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Beginning Statistical Concepts
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Statistics
— the study of the summary, analysis, and evaluation
of data.
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statistic – value calculated based upon information obtained
from a sample that is used to estimate population information
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parameter – value calculated based upon information obtained
from a population
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Levels of Measurement (types of scores)
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Nominal
– Merely classifies objects in accordance with similarities
and differences with respect to some property; no
hierarchy of scores
– Examples color of hair
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gender response to a yes/no question shoe preference
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Ordinal
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– Type of data that is rank ordered on the basis of
an underlying continuum
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– No common unit of measurement between each
score, but are ordered from high to low

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– Examples class ranks place of finish in a race
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Interval
– Data having a common unit of measurement, equal
distances between score units, but having an arbitrary
zero point (not a true zero)
– Example temperature on Fahrenheit scale score on a
knowledge test
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Ratio
– Possesses same properties of interval data, but does
have a true zero point
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Allows statements about equality of ratios to be made –
Examples
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height or weight distance measurement
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Indicate the level of measurement for the following:
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Driving on U.S. Highway 280
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A runner’s time of 18 min 30 sec in a road race
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A student 27th in a class of 157 students
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44 women in a recreational golf league

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The average daily temperature of 550 last March
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Locker number 16
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A systolic blood pressure reading of 124 mm Hg
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A football lineman who weighs 295 lb
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A swimmer who finished third in a race
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Descriptive Statistics
– Measures a trait or characteristic of a group without
generalizing that statistic beyond that group.
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Inferential Statistics
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– Used to make generalizations or inferences from
a smaller group (sample) to a larger group (population).
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– The ability to make valid inferences is a function
of how representative your sample is.
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Central Tendency, Variability, and the Normal Curve
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Measures of
central tendency
and
variability
are the most
commonly used and important descriptive statistics.
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Central Tendency

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The one value that best typifies or is
the most representative
of
all the scores in a distribution. Three measures:
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Mean – the arithmetic average of all the scores
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Median – the score that is the midpoint of the distribution
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Mode – the most frequently occurring score
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Central Tendency, Variability, and the Normal Curve
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Measures of Variability
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Indicators of the dispersion, or spread, of the scores in a
distribution.
– Degree of similarity among the scores. – Used with
interval or ratio level data.
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Central Tendency, Variability, and the Normal Curve
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Range – the distance between the highest and lowest score in
a distribution

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Standard Deviation (S, or SD) – Most frequently used measure
of variability. – Provides information on the average algebraic
distance
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of each score from the mean. 3. Variance – the square of the
SD, or (SD2)
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