A histogram is a type of graph very similar to a bar chart, that easily shows
us the shape of the distribution, such as the skewness or the bimodality.
Histograms can show us if the data are bimodal - with two major peaks. We see
skewness, such as a positive skew, kurtosis - how peaked or flat the
distribution is - which also shows the spread or variability in scores and
unusual extreme scores or data entry errors called outliers. Histograms show
us the shape of the distribution. When all of the scores are stacked on one end
of the distribution, it is said to be skewed, and the histogram shows us the
skewness. When the scores have two major, peaks they are bimodal, and the histogram
shows us the bimodality. If we have outliers in the data, these will show up
on the histogram as will the shape of the kurtosis, or the spread of the data.
Unlike a bar chart, the adjacent bars in a histogram touch. This indicates that
the data are connected to each other. We could not rearrange the numbers 1-5
to run 1, 4, 2, 5, 4. . . they must be in numerical order, and
each bar is therefore connected to the next. Like the bar graph, the vertical
bars are centered over the scores on the x-axis. The width of the bar corresponds
to the real upper and lower limits of the interval. So for instance, a bar for
the 4 actually includes scores from 3.5 to 4.49
because of rounding. The edges of the bar will actually be at those points.
Now histograms are used with interval and ratio level data what we will call scale
data in SPSS. They are particularly useful when the
scale data are in ranges, or banded, such as age 25 to 30, 31 to 45, 46 to 50, etc. If
you have a scale however, it is always a good idea to not band your data if you
don't have to, because this causes a loss of information. A frequency polygon, also
known as a line graph, is similar to a histogram except that instead of bars, a
data point is placed over each x-axis score and then the dots are connected by
a single line. Frequency polygons are used for large numbers of interval or
ratio i.e. scale level scores. Typically the x-axis begins one unit lower than
the lowest appearing score, and frequencies are still plotted on the
y-axis. As the frequency of scores goes up you see increases in the line of the
frequency polygon. Frequency polygons are often used to show change over time Such
as in this example, gun murders in Canada between 1961 and 1991. If the area below
the graph is filled in with color or shading, it is an area graph. So returning
to our clickers ".sav" dataset, we will use a histogram to show us the shape of the
data, and to identify potential outliers. This will help us identify what is wrong
and if anything can be done to fix it. You may recall that when we created a
bar chart with error bars for each of the three rounds of group interaction, we
noticed that the error bar for the mean around round one was greater than for
the other rounds. I suspect we may have some outliers that are causing that.
Let's use a histogram to get a closer look at our data. In SPSS we're using the
clickers ".sav" dataset. Let's go to graphs > charts builder. The information from
a previous analysis is still in so we'll click reset to clear that out, and now
we're ready to move to the gallery. Now here in the gallery
start by choosing "histogram." You notice there are four options, and we're gonna
be using the simple histogram. So drag simple histogram into the canvas, and if
you want to see not the variable labels with the variable names, you can
right-click or control-click on mac to display variable names. For this example,
we're going to drag the participation from round one into the x-axis and the
y-axis will change automatically, and by default it will change to histogram. Now
we can change that - here in the elements property window from histogram we could
choose "histogram percent." From here let's make some other changes. Click on "Set Parameters"
under "Anchor First Bin" choose "Custom Value for Anchor." We're going to
set the value to zero. Under "Bin Sizes" click "Custom" and set the interval width
to 1. Click continue, and then apply, and then "Ok". There's our histogram. Something
may be wrong; let's take a closer look. Now check the histogram. See any obvious
problems? Looking at the resulting histogram, we see that the scores are all
collected on the left side of the graph, and there are these two unexpected bars
on the right end. The x-axis goes to 60, but the options for the Likert scale
only ran from 1 to 7. Something is clearly wrong. It looks like we have an
outlier. In fact, we have two outliers as the great philosopher Rick Perry once
said, "Oops!" This histogram does not look like what we expected to see. These
values are supposed to be between 1 and 7; it looks like something really has
gone wrong, and we're gonna need to do something about that. And so we're
going to sniff out those outliers with a boxplot.