• What is the scientific research process
• Scientific and non-scientific hypotheses
• What is a hypothesis that can be falsified?
• How to get started with R / R Markdown
• What are response and predictor variables, what is a ‘treatment’ and a 'control'
• Binomial, nominal, ordinal, and continuous variables
• Predictor vs. response variables
• Systematic vs. unsystematic variation in data, what are its sources?

• What is the signal-noise ratio? How can we increase it?

• PLEASE: lab reports (filenames!)

• Describe a study which uses 2 predictor variables, one continuous, one categorical, and one binomial response variable
• In R, create three variables of the same length, one continuous, one categorical and one binomial
• Explain why unsystematic variation in data can prevent us from detecting a signal
• Explain 2 sources of systematic variation

• We use the c() function and list all values in quotations so that R knows that it is string data.
• As such, we can create a variable called name as follows:

name <- c("Ben", "Martin", "Andy", "Pauline", "Eva", "Carina")
name
[1] "Ben"     "Martin"  "Andy"    "Pauline" "Eva"     "Carina" 

• It does not matter whether you use single or double quotes
• Note that if you don't type 'name' again, then the variable is not displayed
• What does the '[1]' mean in front of the variable?

• Imagine we had 3 males and 3 females in a data set and we wanted to create a coding variable called 'gender', 1 means male, 2 female.
• Enter the data:

gender <- c(1, 1, 1, 2, 2, 2)

• Where can we leave a space in the R code, where can't we?

• Numeric variables are the easiest ones to create:

alcohol <- c(0.75, 1.2, 2.4, 0.23, 0.9, 1.36) #standard drinks/day
income <- c(58000, 38000, 28000, 63000, 90500, 17000)
alcohol
[1] 0.75 1.20 2.40 0.23 0.90 1.36
income
[1] 58000 38000 28000 63000 90500 17000

• What does the '#' sign do again?
• Are those continuous or categorical variables?
• Are they predictor or response variables

• We can combine variables into a data frame:

d1 <- data.frame(name, alcohol, income, gender)
d1
     name alcohol income gender
1     Ben    0.75  58000      1
2  Martin    1.20  38000      1
3    Andy    2.40  28000      1
4 Pauline    0.23  63000      2
5     Eva    0.90  90500      2
6  Carina    1.36  17000      2

• What are the dimensions of the data frame?
• Why call it 'd1'? Can we call it something else…?

Say you have a folder in ‘My Documents’ called ‘BIOL501’ in where your data files are and where your input should go:

• Either click on 'Session', then 'set work directory', then select the above folder

• Or even better: include a setwd() ('set work directory') command in a chunk that you place at the beginning of your RMarkdown document:

setwd("C:/Documents/BIOL501") #adjust path to your system!

We can now access files in that folder directly. For example: myData <- read.csv("data.csv")

• The histogram! Always THE first thing to look at:

hist(x)
hist(y)

• The box plot! Very useful when you want to look at a continuous variable that is grouped by another (categorical variable):

boxplot(d1$income ~ d1$gender) #note the use of '$' and '~'!

• A perfect fit (rare!):

• More often it looks like this:

• A deviation is the difference between the mean and an actual data point.
• Deviations can be calculated by taking each score and subtracting the mean from it:

\(deviation = x_i - \bar{x}\)

• NB: 'Deviation' is called 'residual' in linear models

What do you think? How could we compute a number that is large when the variation is large, and small when the variation is small?

• The problem with summing up deviations is that they cancel out because some are positive and others negative
• Therefore, we square each deviation.
• If we add these squared deviations we get the sum of squared errors (SS).

\[SS = \sum(x_i - \bar{x})^2\]

• The sum of squares is a good measure of overall variability, but it is dependent on the number of scores/values
• We calculate the average variability by dividing by the number of scores (\(n\)) minus 1.
• This value is called the variance (\(s^2\)).

\[variance (s^2) = \frac{SS}{n-1} = \frac{\sum(x_i-\bar{x})^2}{n-1} = \frac{5.2}{4} = 1.3\]

• The variance has one problem: it is measured in units squared
• This isn’t a very meaningful metric so we take the square root value
• This is the standard deviation (\(s\), sometimes \(sd\)):

\[s = \sqrt{\frac{\sum(x_i-\bar{x})^2}{n-1}} = \sqrt{\frac{5.2}{4}} = 1.14\]

In R:

friends <- c(1, 2, 3, 3, 4)
sd(friends)
[1] 1.140175

Calculating metrics e.g. the mean 'cost' you degrees of freedom!

• Organise and import your data, create a data frame in R
• Measuring variability graphically
  • draw a histogram and interpret it
• Computing and understanding
  • the sum of squared errors
  • the variance
  • the standard deviation