      163
 SS            132 11.8 46    110.0      158

Results are averaged over the levels of: gr_bem 
Confidence level used: 0.95 
Intervals are back-transformed from the log scale 

$contrasts
 contrast ratio    SE df null t.ratio p.value
 Ref / LB 1.090 0.138 46    1   0.681  0.9036
 Ref / SB 0.934 0.118 46    1  -0.537  0.9495
 Ref / SS 0.967 0.122 46    1  -0.267  0.9933
 LB / SB  0.857 0.108 46    1  -1.229  0.6121
 LB / SS  0.887 0.112 46    1  -0.950  0.7784
 SB / SS  1.035 0.130 46    1   0.271  0.9930

Results are averaged over the levels of: gr_bem 
P value adjustment: tukey method for comparing a family of 4 estimates 
Tests are performed on the log scale 
$emmeans
 ondgr_bw gr_bem        response   SE df lower.CL upper.CL
 Ref      Fodder radish    129.6 20.4 46     94.4      178
 LB       Fodder radish    121.1 19.3 46     88.0      167
 SB       Fodder radish    151.0 24.0 46    109.6      208
 SS       Fodder radish     83.1 12.8 46     61.0      113
 Ref      Black oats       129.5 20.1 46     94.7      177
 LB       Black oats       127.3 19.9 46     93.0      174
 SB       Black oats       128.6 19.9 46     94.2      176
 SS       Black oats       143.9 22.7 46    104.8      198
 Ref      Tall fescue      122.9 19.3 46     89.5      169
 LB       Tall fescue      103.1 17.5 46     73.2      145
 SB       Tall fescue      130.1 20.2 46     95.2      178
 SS       Tall fescue      190.8 30.0 46    139.0      262

Confidence level used: 0.95 
Intervals are back-transformed from the log scale 

$contrasts
 contrast                             ratio     SE df null t.ratio p.value
 Ref Fodder radish / LB Fodder radish 1.070 0.2428 46    1   0.298  1.0000
 Ref Fodder radish / SB Fodder radish 0.859 0.1883 46    1  -0.695  0.9999
 Ref Fodder radish / SS Fodder radish 1.560 0.3459 46    1   2.004  0.6883
 Ref Fodder radish / Ref Black oats   1.001 0.2249 46    1   0.005  1.0000
 Ref Fodder radish / LB Black oats    1.018 0.2304 46    1   0.079  1.0000
 Ref Fodder radish / SB Black oats    1.008 0.2252 46    1   0.034  1.0000
 Ref Fodder radish / SS Black oats    0.901 0.2056 46    1  -0.458  1.0000
 Ref Fodder radish / Ref Tall fescue  1.055 0.2389 46    1   0.237  1.0000
 Ref Fodder radish / LB Tall fescue   1.257 0.2775 46    1   1.036  0.9959
 Ref Fodder radish / SB Tall fescue   0.996 0.2212 46    1  -0.018  1.0000
 Ref Fodder radish / SS Tall fescue   0.680 0.1497 46    1  -1.754  0.8331
 LB Fodder radish / SB Fodder radish  0.802 0.1786 46    1  -0.989  0.9972
 LB Fodder radish / SS Fodder radish  1.458 0.3236 46    1   1.697  0.8604
 LB Fodder radish / Ref Black oats    0.936 0.2080 46    1  -0.299  1.0000
 LB Fodder radish / LB Black oats     0.952 0.2113 46    1  -0.224  1.0000
 LB Fodder radish / SB Black oats     0.942 0.2074 46    1  -0.273  1.0000
 LB Fodder radish / SS Black oats     0.842 0.1871 46    1  -0.775  0.9997
 LB Fodder radish / Ref Tall fescue   0.986 0.2224 46    1  -0.062  1.0000
 LB Fodder radish / LB Tall fescue    1.175 0.2827 46    1   0.669  0.9999
 LB Fodder radish / SB Tall fescue    0.931 0.2101 46    1  -0.318  1.0000
 LB Fodder radish / SS Tall fescue    0.635 0.1398 46    1  -2.063  0.6497
 SB Fodder radish / SS Fodder radish  1.816 0.4056 46    1   2.673  0.2720
 SB Fodder radish / Ref Black oats    1.166 0.2636 46    1   0.679  0.9999
 SB Fodder radish / LB Black oats     1.186 0.2696 46    1   0.749  0.9998
 SB Fodder radish / SB Black oats     1.174 0.2624 46    1   0.715  0.9999
 SB Fodder radish / SS Black oats     1.049 0.2402 46    1   0.209  1.0000
 SB Fodder radish / Ref Tall fescue   1.229 0.2819 46    1   0.898  0.9988
 SB Fodder radish / LB Tall fescue    1.464 0.3302 46    1   1.689  0.8639
 SB Fodder radish / SB Tall fescue    1.160 0.2617 46    1   0.657  0.9999
 SB Fodder radish / SS Tall fescue    0.791 0.1723 46    1  -1.075  0.9944
 SS Fodder radish / Ref Black oats    0.642 0.1397 46    1  -2.036  0.6674
 SS Fodder radish / LB Black oats     0.653 0.1424 46    1  -1.955  0.7197
 SS Fodder radish / SB Black oats     0.646 0.1406 46    1  -2.007  0.6866
 SS Fodder radish / SS Black oats     0.578 0.1264 46    1  -2.508  0.3606
 SS Fodder radish / Ref Tall fescue   0.677 0.1478 46    1  -1.789  0.8155
 SS Fodder radish / LB Tall fescue    0.806 0.1865 46    1  -0.932  0.9984
 SS Fodder radish / SB Tall fescue    0.639 0.1391 46    1  -2.058  0.6529
 SS Fodder radish / SS Tall fescue    0.436 0.0966 46    1  -3.747  0.0223
 Ref Black oats / LB Black oats       1.017 0.2211 46    1   0.077  1.0000
 Ref Black oats / SB Black oats       1.007 0.2191 46    1   0.030  1.0000
 Ref Black oats / SS Black oats       0.900 0.1959 46    1  -0.485  1.0000
 Ref Black oats / Ref Tall fescue     1.054 0.2295 46    1   0.241  1.0000
 Ref Black oats / LB Tall fescue      1.255 0.2962 46    1   0.964  0.9978
 Ref Black oats / SB Tall fescue      0.995 0.2171 46    1  -0.024  1.0000
 Ref Black oats / SS Tall fescue      0.679 0.1519 46    1  -1.731  0.8444
 LB Black oats / SB Black oats        0.990 0.2156 46    1  -0.047  1.0000
 LB Black oats / SS Black oats        0.885 0.1924 46    1  -0.563  1.0000
 LB Black oats / Ref Tall fescue      1.036 0.2258 46    1   0.164  1.0000
 LB Black oats / LB Tall fescue       1.235 0.2947 46    1   0.883  0.9990
 LB Black oats / SB Tall fescue       0.978 0.2142 46    1  -0.101  1.0000
 LB Black oats / SS Tall fescue       0.667 0.1500 46    1  -1.799  0.8100
 SB Black oats / SS Black oats        0.894 0.1950 46    1  -0.514  1.0000
 SB Black oats / Ref Tall fescue      1.047 0.2291 46    1   0.210  1.0000
 SB Black oats / LB Tall fescue       1.247 0.2931 46    1   0.941  0.9982
 SB Black oats / SB Tall fescue       0.988 0.2164 46    1  -0.053  1.0000
 SB Black oats / SS Tall fescue       0.674 0.1494 46    1  -1.779  0.8208
 SS Black oats / Ref Tall fescue      1.171 0.2555 46    1   0.725  0.9998
 SS Black oats / LB Tall fescue       1.395 0.3371 46    1   1.379  0.9618
 SS Black oats / SB Tall fescue       1.106 0.2431 46    1   0.457  1.0000
 SS Black oats / SS Tall fescue       0.754 0.1705 46    1  -1.247  0.9816
 Ref Tall fescue / LB Tall fescue     1.191 0.2827 46    1   0.737  0.9998
 Ref Tall fescue / SB Tall fescue     0.944 0.2059 46    1  -0.264  1.0000
 Ref Tall fescue / SS Tall fescue     0.644 0.1463 46    1  -1.937  0.7303
 LB Tall fescue / SB Tall fescue      0.792 0.1825 46    1  -1.011  0.9967
 LB Tall fescue / SS Tall fescue      0.541 0.1237 46    1  -2.689  0.2641
 SB Tall fescue / SS Tall fescue      0.682 0.1531 46    1  -1.704  0.8574

P value adjustment: tukey method for comparing a family of 12 estimates 
Tests are performed on the log scale