Descriptive statistics

Question 1

Basic data types

Answer 1

Nominal: no inherent rank to values; mutually exclusive categories
Binary: Special case of nominal (2 levels)
Ordinal: Inherent rank, mutually exclusive categories, difference between categories not meaningful
Interval: exhaustive, mutually exclusive, with rank order, differences between values meaningful
Ratio: same properties of interval but with meaningful zero point, ratio of values is meaningful

Question 2

Ecological fallacy

Answer 2

Drawing conclusions from the wrong level of analysis.
Observe a relationship at the county level and conclude that this relationship holds for individuals.
Example: Note an association between % minority population in a county & the mortality rate. Conclude that minorities have higher mortality. WRONG! Everyone in the county has higher mortality chances.

Question 3

Basic graphical techniques

Answer 3

Pie charts: Proportion of data in set of unique, mutually exclusive categories
Bar charts: Like pie chart but shows frequency
Histogram: Special case of bar chart, represent distribution of data; frequency histogram (raw count) & relative frequency histogram (% of data)
Stem & leaf plot: Related to histogram, show frequency of specific values in data
Time series plots: Show trends in data
Scatter plots: Two variables on single plot, look at relationships
Scatterplot matrix: Scatter plots for many relationship simultaneously

Question 4

Measures of central tendency

Answer 4

Mode, median, mean
Population mean using mu
Sample mean using x bar

Question 5

Measures of variation

Answer 5

Range: Highest value - lowest value
Percentiles/quantiles: Construct quantile or Q-Q plot of values of x versus percentile of distribution it represents
Interquartile range: 75th percentile - 25th percentile
Box & whisker plot
Sample variance: Observation-specific deviations from the mean (deviation = x-xbar)

Question 6

Variance

Answer 6

x^2 = (Sum(xi - xbar)^2)/(n-1)
Population variance: σ^2
Sample variance=s^2

Question 7

Standard deviation

Answer 7

Square root of variance
s=SQRT((Sum(xi - xbar)^2)/(n-1))
Population standard deviation: σ
Sample standard deviation: s
Variance is in squared units, but taking square root gives measure of variability in same units as data