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Univariate Descriptive Statistics And Basics of Normal Distributions. Probability and Statistics. Statistics deal with what we observe and how it compares to what might be expected by chance . For now, we especially care about the normal (Gaussian) distribution. The Normal Curve.

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univariate descriptive statistics and basics of normal distributions
Univariate Descriptive Statistics

And Basics of Normal Distributions

probability and statistics
Probability and Statistics
  • Statistics deal with what we observe and how it compares to what might be expected by chance.
  • For now, we especially care about the normal (Gaussian) distribution
describing simple distributions of data
Describing Simple Distributions of Data
  • Central Tendency
    • Some way of “typifying” a distribution of values, scores, etc.
      • Mean
        • sum of scores divided by number of scores
      • Median
        • middle score, as found by rank
      • Mode
        • most common value from set of values
    • In a normal distribution, all 3 measures are equal.
special features of the mean
Special Features of the Mean
  • Sum of the deviations from the mean of all scores = zero.
  • It is the point in a distribution where the two halves are balanced.
using central tendencies in recoding
Using Central Tendencies in Recoding
  • “splitting” metrics into binary variables
    • High/Low (mean or median)
    • Most common, least common (mode)
  • “collapsing” variables (less from more)
    • Groups of scores in different ranges above and below the mean (eg., Age in years recoded as teenagers, young adult, adult, elder adult, etc).
dispersion
Dispersion
  • Range
    • Overall measure of distance between all values in a variable.
    • Difference between highest value and the lowest value.
  • Standard Deviation
    • A measure of spread
    • A statistic that describes how tightly the values are clustered around the mean.
  • Variance
    • A measure of spread
    • Computed as the average squared deviation of each value from its mean
properties of standard deviation s d
Properties of Standard Deviation (S.D.)
  • If a constant is added to all scores, it has no impact on S.D.
  • If a constant is multiplied to all scores, it will affect the dispersion (S.D. and variance)
  • Remember, variance is just the square of the S.D. (or, S.D is the square root of the variance)

S = standard deviationX = individual scoreM = mean of all scoresn = sample size (number of scores)

common data representations
Common Data Representations
  • Histograms (hist command in STATA)
    • Simple graphs of the density or frequency
    • With density, area comes out in percent and total area = 100%
  • Box Plots (graph box command in STATA)
    • Yet another way of displaying dispersion.
in class examples in stata
In-Class Examples in STATA

Using GSS93_data.dta from Resources Page on course website

Also, look at notes on syllabus for today’s lecture.