Essentials of Statistics For The Behavioral Sciences ch. 3

Types of chartjunk

1. Moire vibrations 2. grid 3. ducks

How to create a bar graph:

1. The x-axis of a bar graph indicates discrete levels of a nominal variable or an ordinal variable. 2. The y-axis of a bar graph may represent counts or percentages. But the y-axis of a bar graph can also indicate many other scale variables, such as average running speeds, scores on a memory task, or reaction times. 3. For every level of the independent variable, draw a bar with the height of that level's value on the dependent variable.

Deciding which type of variables you are working with before choosing graph type.

1. examine variables 2. Decide which is the independent variable and which is the dependent variable. 3. identify which type of variable—nominal, ordinal, or scale (interval/ratio)—each is. Most of the time, the independent variable belongs on the horizontal x-axis and the dependent variable goes on the vertical y-axis.

grid

A background pattern, almost like graph paper, on which the data representations, such as bars, are superimposed. Final versions of graphs use only very light grids if necessary.

chartjunk

Any unnecessary information or feature in a graph that detracts from a viewer's ability to understand the data.

moire vibrations

Any visual patterns that create a distracting impression of vibration and movement.

Mastering the concept 3-5:

Avoid chartjunk - any unnecessary aspect of a graph that detracts from its clarity.

Mastering the concept 3-3:

Bar graphs depict data for two or more categories. They tell a data story more precisely than do either pictorial graphs or pie charts.

example of line graph

Calories and hours are both scale variables, and the question is about prediction rather than relation. In this case, we would calculate and graph a line of best fit.

ducks

Features of data that have been dressed up to be something other than merely data. Ducks are data in costume.

linear relation

This relation between variables means that the relation between variables is best described by a straight line.

Graphs can....

...reveal or obscure information. To understand what a graph actually conveys, we must examine it and ask critical questions about it.

How to select appropriate graph

1. If there is one scale variable (with frequencies), use a histogram or a frequency polygon (Chapter 2). 2. If there is one scale independent variable and one scale dependent variable, use a scatterplot or a line graph. (Figure 3-9 on page 55 provides an example of how to use more than one line on a time plot.) 3. If there is one nominal or ordinal independent variable and one scale dependent variable, use a bar graph. 4. Consider using a Pareto chart if the independent variable has many levels. 5. If there are two or more nominal or ordinal independent variables and one scale dependent variable, use a bar graph.

How to create scatterplot with a line of best fit:

1. Label the x-axis with the name of the independent variable and its possible values, starting with 0 if practical. 2. Label the y-axis with the name of the dependent variable and its possible values, starting with 0 if practical. 3. Make a mark above each study participant's score on the x-axis and next to his or her score on the y-axis. 4. Visually estimate and sketch the line of best fit through the points on the scatterplot. 5. Consider maximizing the data-ink ratio by converting to a range frame: Erase the axes below the minimum score and above the maximum score.

Steps to create a time series plot:

1. Label the x-axis with the name of the independent variable and its possible values. The independent variable should be an increment of time (e.g., hour, month, year). 2. Label the y-axis with the name of the dependent variable and its possible values, starting with 0 if practical. 3. Make a mark above each value on the x-axis at the value for that time on the y-axis. 4. Connect the dots. As you did with the scatterplot, consider maximizing the data-ink ratio by converting to a range-frame: Erase the y-axis below the minimum y value and above the maximum y value.

Techniques for misleading with graphs

1. The biased scale lie. 2. The sneaky sample lie. 3. The interpolation lie. Interpolation involves assuming that some value between the data points lies on a straight line between those data points. Make sure that a reasonable number of in-between data points have been reported. 4. The extrapolation lie. This lie assumes that values beyond the data points will continue indefinitely. 5. The inaccurate values lie. This lie tells the truth in one part of the data but visually distorts it in another place.

How to create a scatterplot

1. organize the data by participant; each participant will have two scores, one on each scale variable. 2. label the horizontal x-axis sith the name of the independent variable and its possible values, starting with 0 if practical. 3. label the vertical y-axis with the name of the dependent variable and its possible values, starting with 0 if practical. 4. make a mark on the graph above each study participant's score on the x-axis and next to his or her score on the y-axis. 5. to convert to a range-frame, simply erase the axes below the minimum score and above the maximum score.

3 meanings of scatterplots

1. there may be no relation at all - the scatterplot looks like a jumble of random dots. This is important if we thought there was a systematic pattern. 2. There is a linear relation between variables, and when positive, it flows upward and to right. When negative, flows downward and to right.

pie chart

A graph in the shape of a circle, with a slice for every level (category) of the independent variable. The size of each slice represents the proportion (or percentage) of each category. A pie chart's slices should always add up to 100% (or 1.00, if using proportions).

scatterplot

A graph that depicts the relation between two scale variables. The values of each variable are marked along the two axes, and a mark is made to indicate the intersection of the two scores for each participant. The mark is above the participant's score on the x-axis and across from the score on the y-axis.

time series plot

A graph that plots a scale variable on the y-axis as it changes over an increment of time (for example, hour, day, century) labeled on the x-axis.

Example of scatterplot

A scatterplot is the best graph choice to depict the relation between two scale variables such as depression and stress.

range-frame

A scatterplot or related graph that indicates the range of the data on each axis to the minimum and maximum scores. Eliminating the ends of the axes frames the same data within its minimum and maximum values, and increases the data-to-ink ratio.

example of time series plot

A time plot, or time series plot, is the best graph choice to depict the change in a scale variable, such as the rise or decline in the number of facilities over time.

pareto chart

A type of bar graph in which the categories along the x-axis are ordered from highest bar on the left to lowest bar on the right.

bar graph

A visual depiction of data in which the independent variable is nominal or ordinal and the dependent variable is scale. The height of each bar typically represents the average value of the dependent variable for each category.

pictorial graph

A visual depiction of data typically used for an independent variable with very few levels (categories) and a scale dependent variable. Each level uses a picture or symbol to represent its value on the scale dependent variable.

line of best fit

Allows us to make predictions about a person's value on the y variable from his or her value on the x variable.

What bar graphs, pictorial graphs, and pie charts do.

Bar graphs, pictorial graphs, and pie charts depict summary values (such as means or percentages) on a scale variable for various levels of a nominal or ordinal variable. We should typically avoid using pictorial graphs and pie charts because the data can almost always be presented more clearly in a table or in a bar graph.

helpful checklist of questions to ask when you encounter a graph or when you're creating a graph

Does the graph have a clear, specific title? Are both axes labeled with the names of the variables? Do all labels read left to right—even the one on the y-axis? Are all terms on the graph the same terms that are used in the text that the graph is to accompany? Have all unnecessary abbreviations been eliminated? Are the units of measurement (e.g., minutes, percentages) included in the labels? Do the values on the axes either go down to 0 or have cut marks (double slashes) to indicate that they do not go down to 0? Are colors used in a simple, clear way—ideally, shades of gray instead of other colors? Has all chartjunk been eliminated?

Mastering the concept 3-1:

Graphs can be misleading. As critical thinkers, we want to know whether a sample represents a population, how the variables were actually measured, and whether a graph tells an accurate data story.

Concepts to remember

Graphs should be used when they add information to written text or help to clarify difficult material. To decide what kind of graph to use, determine whether the independent variable and the dependent variable are nominal, ordinal, or scale variables. A brief checklist will help you create an understandable graph. Label graphs precisely and avoid chartjunk. The future of graphs is now! Online interactive graphs, computerized mapping, and multivariable graphs are becoming increasingly common.

Example of bar graph

In this case, there is a nominal variable (region of the United States) and a scale variable (years of education). The best choice would be a bar graph, with one bar depicting the mean years of education for each region. In a Pareto chart, the bars would be arranged from highest to lowest, allowing for easier comparisons.

example of frequency histogram or polygon

Number of siblings reported by 100 people. What size family is most common?

Mastering the concept 3-2:

Scatterplots and line graphs are used to depict relations between two scale variables.

defaults

The options that the software designer has preselected; these are the built-in decisions that the software will implement if you do not instruct it otherwise. You can't assume defaults represent APA guidelines. You can usually point cursor at a part of graph and click to view available options.

What is the purpose of a graph?

The purpose of a graph is to reveal and clarify relations between variables.

scatterplot numbers

The values do not have to go down to zero. The pattern in the data might be clearer by adjusting the range, and if it's not practical for the scores to go down to zero, be sure to indicate this with cut marks.

pie chart difficulties

They make it more difficult to make comparisons.

line graph

This graph is used to illustrate the relation between two scale variables. One type is based on scatterplot and we can construct a line of best fit that represents the predicted y score for each x value. A second type allows us to visualize changes in the values on the y-axis over time.

nonlinear relation

This relation between variables is best described by a line that breaks or curves in some way...it is not straight.

Distorting data with pictures

Tripling the height of a picture is often coupled with tripling the width- which is multiplying by 3 twice. So instead of being 3 times as big, the pictures is 9 times as big.