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Quantitative Data Display: Part II

Quantitative Data Display: Part II. 8/30/11. Timeplots (AKA Time Series). A time series or timeplot plots a variable measured on interval or ratio scale against time.

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Quantitative Data Display: Part II

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  1. Quantitative Data Display: Part II 8/30/11

  2. Timeplots (AKA Time Series) • A time series or timeplot plots a variable measured on interval or ratio scale against time. • For true timeplots, the intervals in-between measurements is exactly the same. If the responses are not identically spaced in time, a lot of the data that we are interested in is lost. • Often, we can look at differencing the data and graphing that against time. • This will be readdressed during the regression analysis unit.

  3. Comparative Graphical analysis • If the graphical representation is clear, then we can sometimes make inferences about properties of two data sets. • Comparison of histograms and dotplots can be used to see if the median or mode is different. • Comparison of histograms and dotplots can be used to see if the spread of data or skewness is different. • Back-to-back stem and leaf plots (p. 56)

  4. Transforming data • With severely skewed data, it is sometimes a good idea to transform the data to see if there is a more useful representation. • Extreme positive skew: Log transformation • Moderate positive skew: Square-root transformation. • Moderate or extreme negative skew: Reverse the scale and perform the above transformations.

  5. Extreme positive skew • Consider the data set: • The histogram follows:

  6. Extreme positive skew • Notice how skewed the histogram is. • Does this give us much information? • We transform with the base 10 logarithm.

  7. Extreme positive skew • See how much less skew there is after? • The data is transformed now and we can undo the transformation by raising each of the data points to the power of ten.

  8. The transformed data • This is how the data looks after transformation

  9. Moderate Skew • The following data are skewed, but not as much as before: • The histogram follows

  10. Moderate Skew • The long tail to the right indicates a positive skew. • The square root transformation could help out.

  11. The new histogram The transformed data:

  12. Group Practice • In elbow partners, take a look at question 18 on p. 67 and question 39 on p. 71.

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