So What Do We Know?

1. So What Do We Know? • Variables can be classified as qualitative/categorical or quantitative. • The context of the data we work with is very important. Always think about the “Five W’s”—Who, What, When, Where, Why (and How)—when examining a set of data.

2. The Three Rules of Data Analysis • The three rules of data analysis won’t be difficult to remember: • Make a picture—things may be revealed that are not obvious in the raw data. These will be things to think about. • Make a picture—important features of and patterns in the data will show up. • Make a picture—the best way to tell others about your data is with a well-chosen picture.

3. Qualitative Data :: Making Piles • We can “pile” the data by counting the number of data values in each category of interest. • We can organize these counts into a frequency table, which records the totals & category names. • A relative frequency table is similar, but gives the percentages (instead of counts) for each category.

4. What Do Frequency Tables Tell Us? • Frequency tables and relative frequency tables describe the distribution of a categorical variable because they name the possible categories and tell how frequently each occurs. • Graphs … Pie Charts & Bar Graphs (software)

5. A contingency table allows us to look at two qualitative variables together. • Note the totals in the margins of the table. Each set of totals gives us the marginal distribution of the respective variable.

6. So What Do We Know? • Qualitative variables can be summarized in frequency or relative frequency tables. • Categorical variables can be displayed with bar graphs and/or pie charts. • A contingency table summarizes two variables at a time. From a contingency table we can find the marginal distribution for each variable or the conditional distribution for one variable conditioned on the other variable.

7. Displaying Quantitative Data HISTOGRAMS • First, slice up the entire span of values covered by the quantitative variable into equal-width piles called classes/bins. “selection = art form” • The bins and the counts in each bin give the distribution of the quantitative variable. • One graphical display of the distribution of a quantitative variable is called a histogram, which plots the bin counts as the heights of bars (like a bar graph). • A relative frequency histogram displays the percentage of cases in each bin instead of the count.

8. Stem-and-leaf displays show the distribution of a quantitative variable, like histograms do, while preserving the individual values. • Stem-and-leaf displays contain all the information found in a histogram.

9. First, cut each data value into leading digits (“stems”) and trailing digits (“leaves”). • Use the stems to label the bins. • Use only one digit for each leaf if necessary either round or truncate the data values.

10. A dotplot is a simple display. It just places a dot for each case in the data.

11. When describing a distribution, make sure to always tell about L.O.S.S. !!! Location/Center/Typical Value Outliers Spread/Dispersion Shape/Distribution

12. SHAPE • Symmetric • Skewed • Uniform or rectangular

13. Symmetric

14. SkewedRight-Tailed … Left-Tailed

15. Uniform

16. So What Do We Know? • Quantitative variables can be displayed using histograms, dotplots, and/or stem-and-leafdisplays. These displays help us to see the distributions of the variables. • Consider L.O.S.S. when looking at these displays! • Distributions can be classified as symmetric or skewed (look at how the tails behave with respect to the rest of the distribution).