·
A Problem: Many statistics instructors prefer to concentrate
on statistics—descriptive statistics, data analysis, and inferential
statistics—and, thereby, limit coverage of probability. However, traditional methods
of presenting statistics require significant coverage of probability.
·
A Solution: Although,
strictly speaking, probability provides the mathematical foundation for
inferential statistics, it is possible to almost completely eliminate
probability in an introductory statistics course by taking a more intuitive and
conceptual approach.
·
The Approach: Following is a table comparing several aspects of a
formal probability approach with a more intuitive and conceptual approach, an
approach that permits a brief treatment of probability (one or two lectures) as
prerequisite to inferential statistics.
|
Formal
probability approach |
Conceptual
probability approach |
|
Probability |
Percentage |
|
Probability
distribution |
Percentage
distribution |
|
Random
variable |
Variable |
|
Probability
density |
Histogram |
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Example: Sampling Distribution of the Sample Mean.
Formal Probability Approach: The probability distribution of the random variable Xbar is
approximately a normal distribution.
Conceptual Probability Approach: A histogram of the possible values of the variable xbar (i.e., of
the possible sample means) is roughly bell-shaped.
·
Example: Confidence Intervals for a Population Mean.
Formal Probability Approach: The probability is 0.95 that the population mean lies in the
random interval from Xbar-E to Xbar+E, where E denotes the margin of error for
a 95% confidence interval.
Conceptual Probability Approach: 95% of all possible samples (of the given sample size) have the property that the interval from xbar-E to xbar+E contains the population mean.