Effective Visual Techniques for Summarizing Data

1. Today’s Questions • Once we have collected a large number of measurements, how can we summarize or describe those measurements most effectively by using visual techniques?

2. First Example How stressed have you been in the last 2 ½ weeks? Scale: 0 (not at all) to 10 (as stressed as possible) 4 7 7 7 8 8 7 8 9 4 7 3 6 9 10 5 7 10 6 8 7 8 7 8 7 4 5 10 10 0 9 8 3 7 9 7 9 5 8 5 0 4 6 6 7 5 3 2 8 5 10 9 10 6 4 8 8 8 4 8 7 3 7 8 8 8 7 9 7 5 6 3 4 8 7 5 7 3 3 6 5 7 5 7 8 8 7 10 5 4 3 7 6 3 9 7 8 5 7 9 9 3 1 8 6 6 4 8 5 10 4 8 10 5 5 4 9 4 7 7 7 6 6 4 4 4 9 7 10 4 7 5 10 7 9 2 7 5 9 10 3 7 2 5 9 8 10 10 6 8 3 from Aron & Aron’s text, Statistics for Psychology

3. Frequency Tables • A frequency table shows how often each value of the variable occurs

4. Frequency Polygon • A visual representation of information contained in a frequency table • Align all possible values on the bottom of the graph (the x-axis) • On the vertical line (the y-axis), place a point denoting the frequency of scores for each value • Connect the lines • (Typically add an extra value above and below the actual range of values)

5. Histograms • Another way of visually representing information contained in a frequency table • Histograms are kind of like bar charts; bars are used instead of connected points • The bars typically cover “intervals” of values. The first bar here covers scores > 0 and < 1.

6. Pie Charts and Nominal Data • Pie charts are commonly used to represent the frequency of scores for nominal data • Here, frequency of referents in a letter written by a subject in a psychological study. • 70% of the pronouns are in reference to the writer; 10% are in reference to the person being written to.

7. Barcharts and Nominal Data • Barcharts are sometimes used to represent the frequency of scores for nominal data • Here, frequency is expressed as a percentage of the total number of males and females • (78% and 68%)

8. Shapes of Distributions • These representational aides all describe frequency distributions: the way score frequencies are distributed with respect to the values of the variable • Distributions can take on a number of shapes or forms

9. Unimodal Distributions • The mode of a distribution refers to the most frequently occurring score • In a unimodal distribution, one score occurs much more frequently than others

10. Multimodal Distributions • In multimodal distributions, more than one mode exists (or approximately so) • In a bimodal distribution, two modes exist

11. Rectangular or Uniform Distributions • In a uniform distribution, all values are observed equally often

12. Symmetrical and Skewed Distributions • A symmetrical distribution is balanced: if we cut it in half, the two sides would be mirror images of one another • normal distribution: a particular kind of distribution that resembles a bell (bell-shaped distribution)

13. Skewed Distributions • A skewed distribution is unbalanced; there may be a cluster of scores piling on one end of the scale

14. Skew negative skew positive skew reasons for skew?