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So What Do We Know?

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. The Three Rules of Data Analysis.

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So What Do We Know?

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  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).

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