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Data

# A tibble: 45 × 19
   Weeds Concentr…¹       T0      T1      T2       T3       T4       T5       T6
   <chr> <chr>         <dbl>   <dbl>   <dbl>    <dbl>    <dbl>    <dbl>    <dbl>
 1 Weed1 0.5% T      3.33e-5 1.77e-2 7.91e-2  1.61e-1  1.72e-1  1.81e-1  0.185  
 2 Weed1 0.3% T     -3.33e-5 9.76e-2 2.21e-1  2.10e-1  1.96e-1  1.75e-1  0.157  
 3 Weed1 0.1% T      0       1.07e-3 6.3 e-3  7.00e-3  9.13e-3  1.06e-2  0.0112 
 4 Weed1 Enro        0       3.33e-5 4.33e-4 -5.67e-4 -6.00e-4 -8.33e-4 -0.00107
 5 Weed1 5% DMSO     0       8.90e-3 2.44e-2  2.82e-2  6.39e-2  6.69e-2  0.113  
 6 Weed2 0.5% T      3.33e-5 2.00e-2 7.55e-2  1.58e-1  1.81e-1  1.91e-1  0.194  
 7 Weed2 0.3% T     -3.33e-5 5.00e-4 2.30e-2  7.32e-2  1.67e-1  1.81e-1  0.189  
 8 Weed2 0.1% T     -3.33e-5 5.14e-2 7.52e-2  7.32e-2  6.85e-2  4.98e-2  0.00703
 9 Weed2 Enro        0       3.33e-5 4.33e-4 -5.67e-4 -6.00e-4 -8.33e-4 -0.00107
10 Weed2 5% DMSO     0       8.90e-3 2.44e-2  2.82e-2  6.39e-2  6.69e-2  0.113  
# … with 35 more rows, 10 more variables: T7 <dbl>, T8 <dbl>, T9 <dbl>,
#   T10 <dbl>, T11 <dbl>, T12 <dbl>, T13 <dbl>, T14 <dbl>, T15 <dbl>,
#   T16 <dbl>, and abbreviated variable name ¹​Concentrations
# ℹ Use `print(n = ...)` to see more rows, and `colnames()` to see all variable names
tibble [45 × 19] (S3: tbl_df/tbl/data.frame)
 $ Weeds         : chr [1:45] "Weed1" "Weed1" "Weed1" "Weed1" ...
 $ Concentrations: chr [1:45] "0.5% T" "0.3% T" "0.1% T" "Enro" ...
 $ T0            : num [1:45] 3.33e-05 -3.33e-05 0.00 0.00 0.00 ...
 $ T1            : num [1:45] 1.77e-02 9.76e-02 1.07e-03 3.33e-05 8.90e-03 ...
 $ T2            : num [1:45] 0.079067 0.221 0.0063 0.000433 0.0244 ...
 $ T3            : num [1:45] 0.161433 0.209933 0.007 -0.000567 0.02825 ...
 $ T4            : num [1:45] 0.17247 0.1963 0.00913 -0.0006 0.06385 ...
 $ T5            : num [1:45] 0.180567 0.175 0.010567 -0.000833 0.0669 ...
 $ T6            : num [1:45] 0.18477 0.15697 0.01117 -0.00107 0.11285 ...
 $ T7            : num [1:45] 0.1877 0.1468 0.019 -0.0012 0.153 ...
 $ T8            : num [1:45] 0.1986 0.1363 0.0192 -0.0012 0.1774 ...
 $ T9            : num [1:45] 0.201 0.12873 0.00843 -0.0014 0.1847 ...
 $ T10           : num [1:45] 0.1836 0.11707 0.00783 -0.00153 0.1978 ...
 $ T11           : num [1:45] 0.1525 0.1054 0.00697 -0.00163 0.21125 ...
 $ T12           : num [1:45] 0.1199 0.1047 0.0065 -0.00173 0.21145 ...
 $ T13           : num [1:45] 0.10057 0.09963 0.00617 -0.0017 0.2341 ...
 $ T14           : num [1:45] 0.08703 0.09693 0.00587 -0.00183 0.2398 ...
 $ T15           : num [1:45] 0.0765 0.0958 0.0056 -0.0019 0.2631 ...
 $ T16           : num [1:45] 0.0561 0.0924 0.00383 -0.002 0.26145 ...

Some Summary Statistics for the different types of Weeds

# A tibble: 9 × 5
  Weeds variable     n  mean    sd
  <fct> <chr>    <dbl> <dbl> <dbl>
1 Weed1 BacCon      85 0.081 0.085
2 Weed2 BacCon      85 0.079 0.107
3 Weed3 BacCon      85 0.088 0.091
4 Weed4 BacCon      85 0.076 0.084
5 Weed5 BacCon      85 0.054 0.102
6 Weed6 BacCon      85 0.102 0.099
7 Weed7 BacCon      85 0.103 0.091
8 Weed8 BacCon      85 0.096 0.1  
9 Weed9 BacCon      85 0.06  0.073

Some Summary Statistics for the different levels of Concentrations

# A tibble: 5 × 5
  Concentrations variable     n   mean    sd
  <fct>          <chr>    <dbl>  <dbl> <dbl>
1 0.1% T         BacCon     153  0.016 0.073
2 0.3% T         BacCon     153  0.111 0.072
3 0.5% T         BacCon     153  0.142 0.077
4 5% DMSO        BacCon     153  0.143 0.091
5 Enro           BacCon     153 -0.001 0.001

Some Summary Statistics for the different levels of Concentrations and types of Weeds

Warning: `tbl_df()` was deprecated in dplyr 1.0.0.
Please use `tibble::as_tibble()` instead.
This warning is displayed once every 8 hours.
Call `lifecycle::last_lifecycle_warnings()` to see where this warning was generated.
# A tibble: 45 × 6
   Weeds Concentrations variable     n   mean    sd
   <fct> <fct>          <chr>    <dbl>  <dbl> <dbl>
 1 Weed1 0.1% T         BacCon      17  0.008 0.005
 2 Weed1 0.3% T         BacCon      17  0.128 0.054
 3 Weed1 0.5% T         BacCon      17  0.127 0.065
 4 Weed1 5% DMSO        BacCon      17  0.143 0.094
 5 Weed1 Enro           BacCon      17 -0.001 0.001
 6 Weed2 0.1% T         BacCon      17 -0.038 0.076
 7 Weed2 0.3% T         BacCon      17  0.147 0.072
 8 Weed2 0.5% T         BacCon      17  0.145 0.067
 9 Weed2 5% DMSO        BacCon      17  0.143 0.094
10 Weed2 Enro           BacCon      17 -0.001 0.001
11 Weed3 0.1% T         BacCon      17  0.043 0.073
12 Weed3 0.3% T         BacCon      17  0.088 0.063
13 Weed3 0.5% T         BacCon      17  0.167 0.072
14 Weed3 5% DMSO        BacCon      17  0.143 0.094
15 Weed3 Enro           BacCon      17 -0.001 0.001
16 Weed4 0.1% T         BacCon      17  0.025 0.039
17 Weed4 0.3% T         BacCon      17  0.086 0.064
18 Weed4 0.5% T         BacCon      17  0.124 0.08 
19 Weed4 5% DMSO        BacCon      17  0.143 0.094
20 Weed4 Enro           BacCon      17 -0.001 0.001
21 Weed5 0.1% T         BacCon      17 -0.043 0.106
22 Weed5 0.3% T         BacCon      17  0.033 0.036
23 Weed5 0.5% T         BacCon      17  0.139 0.061
24 Weed5 5% DMSO        BacCon      17  0.143 0.094
25 Weed5 Enro           BacCon      17 -0.001 0.001
26 Weed6 0.1% T         BacCon      17  0.058 0.077
27 Weed6 0.3% T         BacCon      17  0.126 0.082
28 Weed6 0.5% T         BacCon      17  0.186 0.081
29 Weed6 5% DMSO        BacCon      17  0.143 0.094
30 Weed6 Enro           BacCon      17 -0.001 0.001
31 Weed7 0.1% T         BacCon      17  0.065 0.087
32 Weed7 0.3% T         BacCon      17  0.163 0.061
33 Weed7 0.5% T         BacCon      17  0.145 0.056
34 Weed7 5% DMSO        BacCon      17  0.143 0.094
35 Weed7 Enro           BacCon      17 -0.001 0.001
36 Weed8 0.1% T         BacCon      17  0.021 0.028
37 Weed8 0.3% T         BacCon      17  0.149 0.064
38 Weed8 0.5% T         BacCon      17  0.167 0.109
39 Weed8 5% DMSO        BacCon      17  0.143 0.094
40 Weed8 Enro           BacCon      17 -0.001 0.001
41 Weed9 0.1% T         BacCon      17  0.005 0.003
42 Weed9 0.3% T         BacCon      17  0.081 0.052
43 Weed9 0.5% T         BacCon      17  0.073 0.03 
44 Weed9 5% DMSO        BacCon      17  0.143 0.094
45 Weed9 Enro           BacCon      17 -0.001 0.001

#Visualization

Weeds

Boxplot

Concentrations

Boxplot

#Analysis

ANOVA Table (type III tests)

                Effect   DFn    DFd      F        p p<.05   ges
1                Weeds  1.92  30.64 13.794 6.52e-05     * 0.060
2       Concentrations  1.55  24.74 27.895 1.95e-06     * 0.484
3 Weeds:Concentrations 32.00 512.00  9.831 5.03e-36     * 0.107

It shows that Weeds, Concentrations and the interaction between Weeds and Concentrations are statistically significant.

#Effect of Weeds at each concentration

# A tibble: 5 × 9
  Concentrations Effect   DFn   DFd     F        p `p<.05`   ges    p.adj
  <fct>          <chr>  <dbl> <dbl> <dbl>    <dbl> <chr>   <dbl>    <dbl>
1 0.1% T         Weeds   2.02  32.4  11.3 0.000177 "*"     0.242 0.000885
2 0.3% T         Weeds   1.45  23.2  11.4 0.000962 "*"     0.301 0.00481 
3 0.5% T         Weeds   2.44  39.0  13.6 0.000011 "*"     0.163 0.000055
4 5% DMSO        Weeds   8    128     0   1        ""      0     1       
5 Enro           Weeds   8    128     0   1        ""      0     1       

Considering the Bonferroni adjusted p-value (p.adj), it can be seen that the simple main effect of weeds was not significant at the concentrations 5%DMSO and Enro. It becomes significant at 0.1% T (p = 0.0.000177), 0.3% T (p=0.000962), and 0.5% (p = 0.0.000011).

Pairwise comparisons among types of weeds

# A tibble: 36 × 10
   .y.    group1 group2    n1    n2 statistic    df            p   p.adj p.adj…¹
   <chr>  <chr>  <chr>  <int> <int>     <dbl> <dbl>        <dbl>   <dbl> <chr>  
 1 BacCon Weed1  Weed2     85    85     0.312    84      7.56e-1 1   e+0 ns     
 2 BacCon Weed1  Weed3     85    85    -1.12     84      2.66e-1 1   e+0 ns     
 3 BacCon Weed1  Weed4     85    85     1.57     84      1.2 e-1 1   e+0 ns     
 4 BacCon Weed1  Weed5     85    85     3.90     84      1.92e-4 7   e-3 **     
 5 BacCon Weed1  Weed6     85    85    -2.83     84      6   e-3 2.09e-1 ns     
 6 BacCon Weed1  Weed7     85    85    -3.78     84      2.88e-4 1   e-2 *      
 7 BacCon Weed1  Weed8     85    85    -3.57     84      6   e-4 2.2 e-2 *      
 8 BacCon Weed1  Weed9     85    85     5.40     84      6.07e-7 2.19e-5 ****   
 9 BacCon Weed2  Weed3     85    85    -1.04     84      3.01e-1 1   e+0 ns     
10 BacCon Weed2  Weed4     85    85     0.516    84      6.07e-1 1   e+0 ns     
11 BacCon Weed2  Weed5     85    85     3.71     84      3.72e-4 1.3 e-2 *      
12 BacCon Weed2  Weed6     85    85    -3.64     84      4.66e-4 1.7 e-2 *      
13 BacCon Weed2  Weed7     85    85    -4.36     84      3.61e-5 1   e-3 **     
14 BacCon Weed2  Weed8     85    85    -3.17     84      2   e-3 7.7 e-2 ns     
15 BacCon Weed2  Weed9     85    85     2.56     84      1.2 e-2 4.43e-1 ns     
16 BacCon Weed3  Weed4     85    85     2.35     84      2.1 e-2 7.52e-1 ns     
17 BacCon Weed3  Weed5     85    85     5.45     84      4.99e-7 1.8 e-5 ****   
18 BacCon Weed3  Weed6     85    85    -1.57     84      1.19e-1 1   e+0 ns     
19 BacCon Weed3  Weed7     85    85    -1.88     84      6.4 e-2 1   e+0 ns     
20 BacCon Weed3  Weed8     85    85    -0.998    84      3.21e-1 1   e+0 ns     
21 BacCon Weed3  Weed9     85    85     3.84     84      2.38e-4 9   e-3 **     
22 BacCon Weed4  Weed5     85    85     3.84     84      2.41e-4 9   e-3 **     
23 BacCon Weed4  Weed6     85    85    -3.46     84      8.51e-4 3.1 e-2 *      
24 BacCon Weed4  Weed7     85    85    -4.70     84      9.93e-6 3.57e-4 ***    
25 BacCon Weed4  Weed8     85    85    -4.23     84      5.87e-5 2   e-3 **     
26 BacCon Weed4  Weed9     85    85     3.49     84      7.82e-4 2.8 e-2 *      
27 BacCon Weed5  Weed6     85    85    -5.81     84      1.08e-7 3.89e-6 ****   
28 BacCon Weed5  Weed7     85    85    -6.39     84      8.81e-9 3.17e-7 ****   
29 BacCon Weed5  Weed8     85    85    -5.33     84      8.21e-7 2.96e-5 ****   
30 BacCon Weed5  Weed9     85    85    -0.827    84      4.1 e-1 1   e+0 ns     
31 BacCon Weed6  Weed7     85    85    -0.129    84      8.98e-1 1   e+0 ns     
32 BacCon Weed6  Weed8     85    85     1.04     84      3.01e-1 1   e+0 ns     
33 BacCon Weed6  Weed9     85    85     5.29     84      9.49e-7 3.42e-5 ****   
34 BacCon Weed7  Weed8     85    85     1.27     84      2.07e-1 1   e+0 ns     
35 BacCon Weed7  Weed9     85    85     6.50     84      5.46e-9 1.97e-7 ****   
36 BacCon Weed8  Weed9     85    85     5.50     84      4.09e-7 1.47e-5 ****   
# … with abbreviated variable name ¹​p.adj.signif

Pairwise comparisons show that the mean bacterial concentration was significantly different between Weeds 1 and 5, Weeds 1 and 9, Weeds 2 and 5, Weeds 2 and 6, Weeds 2 and 7, Weeds 3 and 5, Weeds 3 and 9, Weeds 4 and 5, Weeds 4 and 6, Weeds 4 and 7, Weeds 4and 8, Weeds 4 and 9, Weeds 5 and 6, Weeds 5 and 7, Weeds 5 and 8, Weeds 6 and 9, Weeds 7 and 9, and Weeds 8 and 9.