expmeth_2/01_exp_methods2_2020_intro_GLM_code.Rmd at master · mortgad/expmeth_2 · GitHub

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---
title: "lecture1_intro_glm_code"
author: "Mikkel Wallentin"
date: "February 1 2019"
output:
  pdf_document: default
  html_document: default
---

#Notes and code for lecture 1 in Experimental Methods 2.

```{r}
#make dataset with 1000 z-scaled data points
n1000=rnorm(1000, mean=0, sd=1)
#Plot them sequentially
plot(seq(1,1000,1),n1000 )
```
```{r}
#Histogram/Probability density plot using ggplot
library(ggplot2)
#Make dataframe
n1000<-data.frame(n1000)
p<- ggplot(data=n1000, aes(x=n1000, ..density..,))
p + stat_bin(data=n1000,bins=40)
```

```{r}
#Find the upper 97.5 percentile
n1000_sort<-sort(n1000$n1000)
n1000_sort[975]
#Scores above this number are considered ???abnormal??? p<0.05, two-tailed
```


```{r}
#Visualizing the Libido model
#--------Viagra data----------
libido<-c(3,2,1,1,4,5,2,4,2,3,7,4,5,3,6)

#matrix for data model
viagramat=matrix(data=0,nrow=15, ncol=4)
viagramat[,c(1)]<-as.matrix(libido)
viagramat[c(1:5),c(2)]<-1
viagramat[c(6:10),c(3)]<-1
viagramat[c(11:15),c(4)]<-1

#Visualize a transposed (t()) scaled (scale()) matrix with data point 1 on top ([15:1])
image(t(scale(viagramat[15:1,])), axes=FALSE, col=gray(1:10/10))
```
####Making a plot with F distribution
```{r}
#Making a string of 100 numbers beteen 0 and 20 to use when finding the F distribution
nn<-seq(0,20,len=100)
#Getting the F distribution using df()
fdist<-df(nn,2,12)
plot(nn,fdist, type='l',xlab='F value - df(2,12)',ylab='Density')
```

###F-statistics
```{r}
#The F statistics for the effect of viagra
model<-lm(viagramat[,c(1)] ~1+viagramat[,c(3:4)] )
res=anova(model)
res
#Checking p-value using probability function pf()
pval<-1-pf(res$`F value`[1],2,12)
'p-value:'
pval
#Getting the F-score for the 95% significance cutoff using the quantile function qf()
cutoff<-qf(0.95,2,12)
'p=0.05 cutoff value with df(2,12)'
cutoff
```
####Making a F-distribution plot with the cutoff and the resulting F-value
```{r}
#Making a string of 100 numbers beteen 0 and 20 to use when finding the F distribution
nn<-seq(0,20,len=100)
#Getting the F distribution using df()
fdist<-df(nn,2,12)
plot(nn,fdist, type='l',xlab='F value - df(2,12)',ylab='Density')
#plotting a vertical line at the cutoff
lines(c(cutoff,cutoff),c(0,1),col='darkgreen')
#Add explanation for the line
text(cutoff+2,0.5,'p=0.05',col='darkgreen')
#draw F-value as point on the curve
points(res$`F value`[1],df(res$`F value`[1],2,12),col='red')
```
###Or a pretty F distribtion using sjPlot
```{r}
library(sjPlot)
dist_f(f=0, deg.f1 = 2, deg.f2 = 12,xmax=20)
```

###Getting the t-statistics using lm()
```{r}
#Model estimation using lm() and the two dose columns as model
#1st column (Placebo) is baseline, thus not included in the model.
model<-lm(viagramat[,c(1)] ~1+viagramat[,c(3:4)] )
summary(model)

```

###F-statistiscs show that the overall model explains more variance than what would have been expected by chance (F=5.12,p<0.05).

###Post hoc t-tests show that the low dose is not significantly different from baseline (t=1.12, p<0.05), however the high dose group have a significantly higher libido than the placebo group (t=3.15, p<0.05). Even after correcting for multiple comparisons (dividing by 2), this effect is still significant.