STA291

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# STA291 - PowerPoint PPT Presentation

STA291. Statistical Methods Lecture 9. About those boxplots …. Often used to compare samples (&amp; make inferences about populations) Example: Barry Bonds’ home runs. Boxplots or other graphs used for comparison/outlier checking:. The good: Quick Simple

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### STA291

Statistical Methods

Lecture 9

Often used to compare samples (& make inferences about populations)

Example: Barry Bonds’ home runs

• The good:
• Quick
• Simple
• Don’t depend on distribution of sample
• The not-so-good:
• Non-numeric
• Depend on samples being compared having same units
An alternative: z-scores

Often used to standardize individual values, either within samples/populations or between them, the z-score, or standardized score:

is the number of standard deviations an observation is away from its mean.

Assumptions?

Since both the population or sample versions of the z-score use the mean and standard deviation, we have the same concern when calculating it that we did when using the mean to describe the center of a distribution or the standard deviation to describe its variability.

While it can be and sometimes is used in describing/comparing observations in the absence of knowledge about the distribution, more properly done so having determined that we have a “roughly symmetric and mound-shaped” distribution.

Empirical Rule Example

Distribution of SAT score is scaled to be

approximately bell-shaped with mean 500

and standard deviation 100

About 68% of the scores are between __ ?

About 95% are between ____ ?

If you have a score above 700, you are in the top ___________%?

Looking back
• Side-by-side boxplots
• z-scores
• Empirical, or 68-95-99.7 Rule