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Univariate Descriptive Statistics And Basics of Normal Distributions

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

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  1. Univariate Descriptive Statistics And Basics of Normal Distributions

  2. 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

  3. The Normal Curve

  4. 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.

  5. 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.

  6. 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).

  7. 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

  8. 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)

  9. 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.

  10. Issues with Normal Distributions • Skewness • Kurtosis

  11. 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.

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