Lecture 1.2 - Characteristics of distributions
Characteristics of distributions
Distribution of common quantities
Many phenomena in nature have a relatively easily guessed distribution characteristics
- What is the distribution of length of rivers in the U.S.?
- What is the distribution of width of flower sepals?
- What is the distribution of life expectancy across countries in 2007?
Features to guess:
- Shape
- Center
- Spread
Graphs of common quantities
Length of rivers in the U.S.
Flower sepal width
Life expetancy in 2007
Distribution of our data
Let’s now collect some data about our class
- Information about handedness
- Information about heights
Guessing the shape of our data
Take a guess at what each question’s distribution characteristics will be:
- Shape
- Skew
- Modes
- Center
- Mean
- Median
- Spread
- Range
- IQR
- Standard deviation
- Also think carefully about the difference between the three different calculations of handedness - how do they differ? Discuss with your partner.
Height summary statistics
- Shape
- Skew:
- Modes: 163
- Center
- Mean 170.1818182
- Median 169.5
- Spread
- Range 152, 188
- IQR 10
- Standard deviation 8.7757044
Height graph
Handedness l-r summary statistics
- Shape
- Skew:
- Modes: -12
- Center
- Mean -12.12
- Median -12
- Spread
- Range -16, -8
- IQR 3
- Standard deviation 2.2233608
- What does this measure?
Handedness l-r graph
Handedness l+r summary statistics
- Shape
- Skew:
- Modes: 20
- Center
- Mean 18.64
- Median 20
- Spread
- Range 10, 20
- IQR 2
- Standard deviation 2.3430749
- What does this measure?
Handedness l+r graph
Handedness left - right / left + right graph
Closing thoughts
- Many distributions can be guessed in advanced based on the data generating process
- You should have at least a guess as to what the distribution is before starting your exploratory data analysis
- Think carefully about what your variable is actually measuring
- Characteristics of distributions are summaries of the data, almost always obscure features of the data
- Don’t mislead your readers!!