Frequency Distribution Graphs (Visualizations)
Numeric and Ordinal Variables

 

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".

Example: Data and frequencies for example given by Gravetter & Wallnau on page 39.

Scores on a 10-point quiz.	Frequency Table

Here is one of the histograms produced by ViSta of these data. This histogram is based on the frequency table given above.

Histogram

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

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.

The BinWidth button lets you change the intervals dynamically to see what other histograms look like.

Here is ViSta's help information for Histograms:

Hollow Histograms

A Hollow Histogram shows the same information as a histogram or a frequency polygon. It is simply the histogram drawn without including the sides of the bars.

Here is the hollow histogram for the data given above:

Hollow Histogram

ViSta 5.2 can do hollow histograms. They are produced by clicking on the Plots button at the bottom of the window.

Frequency Polygons

A frequency distribution graph pictures the (grouped) frequency distribution of a variable at the interval or ratio level of measurement, using 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 (the center of the bin)
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, as it can be very misleading.
5. Example: The same data are used here as for the histogram.
   

   Frequency Polygon

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

ViSta 5.2 can do frequency plots. They are produced by clicking on the Plots button at the bottom of the window.

Dotplots

A dotplot uses dots to show where the scores in a distribution are. This does not portray frequencies, but the actual observations, although by observing the density of thge dots one can see the frequency distribution. 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. A side-by-side dot plot shows two or more dotplots side-by-side.

Side-by-side Dot Plot Psych 30 GPA by Gender

This side-by-side dot plot uses data gathered in this class. It shows the GPA of the students in the class for both previous years, classified by Gender. We can see that the Males tend to have a higher GPA than the Females.

Boxplots

A boxplot (also called a box-and-whisker plot) pictures the (grouped) frequency distribution of a variable at the interval or ratio level of measurement. It 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 horizontal lines show the scores at the middle, the upper and lower quarters of the distributions, and the upper and lower tenths of the distribution. Shown here is a box-and-whisker plot, since it has a vertical line (whisker) connecting the upper and lower horizontal lines. This is also a side-by-side box-and-whisker plot, since it shows two or more boxplots side-by-side.

Side-by-Side Box and Dot Plot Psych 30 GPA by Gender

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).
4. The width of the box is proportional to the number of scores in the distribution. There are more females than males, so the female box is wider.

This boxplot shows the Psych 30 GPA by Gender data that we used for the dot plot.

Diamond Plots

A Diamond Plot is similar to a boxplot. It pictures the (grouped) frequency distribution of a variable at the interval or ratio level of measurement. 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.

Side-by-side Diamond and Dot Plot Psych 30 GPA by Gender

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) pictures the (grouped) frequency distribution of a variable at the interval or ratio level of measurement. It 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.

Quantile Plot Psych 30 GPA for Females

Here is ViSta's help information for Quantile plots:

Normal Probability Plots

A Normal Probability Plot (NP-Plot) pictures the (grouped) frequency distribution of a variable at the interval or ratio level of measurement. It 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.

Normal Probability Plot Psych 30 GPA for Females

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

Quantile-Quantile Plots

A Quantile-Quantile Plot (QQ-Plot) represents the relationship between the distributions of two variables, each at the interval or ratio level of measurement. 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.

Quantile-Quantile Plot Psych 30 GPAMales and Females

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

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