Practice Problems (includes Frequency Distributions from the previous section) (Answers)
Homework

I. Background

A two-dimensional graph has two axes called the X-axis or abscissa and the Y-axis or ordinate. Example:

1. Conventions or Rules
1. The intersection of X and Y is zero (which is not typically written on the graph).
2. While the abscissa portrays the score values or categories, the ordinate depicts quantities like: frequency, proportion, percent, cumulative frequency, cumulative proportion, and cumulative percent.
3. The axes go from low to high. This is relevant to rank and metric data.
4. Both axes of the graph are given verbal labels and the total graph is given a clear concise title.
5. The 3/4 high rule is typically used when constructing a graph. That is, the ratio of the ordinate to the abscissa should be about 3:4. Actually, anything in the range of 2:3 to 3:5 is fine.
6. Frequency polygons get both ends tied down to the axis, while cumulative frequency polygons get the lower end tied down.
7. Each graph gets its own page. Center the whole graph (titles, labels, & all) and fill the page with it (the example below gives a good idea of the layout of the page).

2. General Steps in Constructing a Graph (using graph paper)
1. Determine the number of boxes in both the horozontal and vertical dimensions of the graph paper.
2. Determine the Range of your data, since it will determine the length of the X-axis. If it is a bar graph (discussed in more detail below), you will need to figure out how many bars you need, how thick you want them, and how much space you want in between the bars.
3. Multiply the determined length of the X-axis by 3/4 to determine the approximate length of the Y axis. Now divide the length of each axis by the number of boxes available for it on the page to determine the number of units each box of graph paper represents. For example, if an axis needs to be 90 units and there are only 30 boxes available, then each box must represent three units for that axis.
4. Center the whole graph (titles, labels, & all) and fill the page with it. Centering means that the top and bottom margins of the page should be equal in size (and should be at least an inch), as should the left and right margins. In order to do this, you will need to figure in some boxes for the axis labels and graph title when doing your centering. Here is an example on graph paper:

II. Types of Graphs

There are a number of types of graphic representations of data. For now, however, you should be familiar with three of the more basic types.

1. Bar Graphs
Are used with qualitative (or non-metric) data.

Example 1 Nominal Data: Frequency of Therapy Seeking in Folks of Different Occupations (note this graph is in presentation style) [Spreadsheet1]

Example 2 - Ordinal Data: Grades on an Exam (note this graph is in journal publication style) [Spreadsheet2]

Example 3 - Ordinal Data: Percent of Married Women Having Orgasm During Intercourse with Their Husbands [Spreadsheet3]

2. Histograms
Used with metric data that is typically in a grouped format. Rectangles are used for each group, with the width spanning from the lower to upper exact limits of the interval (midpoints are labeled). The height of the rectangle is determined by the measure used for the Y-axis. Example:

Expected Scores for PSY300 on Exam 1 [Spreadsheet]

1. Frequency Polygons
Also used with metric data. Are especially good at showing the form or shape of the distribution. It is often the method of choice when two or more distributions are to be compared.

Example 1 - Expected Scores for PSY300 on Exam 1 [Spreadsheet]

Note that with this type of graph, we usually "tie it down". In other words, we include an interval below the lowest as well as above the highest. Since these intervals have zero values, the polygon is thus anchored to the x axis. Note that when using cumulative frequency, proportion, or percent, you would only tie down the lower end of the polygon.

2. Overall Example - Two ways of presenting the same data. [Spreadsheet]

Thus, graphs can be constructed in a manner that gives a false impression. The moral of the story is that the statistical test (i.e., inferential statistics) determines which differences are worth paying attention to and not the graph.

3. Example Graph for a Factorial Design [Spreadsheet]
This graph is from the data in the table we used when discussing the factorial design (simple 2x2 between groups) used by Weil et al., 1968. Note that this graph requires a key which helps explain the groups used.

III. Some Common Forms of Distributions
1. Normal, Bell-Shaped, or Gaussian Curve

• Is theoretical (in reality it would be more jagged).
• Is bilaterally symetrical (a vertical mirror image).
• Tails are asymptotic to the x-axis (they come closer & closer, but will never touch).

1. + Skewed

Actual data from www.visualizingeconomics.com
2. - Skewed

3. Rectangular

4. Bimodal

• Modes can be unequal (so can have minor and major modes).
• Can also have a trimodal distribution (one with 3 modes).

5. Ojive (S-shaped)

6. Backward J