Transcript Chapter 7
Chapter 7 Understanding Numbers in Measurements Types of Numbers • • • • 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 • • • • • 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.