Transcript Statistical Reasoning in Everyday Life

STATISTICAL REASONING IN
EVERYDAY LIFE
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In descriptive, correlational, and experimental
research, statistics are tools that help us see and
interpret what the unaided eye might miss.
Apply simple statistical principles to everyday
reasoning.
DESCRIBING DATA
A meaningful description of data is important in
research. Misrepresentation may lead to
incorrect conclusions.
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MEASURES OF CENTRAL TENDENCY:
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A single score that represents a whole
set of scores
Mean: the average of a distribution
 Median: the middle score in a distribution;
half the scores are above it and half are
below it
 Mode: the most frequently occurring score(s)
in a distribution
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Measures of Variation
The need to know how similar or diverse scores
are.
 Range: the difference between the highest and
lowest scores in a distribution
 More useful standard for measuring how much
scores deviate from one another is the standard
deviation
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Standard Deviation: a computed measure of
how much scores vary around the mean score
 It better gauges whether scores are packed
together or dispersed and shows how much
individual
scores differ from the mean
SD= √[(SUM OF
DEVIATIONS)²/NUMBER
OF SCORES]
Think about how scores tend to be distributed
in nature:
 Large numbers of data often form a
symmetrical, bell-shaped distribution
known as a bell curve or normal curve
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Most scores fall near the mean (68% fall within one
standard deviation of it) and fewer and fewer near
the extremes
Percentiles express
the standing of one
score relative to all
other scores in a set
of data.
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SAT score in 85th
percentile. You
scored higher than
85% of other test takers.
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MAKING INFERENCES
When is an Observed Difference Reliable?
Representative samples are better than biased
samples.
Observations with less variation are more
reliable than ones with more variation ones.
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(an average is more reliable when it comes from scores
with low variation)
More cases are better than fewer cases.
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WHEN IS A DIFFERENCE SIGNIFICANT?
When sample averages are reliable and the
difference between them is relatively large, we say
the difference has statistical significance.
Alpha
is the accepted probability that the result of an
experiment can be attributed to chance rather than the
manipulation of the independent variable.
 Given that there is always the possibility that an
experiment’s outcome can happen by chance, psychologists
have set alpha at .05, which means than an experiment’s
results will be considered statistically significant if the
probability of the results happening by chance is less
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than 5%.