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STA291. Statistical Methods Lecture 9. About those boxplots …. Often used to compare samples (& 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

STA291

Statistical Methods

Lecture 9


About those boxplots

About those boxplots …

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

Example: Barry Bonds’ home runs


Boxplots or other graphs used for comparison outlier checking

Boxplots or other graphs used for comparison/outlier checking:

  • 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

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

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.


Outliers lots of useful stuff empirical or 68 95 99 7 rule

Outliers (& lots of useful stuff):Empirical, or 68-95-99.7 Rule


Empirical rule example

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

Looking back

  • Side-by-side boxplots

  • z-scores

  • Empirical, or 68-95-99.7 Rule


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