STA291

1. STA291 Statistical Methods Lecture 9

2. About those boxplots … Often used to compare samples (& make inferences about populations) Example: Barry Bonds’ home runs

3. 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

4. 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.

5. 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.

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

7. 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 ___________%?

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