Introduction:

Background:

The global population rate is predicted to reach 9.8 billion by the year 2050 (UN, 2017). The increased population will place an enormous strain on the agricultural sector who’s current farming practises are already detrimental to the natural environment (Karancsi, Z. et al., 2010). Over-cultivation can lead to permanent damage to the productivity of the land (Tiessen, H. et al., 1982) and failing yields place a greater threat to food security. Fertilisers offer a solution to this problem and can have a significant effect on plant growth through its ability to replenish the topsoil with vital nutrients. Radishes are fast growing crops and have been used to test the variability of growth caused by the usage of fertilisers.

##Aim:

To determine the effects of varying fertilisers on the growth of Radish sprouts.

##Hypothesis- null and alternate:

H0:There is no statistically significant relationship between the application of fertiliser and accelerated growth rate in relevance to radish growth.

H1: If plants are subject to the application of fertiliser, then plants grown with chemical fertiliser will have accelerated growth compared to those grown in regular soil and grown with organic fertiliser.

##Materials and Methods:

A manipulative experiment will be conducted to measure how different types of soil and fertiliser affect the growth rate of radishes in a controlled environment. The independent variable in the experiment will be soil type the radishes are grown in. The independent variable will consist of three treatments of soil; regular soil containing no fertiliser, soil and organic compost and soil with a chemical fertiliser. The dependent variable of the experiment will be the final height in cm of the radishes.

To reduce the risk of confounding variables, blind randomisation will be used. Seed distribution will be delegated to an assistant unaware of the experimental actions. Replication will be ensured by designating each treatment and control with 10 pots containing one seed each. Each seedling will represent one datapoint with ten replicates allowing for more reliable results. In order to ensure that the results obtained are valid, the pots, seeds, seed depth, environment and water will be kept the same. The plants will all be kept in the same room, ensuring equal light exposure, humidity and temperature.

#Equipment:

#Method:

  1. Label each pot within each planting tray with numbers 1-10. This will ensure that data for each plant can be recorded accurately.
  2. Place 100g of soil in each of the 10 pots in all 3 planting trays.
  3. One of the planting trays will receive the organic compost treatment. 30g of compost must be added to each of the 10 pots in one of the planting trays.
  4. The other planting tray will receive the chemical fertiliser. 10ml of the liquid fertiliser must be added to each of the 10 pots in one of the planting trays. (This should be repeated every fortnight).
  5. To ensure all the seeds are at the same depth mark the blunt end of a pencil at 2cm and create an incision in each pot.
  6. The assistant will randomly assign one seed to each pot. Cover the seed with soil and compact the soil slightly.
  7. The planting trays must be placed in a location which will receive sufficient and adequate lighting.
  8. Each seedling will receive 15ml of water each morning at the same time every day.
  9. After 10 days of the first sprouting detach each seedling from the root. Take a ruler and measure the length of the plant. Record each individual data point.

##Analysis:

#Looking at the raw data:

Before conducting any statistical analysis it is evident that there are a few 0 values across the groups. This may cause skewing and eludes that the data may not be normal.

library(tidyverse)
## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ──
## ✓ ggplot2 3.3.3     ✓ purrr   0.3.4
## ✓ tibble  3.1.0     ✓ dplyr   1.0.5
## ✓ tidyr   1.1.3     ✓ stringr 1.4.0
## ✓ readr   1.4.0     ✓ forcats 0.5.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()
library(emmeans)
library(agricolae)
library(readxl)
Radish <- read_excel("~/Documents/ENV2001/Report2.xlsx")
Radish$Fertilizer<-as.factor(Radish$Fertilizer)
str(Radish)
## tibble[,3] [30 × 3] (S3: tbl_df/tbl/data.frame)
##  $ Fertilizer: Factor w/ 3 levels "Chemical Fertilzer",..: 2 2 2 2 2 2 2 2 2 2 ...
##  $ Plot      : num [1:30] 1 2 3 4 5 6 7 8 9 10 ...
##  $ Height(cm): num [1:30] 0 8.6 3.2 11.6 6.2 10.6 7.3 9.3 12.6 0 ...
summary(Radish)
##               Fertilizer      Plot        Height(cm)   
##  Chemical Fertilzer:10   Min.   : 1.0   Min.   : 0.00  
##  No Fertilizer     :10   1st Qu.: 3.0   1st Qu.: 0.00  
##  Organic Fertilzer :10   Median : 5.5   Median : 5.90  
##                          Mean   : 5.5   Mean   : 5.68  
##                          3rd Qu.: 8.0   3rd Qu.: 9.15  
##                          Max.   :10.0   Max.   :12.90
tapply(Radish$`Height(cm)`, Radish$Fertilizer, mean)
## Chemical Fertilzer      No Fertilizer  Organic Fertilzer 
##               6.00               6.94               4.10
tapply(Radish$`Height(cm)`, Radish$Fertilizer, sd)
## Chemical Fertilzer      No Fertilizer  Organic Fertilzer 
##           5.282255           4.551727           3.937286

Assumptions: Testing for normality

hist(Radish$`Height(cm)`,main="Radish Height under different Fertilizers ",xlab="Height (cm)")

boxplot(Radish$`Height(cm)` ~ Radish$Fertilizer,main="Radish Height under different Fertilizer",
xlab="Fertlizer Type",ylab="Height (cm)")

By plotting the data as three boxplots with the fertlisier application on the x-axis and the height (cm) on the y-axis it is evident that there is skewing for organic fertiliser. This may be the causation for non normally distributed data, which can be confirmed by the Shapiro-Wilks tets.

shapiro.test(Radish$`Height(cm)`)
## 
##  Shapiro-Wilk normality test
## 
## data:  Radish$`Height(cm)`
## W = 0.89076, p-value = 0.005029

The p-value is less than 0.05 meaning the distribution of this dataset is therefore significantly different from being normal distributed.

#Assumptions: Testing for constant variance:

Height.aov <- aov(Radish$`Height(cm)` ~ Radish$Fertilizer)
par(mfrow = c(2,2))
hist(rstandard(Height.aov))
qqnorm(rstandard(Height.aov))
qqline(rstandard(Height.aov))

plot(fitted(Height.aov),rstandard(Height.aov))
abline(0,0)
plot(fitted(Height.aov),resid(Height.aov))
abline(0,0)

Examining the residuals shows that the height data is J-shaped meaning it is skewed to the right and is abnormal. The data scatters evenly around the group mean meaning the data possesses equal variance. It is unclear if fanning is present in the fitted graph menaing further variance testing is necessary to make an appropriate judgement. This can be achieved using the Bartlett Test of Homogeneity of Variances.

bartlett.test(Radish$`Height(cm)` ~ Radish$Fertilizer)
## 
##  Bartlett test of homogeneity of variances
## 
## data:  Radish$`Height(cm)` by Radish$Fertilizer
## Bartlett's K-squared = 0.73632, df = 2, p-value = 0.692
outsd <- tapply((Radish$`Height(cm)`),Radish$Fertilizer,sd)
outsd
## Chemical Fertilzer      No Fertilizer  Organic Fertilzer 
##           5.282255           4.551727           3.937286
outsd[1]/outsd[3]
## Chemical Fertilzer 
##           1.341598

The Bartlett Test of Homogeneity of Variances test gives a p-value of 0.692. As the p-value is bigger than the significance level (0.05) we accept the null hypothesis that this dataset is confirmed to have equal variance. This is further proven by finiding the ration between the highest and lowest standard deviation is lower than 2. There is no need to transform the data.

ANOVA

Test statistic: F=0.979 P value: 0.389

The P value is greater than 0.05 therefore we retain the null hypothesis. There is no statistically significant relationship between the application of fertiliser and accelerated growth in relevance to radish growth.

summary(Height.aov)
##                   Df Sum Sq Mean Sq F value Pr(>F)
## Radish$Fertilizer  2   41.9   20.93   0.979  0.389
## Residuals         27  577.1   21.37

#Post hoc:

TukeyHSD(Height.aov)
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Radish$`Height(cm)` ~ Radish$Fertilizer)
## 
## $`Radish$Fertilizer`
##                                       diff       lwr      upr     p adj
## No Fertilizer-Chemical Fertilzer      0.94 -4.186369 6.066369 0.8927688
## Organic Fertilzer-Chemical Fertilzer -1.90 -7.026369 3.226369 0.6332368
## Organic Fertilzer-No Fertilizer      -2.84 -7.966369 2.286369 0.3684872

Running a post hoc test allows us to find differences between each treatment.There is no significant difference to be reported in the present test as the p-values are not significant between the means of the groups.

##Conclusions

##Statistical conclusion:

Scientific conclusion:

Limitations: -should have been randomised within each block rather than each tray of 10 selectively having their own treatment.

Improvements: