Summary
Appropriate measures of central tendency and dispersion, and graphical display, depend on a variable’s level of measurement. The normal distribution follows the Empirical Rule of having 68.3% of its observations within 1 standard deviation of the mean, 95.4% within 2 standard deviations, and 99.7% within 3 standard deviations. The sampling distribution of the mean is distributed normally around the true population value. The Empirical Rule combines with the Law of Large Numbers and the Central Limit Theorem to produce many important tools and insights.
Articles
The Null Hypothesis: Putting It All Together <– THIS ONE IS REALLY IMPORTANT AND I FORGOT TO ADD IT IN THE TEXT ::FACEPALM::
Web Extra: Using Normal Curves to Examine Climate Anomalies
Web Extra: Sampling for Your Own Research
Conventions of Quantitative Notation
Vocab Flashcards
[qdeck random=”true”]
[q] Degree of precision used in the operationalization of a variable; most common in political science are interval-ratio, ordinal, and nominal
[a] level of measurement
[q] Level of measurement: continuous or discrete quantities with consistent units attached such as years or votes; most precise level used in political science
[a] interval-ratio
[q] Level of measurement: rankable categories, where the intervals between categories may or may not be equal or precisely definable; intermediate level of measurement
[a] ordinal
[q] Level of measurement: unrankable but discrete categories, with no implied direction or magnitude; lowest precision of measurement
[a] nominal
[q] Summarize and describe characteristics of data (mean, median, mode, standard deviation, etc.) without reference or generalization beyond the available data itself
[a] descriptive statistics
[q] Branch of statistics that generalizes from samples to populations
[a] inferential statistics
[q] Characteristic of continuous distributions; concerned with distance between mean and median values
[a] skew
[q] In quantitative analysis, name of the column in your dataset; shortest and most abbreviated representation of the data contents
[a] variable
[q] In the statistical sense, an indication that the observed relationship is not 0
[a] significance
[q] sample selection procedure: Equal Probability of Selection Mechanism
[a] EPSEM
[q] Row and column at the edges (margins) of a table indicating total for that row or column; must balance across and down
[a] marginals
[q] Arithmetic average; measure of central tendency for interval-ratio variables
[a] mean
[q] Value above and below which 50% of the values in a distribution lie; measure of central tendency for ordinal variables
[a] median
[q] Value that occurs the most frequently in a distribution; measure of central tendency for nominal variables
[a] mode
[q] Classic bell-shaped distribution for continuous variables; has special known properties for probability under the curve, sampling distribution of mean, and more
[a] normal distribution
[q] Measure of dispersion for ordinal variables
[a] range
[q] Measure of dispersion for interval-ratio variables
[a] standard deviation
[q] The trailing ends of a distribution, at the extremes away from the central tendency
[a] tails
[q] Distribution for discrete data where each value is equally probable
[a] binomial distribution
[q] Family of statistics, like descriptive statistics, calculated on a single variable
[a] univariate
[q] Calculated as the number of standard deviations from the mean
[a] Z score
[q] A value minus the mean of that variable
[a] deviation
[q] Distribution of some statistic, such as a mean, calculated on repeated samples from a population; some have special properties
[a] sampling distribution
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Review Quiz
[qwiz random=”true” random_mc=”true”]
[q multiple_choice=”true”] The BEST measure of central tendency for a nominal variable is the ___.
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[q random_mc=”false” multiple_choice=”true”] A paper provides descriptive statistics for a variable by noting that it has a mode of 4 and a range of [2, 5]. What level of measurement is this variable MOST LIKELY to be?
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[q multiple_choice=”true”] The appropriate measure of variation for an interval-ratio variable is ____.
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[c]IHN0YW5kYXJkIGNvZWZmaWNpZW50[Qq]
[f]IFNvcnJ5LCB0aGF0JiM4MjE3O3Mgbm90IGNvcnJlY3Qu[Qq]
[q multiple_choice=”true”] What kind of figure is this graph?
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[c]IGVycm9yIHZzIHJlc2lkdWFscyBwbG90[Qq]
[f]IE5vLCB0aGF0JiM4MjE3O3Mgbm90IGNvcnJlY3Qu[Qq]
[q multiple_choice=”true”] The principle that a normal distribution has 68% of its observations within 1 s.d., 95% within 2 s.d., and 97% within 3 s.d is known as the ___.
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[c]IEltcG9zc2liaWxpdHkgUHJpbmNpcGxl[Qq]
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[q multiple_choice=”true”] Which of the following statements about the sampling distribution is FALSE?
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[c]IFRoZSBtZWFuIG9mIHRoZSBzYW1wbGluZyBkaXN0cmlidXRpb24gb2YgbWVhbnMgd2lsbCBlcXVhbCB0aGUgcG9wdWxhdGlvbiBtZWFuIGlmIHdlIHRha2UgZW5vdWdoIHNhbXBsZXMu[Qq]
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