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?

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

Frequency Tables

• A frequency table shows how often each value of the variable occurs

Stress rating Frequency

10 14

9 15

8 26

7 31

6 13

5 18

4 16

3 12

2 3

1 1

0 2

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)

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.

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.

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%)

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

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

Multimodal Distributions

• In multimodal distributions, more than one mode exists (or approximately so)

• In a bimodal distribution, two modes exist

Rectangular or Uniform Distributions

• In a uniform distribution, all values are observed equally often

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)

Skewed Distributions

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

Skew

negative skew positive skew

reasons for skew?