Reports and Visualizations

Gravetter & Wallnau, Chapter 2; Young, Chapter 2

Copyright 1997-8 by Forrest W. Young.

P30Home Schedule Labs Homework Project Lectures

Frequency Distribution Graphs (Visualizations)


Histograms
A histogram is used to portray the (grouped) frequency distribution of a variable at the interval or ratio level of measurement. It consists of vertical bars drawn above scores (or score intevals) so that

  1. The height of the bar corresponds to the frequency
  2. The width of the bar extends to the real limits of the score (interval)

In ViSta, these intervals are called "BINS".


Note that the histogram shown here (which is produced by ViSta) does not have exactly the same intervals as the table, resulting in different frequencies.

This is because the histogram follows somewhat different rules for constructing intervals than those given above (which are used for the table).

Since the rules are somewhat arbitrary, neither the plot nor the table are "wrong". They're just different. However, for homework problems from the book we should follow the rules given in the book.

Also, recall the fact that different intervals (bins) produce histograms that can look very different. Some may be misleading, but we don't really know which.

Here is ViSta's help information for Histograms:

Frequency Distribution Graphs
A frequency distribution graph portrays the same thing as a histogram, but uses a line connecting dots rather than bars. It is drawn by locating dots and connecting them so that

  1. The dot is centered above the score
  2. The height of the dot corresponds to the frequency.
  3. A continuous line is drawn connecting the dots.
  4. Gravetter and Wallnau suggest that the line be drawn down to the x-axis (at zero) at each end of the range of scores. This is not done here.
  5. Example:

    This frequency plot shows the same data as used for the histogram (and has the same intervals).

ViSta does not yet do frequency plots.

Dotplots
A dotplot uses dots to show where the scores in a distribution are. The dots are plotted against their actual data values on a vertical (sometimes horizontal) scale. Sometimes the dots are "jittered" by adding a small random value to the horizontal axis so that the dots don't overlap.

Boxplots
A boxplot uses a box and lines to create a schematic of the frequency distribution. The box shows the main "clump" of scores, the dots show where the actual data are, and the lines show the scores at the middle and edges of the distributions. (A variant of the box plot is known as the box-and-whisker plot. It has a vertical line connecting the upper and lower horizontal lines.)

  1. The box covers the middle half of the data (the upper and lower edges of the box lie at the upper and lower quarters (called upper and lower quartiles).
  2. The line inside the box is at the middle score (called the median).
  3. The lines outside the box show the upper and lower 10% (called upper and lower deciles).

This boxplot shows the same data as used for the histogram and frequency plot.

Diamond Plots
A Diamond Plot is similar to a boxplot. It uses a diamond, dots and a line to create a schematic of the frequency distribution. The diamond shows the main "clump" of scores, the dots show where the actual data are, and the line show the middle of the distribution is.

  1. The diamond covers the data between plus and minus one standard deviation.
  2. The line inside the box is at the average score (called the mean).

This boxplot shows the same data as used for the histogram and frequency plot.

Here is ViSta's help information for Box, Diamond and Dot plots:

Quantile Plots
A Quantile Plot (Q-Plot) represents a variable's distribution by plotting each observed value against the fraction of the data that is smaller than the observed value. The fractions are called quantiles. The jagged line represents the variable's distribution.

Here is ViSta's help information for Quantile plots:

Normal Probability Plots
A Normal Probability Plot (NP-Plot) represents a variable's distribution by plotting each observed value against the Z-score that would be obtained for the value under the assumption of normality. This is done by using the Q-Plot's "fraction of data" as a probability under the assumption of normality to obtain a normally-distributed Z-score. The jagged line represents the variable's distribution, and the straight line represents a normal distribution.

Here is ViSta's help information for Normal Probability plots:

Quantile-Quantile Plots
A Quantile-Quantile Plot (QQ-Plot) represents the relationship between two variables' distributions. The jagged line represents the relationship between the two variables' distributions. The line is constructed by plotting the quantiles of one variable versus those of the other. The quantiles of a variable are the fraction of the data that is smaller than each observed value. The two variables do not have to have the same number of observations. If they dont, interpolation is used.

Here is ViSta's help information for Quantile-Quantile plots:

Back