• 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?
• What is a sample? What is a population?

• Describe a study that 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", "Mary", "Andy", "Paul", "Eva", "Carl")
name
[1] "Ben"  "Mary" "Andy" "Paul" "Eva"  "Carl"

• 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?

name1 =  rep(name, times = 3)
name1
 [1] "Ben"  "Mary" "Andy" "Paul" "Eva"  "Carl" "Ben"  "Mary" "Andy" "Paul"
[11] "Eva"  "Carl" "Ben"  "Mary" "Andy" "Paul" "Eva"  "Carl"

The number in square brackets indicates the 'index', the position of the value within the variable:

rnorm(20)
 [1]  1.6739606 -0.1665988  0.4953175 -2.0888457  1.3930438  0.3808360
 [7]  1.0048967  0.1355061  2.8393412 -0.1163399  0.9209963 -0.3198669
[13] -1.3672879 -1.8611386 -0.4684234  1.2762487  2.0978015 -0.5942577
[19]  0.6131022 -0.3829628

• 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?

• 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 Mary    1.20  38000      1
3 Andy    2.40  28000      1
4 Paul    0.23  63000      2
5  Eva    0.90  90500      2
6 Carl    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!

You tested a drug on a group of 7 people, and you have a control group of 6 people. You also recorded the gender, the body height and body weight of your patients. Your response variable is the heart rate before and after administring the drug.

• What does your final data frame look like? (sketch it on paper)
• Describe all your variables (categorical, continuous, response, predictor…?)
• What plots could you use to visualise this data set?
• How would you create this data set in R?

Below, indicate which variable is most likely binomial

1. Hair colour
2. Gender
3. Body height
4. Age class
5. None of the above

Which two variables are most unlikely response variables?

1. 'Hair colour' and 'body height'
2. 'Education of parents' and 'smoking habits of parents'
3. 'Drug dosis' and 'gender'
4. 'Heart rate' and 'blood sugar level'

What is the variance of this sample: [3, 4, 3, 2] ? (Calculate it by hand)

1. \(5\)
2. \(0.66\)
3. \(0\)
4. \(\sqrt 6\)
5. \(4\)

When calculating the standard deviation, we divide by n-1 rather than by n because:

1. This makes the formula look more scientific
2. This makes sure that the sum of squares is not zero
3. This avoids division by zero
4. Otherwise we are computing the variance
5. None of the above

Which line correctly defines a categorical variable that is also nominal (using the software R)?

1. c(4, 2, 2, 5, 9, 10)
2. c(3.78, 5.98, 1.30. 22.43)
3. c('black', 'black', 'black', 'blond', 'brown', 'brown', 'blond')
4. rep(c('A', 'B', 'C'), each = 2)
5. both (3) and (4) are correct

Bozeman Science

• Standard deviation: youtube.com/watch?v=09kiX3p5Vek
• Standard error: youtube.com/watch?v=BwYj69LAQOIset

• Mean: see last week's slides
• Mode
  • The most frequent score or category (the peak of the histogram)
• Median
  • The middle score when scores are ordered. In R: median()
  • Example: number of friends of 11 Facebook users:

22, 40, 53, 57, 93, 98, 103, 108, 116, 121, 252

Which is the median?

• The Range
  • The smallest score subtracted from the largest. In R: range()
• Example
  • Number of friends of 11 Facebook users.
  • 22, 40, 53, 57, 93, 98, 103, 108, 116, 121, 252
  • Range = 252 – 22 = 230
• What could be a problem when you indicate the range of a varible? What could we be missing?

=> this metric is prone to extreme values!

• Quartiles
  • The three values that split the sorted data into four equal parts.
  • Second quartile = median.
  • Lower quartile = median of lower half of the data.
  • Upper quartile = median of upper half of the data.
  • In R: qnorm(p = .25) or qnorm(p = .75)

=> quartiles/medians are not prone to extreme values!

• comma separated values (csv files)
• wide vs. long data format
• value or score
• string or character variable
• categorical variable
• coding variable
• numeric variable
• histogram
• box plot, whisker plot

• deviation
• sum of squared errors (sum of squares)
• variance
• standard deviation
• degrees of freedom
• standard error
• Normal distribution
• mean, mode, median, range
• quartiles, interquartile range
• quantiles
• confidence intervals