Chapter 7

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Transcript Chapter 7

Chapter 7
Understanding Numbers
in Measurements
Types of Numbers
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Nominal numbers
Ordinal numbers
Interval (scalar) numbers
Ratio numbers
Significant Digits and Precision
• Significant digits: The number of digits in a
measurement or calculation that have
meaning.
– For example, the number 75.25 has four
significant digits.
• The greatest danger in PE and athletic
applications is implying more precision
(more significant digits) than we actually
have.
Normal vs. Non-Normal
(Non-Standard) Distributions
• Normal distribution:
– A set of data in which the mean, median, and
mode are identical and are right in the middle
of the distribution.
• Non-normal distributions:
– May occur when the population being sampled
is not usual (for example, a group of athletes
that includes gymnasts and basketball
players).
Types of Non-Normal Distributions
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Leptokurtic distribution
Platykurtic distribution
Bimodal distribution
Skewed negative distribution
Skewed positive distribution
A Normal Curve
Examples of Distribution Curves
Your Viewpoint
• Think about the quote from George
Carlin, shown on p. 141:
“Think about how dumb the average
person is. Now just think, half the people
are stupider than that.”
• What do you think of references to “the
average person” (i.e., in the media)?
Do you consider yourself “average”?
Measures of Dispersion
• Range
• Standard deviation
Range
• Shows us how widely scores are dispersed.
– From the point that is farthest to the right in a
curve (highest score) to the point that is
farthest to the left (lowest score).
• Tells us how far apart the extreme scores
are, and how variable.
• Mathematical range:
– Range = (high–low) + 1
Standard Deviation
• Uses:
– To establish the value of a unit.
– To make predictions about the population
from which the sample was drawn.
• Standard error of the estimate:
– Estimated standard deviation of the error in
a prediction.
Normal Curve
Showing the Standard Deviations
Standard Scores
• When a raw score has been
transformed by use of the standard
deviation; standardization.
• Types:
– Percentile rank
– Percentile
– Z-score
– Z-table
Percentile Ranks and
Percentiles
• Percentile rank:
– The percentage of scores that are
lower than or equal to a specified
score.
• Percentile:
– A particular score, on an ordered list
of scores, at or below which a given
percent of other scores fall.
Z-Scores
• A standard score that allows us to compare
any score to the mean score and then express
it as a fraction of the standard deviation.
• Finding z-scores:
– When a high score is better (i.e., batting average):
Zhigh score better = (score – mean)/SD
– When a low score is better (i.e., golf score):
Zlow score better = (mean – score)/SD
Normal Distribution
Showing Z-Scores
Z-Tables
• A table used to show percentile ranks
or probabilities for a certain z-score for
normally distributed data.
• Z-tables can be found online:
www.stat.lsu.edu/EXSTWeb/statlab/Tables/
TABLES98-Z.html
Checking a
Measurement Technique
• Think about the problem to get a rough
estimate of what the answer should be.
• If the final measurement is very different
from the rough estimate, review
calculations carefully.
• Remember that sometimes the same
units can have different values.