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Some Basic Concepts
Schaum's Outline of Elements of Statistics
I: Descriptive Statistics & Probability
Chapter 1. Functions
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Function: If two variables are related so that
for every permissible specific value x of X
there is associated one and only one specific
value y of Y, then Y is a function of X.
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domain of the function is the set of x values that
X can assume
range is the set of y values associated with the x
values
the rule of association is the function itself
Chapter 1. Functions in statistics
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Independent/dependent variables and cause/effect
In the mathematical function y = f(x), y is said to
be the dependent variable and x the independent
variable because y depends on x
In the research context the dependent variable is a
measurement variable that has values that to some
degree depend on the values of a measurement
variable associated with the cause
Chapter 2. Measurement scales
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Nominal: unique mutually-exclusive categories,
meaning that a measured item is equal to some
category or not – e.g., fish being shark, flounder, or
trout.
Ordinal: nominal plus ordered – e.g., eggs are small,
medium, or large.
Interval: ordinal plus uniform reference units – e.g.,
degrees Celsius.
Ratio: interval plus absolute zero making ratios
meaningful – e.g., degrees Kelvin where 300 K is
twice as hot as 150 K.
Chapter 3. Probabilities for sampling:
with and without replacement
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The probability of drawing an ace from a
deck of 52 cards is P(ace) = 4/52, and if
the sampling is done with replacement,
the probability of drawing an ace on a
second try is also 4/52.
However, if the sampling is without
replacement, the probability of drawing
the second ace is P(second ace) = 3/51
Chapter 4 and 5.
Frequency distributions and
graphing frequency distributions
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Chapter 6
Measures of central tendency
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Mean or average
Median = value that divides an array of
ordered values into two equal parts
Mode = the measurement that occurs
most frequently
Chapter 7
Measures of dispersion
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Variance and Standard Deviation
Normal probability density function (bell
shaped curve): 68% of the values lie
within one sigma from the mean, and
95% within two sigma from the mean
Chapter 8
Probability: four interpretations
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Classical: deals with idealizes situations, like the roll of a
perfect die on a flawless surface having equally likely
(probabilities of 1/6) outcomes
Relative frequency: data from experiments are analyzed to
obtain the relative frequency of events
Set theory: the basis for the mathematical theory of
probability
Subjective: in contrast to the objective determination of
probabilities above, here the probabilities are determined
using “personal judgment” or “educated guesses”
Chapter 9
Calculating rules and counting rules
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Special addition rule - A and B are mutually
exclusive
General addition rule - A and B are not
mutually exclusive
Conditional probability
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General multiplication rule - A and B not independent
Special multiplication rule - A and B independent
Bayes’ Theorem (also known as Bayes’ Law)
Chapter 10
Random variables, probability distributions,
cumulative distribution functions
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Random variable – function having the sample
space as its domain, and an association rule that
assigns a real number to each sample point in the
sample space, and range is the sample space of
numbers defined by the association rule
Discrete random variable – sample space is finite or
countably infinite
Continuous random variable –sample space is
infinite or not countable
Chapter 10 (cont)
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Understand discrete and continuous probability
distributions
Expected value of discrete probability
distribution
Variance of discrete probability distribution
Expected value of continuous probability
distribution
Variance of continuous probability distribution