The statistical analysis behind my thesis

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# The statistical analysis behind my thesis
### Vitor Muller Anunciato
### December 12th, 2019 (updated: 2020-11-17)

---

.pull-left[
##Vitor Muller Anunciato##

🎓

PhD candidate in Crop Protection (Weedscience), [UNESP](https://www.fca.unesp.br/#!/international/eng/), current.

Msc in Crop Protection (Weedscience), [UNESP](https://www.fca.unesp.br/#!/international/eng/), 2018.

BSc in Agronomy, [UEL](http://www.uel.br/portal/en/pages/en.php?lang=PT), 2016.

📧

vitor.muller@gmail.com
[@vitor_anunciato](https://twitter.com/vitor_anunciato)

🔪 [Serial Weed Killer](https://serialweedkiller.netlify.app/) 
  
🎧 [PapoAgro podcast](https://www.papoagro.com.br/) (@papoagropodcast)

]

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##Summary##

- What is hormesis?

- Thesis objective

- My hypotesis

- Material and Methods

- Key results

- Conclusion
]
---
#What is hormesis?#
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"All things are poison and nothing (is) without poison; only the dose makes that a thing is no poison."

*Paracelsus (1493-1541)*
]
--
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![hormesis](https://media.giphy.com/media/QztqDnTHYapKE/giphy.gif)]
---
#What is a posion?#
<div align="center">
<img src="https://github.com/vitoranunciato/Statical-analises-behind-my-thesis/blob/master/docs/img/dl-adapted.png?raw=true" width=700 height=450>
</div>

Source: adapted from [sciencematters.com](https://sciencemattersca.com/about/science-101/)
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###Normal dose response glyphosate vs. susceptible *D.insularis* ###
<div align="center">
<img src="https://github.com/vitoranunciato/Statical-analises-behind-my-thesis/blob/master/docs/img/drc.png?raw=true" width=800 height=450>
</div>

.pull-left[0 g ea ha-¹] 
.right[64000 g ea ha-¹]
---
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###Glyphosate in growth stimulus in *D.insularis* ###
<div align="center">
<img src="https://github.com/vitoranunciato/Statical-analises-behind-my-thesis/blob/master/docs/img/horm.png?raw=true" width=800 height=450>
</div>
.pull-left[0 g ea ha-¹] 
.right[720 g ea ha-¹]
---
#Thesis objective#

Evaluate the effect of glyphosate herbicide in the growth of * Digitaria insularis.*

#My hypotesis#
H0: glyphosate can't stimulate the growth of *Digitaria insularis*
H1: glyphosate can stimulate the growth of *Digitaria insularis*

---
#Material and methods#
`$$f(x) = c + \frac{d-c}{1+\exp(b(\log(x)-\log(e)))}$$`

Source: Seber, G. A. F. and Wild, C. J (1989) Nonlinear Regression, New York: Wiley & Sons (p. 330).

`$$f(x) = c + \frac{d-c+fx}{1+\exp(b(\log(x)-\log(e)))}$$`

Source: Brain, P. and Cousens, R. (1989) An equation to describe dose responses where there is stimulation of growth at low doses, Weed Research, 29, 93--96. 
---
##Model adjustment##

```r
lettuce.m1 <- drm(lettuce[,c(2,1)], fct=BC.5())
lettuce.m2 <- drm(lettuce[,c(2,1)], fct=LL.4())
```
.pull-left[

```r
plot(lettuce.m1)
```

![](index_files/figure-html/unnamed-chunk-2-1.png)
]
.pull-right[

```r
plot(lettuce.m2)
```

![](index_files/figure-html/unnamed-chunk-3-1.png)
]
---
## Model parameters BC.5 ##

```r
summary(lettuce.m1)
```

```
## 
## Model fitted: Brain-Cousens (hormesis) (5 parms)
## 
## Parameter estimates:
## 
##               Estimate Std. Error t-value   p-value    
## b:(Intercept) 1.502065   0.352231  4.2644  0.002097 ** 
## c:(Intercept) 0.280173   0.248569  1.1271  0.288836    
## d:(Intercept) 0.963030   0.078186 12.3171 6.164e-07 ***
## e:(Intercept) 1.120457   0.612908  1.8281  0.100799    
## f:(Intercept) 0.988182   0.776136  1.2732  0.234846    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error:
## 
##  0.1149117 (9 degrees of freedom)
```
---
## Model parameters LL.4 ##

```r
summary(lettuce.m2)
```

```
## 
## Model fitted: Log-logistic (ED50 as parameter) (4 parms)
## 
## Parameter estimates:
## 
##               Estimate Std. Error t-value   p-value    
## b:(Intercept) 1.383314   0.647270  2.1372   0.05831 .  
## c:(Intercept) 0.372180   0.141193  2.6360   0.02491 *  
## d:(Intercept) 1.101071   0.064231 17.1423 9.633e-09 ***
## e:(Intercept) 8.607125   5.175525  1.6630   0.12728    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error:
## 
##  0.143901 (10 degrees of freedom)
```
---
## Model compairason BC.5 vs LL.4 ##

```r
anova(lettuce.m1, lettuce.m2)
```

```
## 
## 1st model
##  fct:      LL.4()
## 2nd model
##  fct:      BC.5()
```

```
## ANOVA table
## 
##           ModelDf     RSS Df F value p value
## 2nd model      10 0.20708                   
## 1st model       9 0.11884  1  6.6819  0.0295
```
---
#Results#
<div align="center">
<img src="https://github.com/vitoranunciato/Statical-analises-behind-my-thesis/blob/master/docs/img/ac5.png?raw=true" width=800 height=500>
</div>
---
#Results#
<div align="center">
<img src="https://github.com/vitoranunciato/Statical-analises-behind-my-thesis/blob/master/docs/img/ac10.png?raw=true" width=800 height=500>
</div>
---
#7 DAA#
<div align="center">
<img src="https://github.com/vitoranunciato/Statical-analises-behind-my-thesis/blob/master/docs/img/hormesis7DAA.jpg?raw=true" width=800 height=480>
</div>
---
#15 DAA#
<div align="center">
<img src="https://github.com/vitoranunciato/Statical-analises-behind-my-thesis/blob/master/docs/img/hormesis15DAA.jpg?raw=true" width=800 height=480>
</div>
---
#21 DAA#
<div align="center">
<img src="https://github.com/vitoranunciato/Statical-analises-behind-my-thesis/blob/master/docs/img/hormesis21DAA.jpg?raw=true" width=800 height=480>
</div>
---
#28 DAA#
<div align="center">
<img src="https://github.com/vitoranunciato/Statical-analises-behind-my-thesis/blob/master/docs/img/hormesis28DAA.jpg?raw=true" width=800 height=480>
</div>
---
#41 DAA#
<div align="center">
<img src="https://github.com/vitoranunciato/Statical-analises-behind-my-thesis/blob/master/docs/img/hormesis41DAA.jpg?raw=true" width=800 height=480>
</div>
---
#48 DAA#
<div align="center">
<img src="https://github.com/vitoranunciato/Statical-analises-behind-my-thesis/blob/master/docs/img/hormesis48DAA.jpg?raw=true" width=800 height=480>
</div>
---
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#Conclusion#
Glyphosate can stimulate the growth of the *Digitaria insularis* up to 60%.
.right[*Thank you*]