Attaching package: 'dplyr'
The following objects are masked from 'package:stats':

    filter, lag
The following objects are masked from 'package:base':

    intersect, setdiff, setequal, union
── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
✔ ggplot2 3.3.6     ✔ purrr   0.3.4
✔ tibble  3.1.8     ✔ stringr 1.4.0
✔ tidyr   1.2.0     ✔ forcats 0.5.2
✔ readr   2.1.2     
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()

Attaching package: 'rstatix'


The following object is masked from 'package:stats':

    filter

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      0       3.73e-2 6.4 e-2  8.92e-2  9.14e-2  9.79e-2  0.0979 
 2 Weed1 0.3% T     -3.33e-5 9.40e-3 3.17e-2  5.33e-2  7.62e-2  1.22e-1  0.173  
 3 Weed1 0.1% T      0       5.80e-3 9.73e-3  2.04e-2  3.53e-2  8.02e-2  0.178  
 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 5.2 e-2 9.38e-2  1.25e-1  1.22e-1  1.20e-1  0.120  
 7 Weed2 0.3% T      3.33e-5 3.50e-3 4.93e-3  5.83e-3  1.14e-2  1.43e-2  0.0481 
 8 Weed2 0.1% T      0       2.24e-2 4.82e-2  7.45e-2  1.05e-1  1.90e-1  0.257  
 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

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 0.129 0.143
2 Weed2 BacCon      85 0.102 0.113
3 Weed3 BacCon      85 0.079 0.186
4 Weed4 BacCon      85 0.103 0.188
5 Weed5 BacCon      85 0.106 0.129
6 Weed6 BacCon      85 0.087 0.103
7 Weed7 BacCon      85 0.117 0.096
8 Weed8 BacCon      85 0.108 0.218
9 Weed9 BacCon      85 0.145 0.139

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  0.256 0.166
2 0.3% T         BacCon     153  0.1   0.164
3 0.5% T         BacCon     153  0.044 0.118
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  0.245 0.18 
 2 Weed1 0.3% T         BacCon      17  0.208 0.135
 3 Weed1 0.5% T         BacCon      17  0.047 0.04 
 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  0.235 0.133
 7 Weed2 0.3% T         BacCon      17  0.073 0.055
 8 Weed2 0.5% T         BacCon      17  0.062 0.052
 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  0.311 0.197
12 Weed3 0.3% T         BacCon      17 -0.133 0.125
13 Weed3 0.5% T         BacCon      17  0.072 0.044
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  0.296 0.202
17 Weed4 0.3% T         BacCon      17  0.187 0.113
18 Weed4 0.5% T         BacCon      17 -0.109 0.123
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  0.252 0.182
22 Weed5 0.3% T         BacCon      17  0.028 0.026
23 Weed5 0.5% T         BacCon      17  0.108 0.045
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  0.195 0.077
27 Weed6 0.3% T         BacCon      17 -0.014 0.024
28 Weed6 0.5% T         BacCon      17  0.113 0.067
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  0.201 0.084
32 Weed7 0.3% T         BacCon      17  0.104 0.069
33 Weed7 0.5% T         BacCon      17  0.137 0.066
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  0.32  0.22 
37 Weed8 0.3% T         BacCon      17  0.221 0.198
38 Weed8 0.5% T         BacCon      17 -0.142 0.107
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  0.244 0.139
42 Weed9 0.3% T         BacCon      17  0.231 0.169
43 Weed9 0.5% T         BacCon      17  0.108 0.05 
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  1.38  22.08 15.320 2.63e-04     * 0.034
2       Concentrations  1.11  17.71 34.702 9.87e-06     * 0.432
3 Weeds:Concentrations 32.00 512.00 23.915 1.78e-81     * 0.307

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   1.42  22.7   7.57   0.006     *       0.066   0.018    
2 0.3% T         Weeds   1.2   19.2  23.6    0.0000533 *       0.517   0.000160 
3 0.5% T         Weeds   1.17  18.6  36.2    0.0000047 *       0.649   0.0000141
4 5% DMSO        Weeds   8    128   NaN    NaN         <NA>    0     NaN        
5 Enro           Weeds   8    128   NaN    NaN         <NA>    0     NaN        

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 = 00.006), 0.3% T (p=0.0000533), and 0.5% (p = 0.0000047).

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    3.28      84 0.001      0.054    ns      
 2 BacCon Weed1  Weed3     85    85    2.46      84 0.016      0.576    ns      
 3 BacCon Weed1  Weed4     85    85    2.65      84 0.01       0.345    ns      
 4 BacCon Weed1  Weed5     85    85    1.89      84 0.062      1        ns      
 5 BacCon Weed1  Weed6     85    85    2.71      84 0.008      0.297    ns      
 6 BacCon Weed1  Weed7     85    85    1.06      84 0.293      1        ns      
 7 BacCon Weed1  Weed8     85    85    1.69      84 0.094      1        ns      
 8 BacCon Weed1  Weed9     85    85   -3.62      84 0.000504   0.018    *       
 9 BacCon Weed2  Weed3     85    85    1.73      84 0.088      1        ns      
10 BacCon Weed2  Weed4     85    85   -0.0584    84 0.954      1        ns      
11 BacCon Weed2  Weed5     85    85   -0.504     84 0.615      1        ns      
12 BacCon Weed2  Weed6     85    85    1.72      84 0.09       1        ns      
13 BacCon Weed2  Weed7     85    85   -2.07      84 0.042      1        ns      
14 BacCon Weed2  Weed8     85    85   -0.363     84 0.718      1        ns      
15 BacCon Weed2  Weed9     85    85   -4.72      84 0.00000936 0.000337 ***     
16 BacCon Weed3  Weed4     85    85   -1.14      84 0.258      1        ns      
17 BacCon Weed3  Weed5     85    85   -2.64      84 0.01       0.356    ns      
18 BacCon Weed3  Weed6     85    85   -0.701     84 0.485      1        ns      
19 BacCon Weed3  Weed7     85    85   -2.38      84 0.02       0.709    ns      
20 BacCon Weed3  Weed8     85    85   -1.16      84 0.249      1        ns      
21 BacCon Weed3  Weed9     85    85   -3.03      84 0.003      0.116    ns      
22 BacCon Weed4  Weed5     85    85   -0.174     84 0.862      1        ns      
23 BacCon Weed4  Weed6     85    85    0.783     84 0.436      1        ns      
24 BacCon Weed4  Weed7     85    85   -0.782     84 0.436      1        ns      
25 BacCon Weed4  Weed8     85    85   -0.769     84 0.444      1        ns      
26 BacCon Weed4  Weed9     85    85   -3.26      84 0.002      0.059    ns      
27 BacCon Weed5  Weed6     85    85    2.47      84 0.016      0.565    ns      
28 BacCon Weed5  Weed7     85    85   -1.33      84 0.186      1        ns      
29 BacCon Weed5  Weed8     85    85   -0.115     84 0.909      1        ns      
30 BacCon Weed5  Weed9     85    85   -3.02      84 0.003      0.122    ns      
31 BacCon Weed6  Weed7     85    85   -4.65      84 0.000012   0.000432 ***     
32 BacCon Weed6  Weed8     85    85   -0.887     84 0.378      1        ns      
33 BacCon Weed6  Weed9     85    85   -3.87      84 0.000218   0.008    **      
34 BacCon Weed7  Weed8     85    85    0.409     84 0.684      1        ns      
35 BacCon Weed7  Weed9     85    85   -2.81      84 0.006      0.222    ns      
36 BacCon Weed8  Weed9     85    85   -2.57      84 0.012      0.428    ns      
# … with abbreviated variable name ¹​p.adj.signif

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