Variables

Types of Variables

• Independent variable: the “cause”, the variable that is varied
• Dependent variable: the “effect”

Categorical

• Nominal
  • Named category with no definite order
  • e.g. Eye colour
• Ordinal
  • Categories where values can be ordered or ranked
  • Distances between values are incomparable (subjective)
  • Ranges are categorical ordinal, even if they are not subjective
  • e.g. Happiness on a scale from 1-5 (my 2 might be different from your 2)

Numerical

• Discrete
  • Possible values of the variable has gaps
  • Values are not subjective
  • e.g. Birth year
• Continuous
  • Variable can take on any value within a range
  • e.g. Time

Summary Statistics

For Numerical Variables

• Central tendencies can be measured (Mean, Median, Mode)
  • Mean (average)
  • Median (middle value in order)
  • Mode (peak of distribution/most common value)
• Dispersion/distribution can be measured
  • Variance
    • $\text{Var}=\frac{(x_1-\bar{x}{)}^2+...+(x_n-\bar{x}{)}^2}{n-1}$
  • Standard Deviation
    • $\sqrt{\text{V}ar}$
    • Spread of the data points about the mean
    • Square root of sum of squares
  • Interquartile Range
    • Q3 - Q1
  • Coefficient of variation
    • Standard deviation / mean
    • Used to compare the spread of data when the mean is different
      • e.g. 500 $\pm$ 2 vs 3 $\pm$ 2
• Quartiles
  • Divide the list into 4 equal parts, the quartiles are where the “cuts” are (take average between two numbers if required)
  • Average between two numbers only if the number of elements is a whole number e.g. Q2 for a list of 10 numbers (5 elements), but not Q1 (2.5 elements)

	$\pm$ +ve number $c$ from all values	$\times$ c to all values
Mean	$\pm c$	$\times c$
Median	$\pm c$	$\times c$
Mode	$\pm c$	$\times c$
SD	No change	$\times |c|$
IQR	No change	$\times |c|$
CoV	Changes	$\times -1$ if $c<0$

For Categorical Variables

• Counts
• Proportions/percentages
• Mode