Chapter 5

What does a histogram show?

A histogram is a graph in which values of observations are plotted on the horizontal axis, and the frequency with which each value occurs in the data set is plotted on the vertical axis.

Produce a histogram and population pyramid for the success scores before the intervention.

First, access the Chart Builder and then select Histogram in the list labelled Choose from: to bring up the gallery. This gallery has four icons representing different types of histogram, and you should select the appropriate one either by double-clicking on it, or by dragging it onto the canvas. We are going to do a simple histogram first, so double-click the icon for a simple histogram. The dialog box will show a preview of the graph in the canvas area. Next, click the variable (Success_Pre) in the list and drag it to X-Axis?. You will now find the histogram previewed on the canvas. To produce the histogram click OK. The resulting histogram is shown below. Looking at the histogram, the data look fairly symmetrical and there doesn't seem to be any sign of skew. To compare frequency distributions of several groups simultaneously we can use a population pyramid. click the population pyramid icon (see the book chapter) to display the template for this graph on the canvas. Then from the variable list select the variable representing the success scores before the intervention and drag it into the Distribution Variable? drop zone. Then drag the variable Strategy to . click to produce the graph. The resulting population pyramid is show below and looks fairly symmetrical. This indicates that both groups had a similar spread of scores before the intervention. Hopefully, this example shows how a population pyramid can be a very good way to visualise differences in distributions in different groups (or populations).

Use what you learnt in Section 5.6.3 to add error bars to this graph and to label both the x- (I suggest 'Time') and y-axis (I suggest 'Mean grammar score (%)').

See figure 5.26 in text book

Produce boxplots for the success scores before the intervention.

To make a boxplot of the pre-intervention success scores for our two groups, double-click the simple boxplot icon, then from the variable list select the Success_Pre variable and drag it into and select the variable Strategy and drag it to . Note that the variable names are displayed in the drop zones, and the canvas now displays a preview of our graph (e.g. there are two boxplots representing each gender). click to produce the graph. Looking at the resulting boxplots above, notice that there is a tinted box, which represents the IQR (i.e., the middle 50% of scores). It's clear that the middle 50% of scores are more or less the same for both groups. Within the boxes, there is a thick horizontal line, which shows the median. The workers had a very slightly higher median than the wishers, indicating marginally greater pre-intervention success but only marginally. In terms of the success scores, we can see that the range of scores was very similar for both the workers and the wishers, but the workers contained slightly higher levels of success than the wishers. Like histograms, boxplots also tell us whether the distribution is symmetrical or skewed. If the whiskers are the same length then the distribution is symmetrical (the range of the top and bottom 25% of scores is the same); however, if the top or bottom whisker is much longer than the opposite whisker then the distribution is asymmetrical (the range of the top and bottom 25% of scores is different). The scores from both groups look symmetrical because the two whiskers are similar lengths in both groups.

Bar chart

a graph in which a summary statistic (usually the mean) is plotted on the y-axis against a categorical variable on the x-axis (this categorical variable could represent, for example, groups of people, different times or different experimental conditions). The value of the mean for each category is shown by a bar. Different-colored bars may be used to represent levels of a second categorical variable.

Line chart

a graph in which a summary statistic (usually the mean) is plotted on the y-axis against a categorical variable on the x-axis (this categorical variable could represent, for example, groups of people, different times or different experimental conditions). The value of the mean for each category is shown by a symbol, and means across categories are connected by a line. Different-colored lines may be used to represent levels of a second categorical variable.

Scatterplot

a graph that plots values of one variable against the corresponding values of another variable (and the corresponding values of a third variable can also be included on a 3-D scatterplot).

Boxplot (box-whisker diagram)

a graphical representation of some important characteristics of a set of observations. At the center of the plot is the median, which is surrounded by a box, the top and bottom of which are the limits within which the middle 50% of observations fall (the interquartile range). Sticking out of the top and bottom of the box are two whiskers which extend to the highest and lowest extreme scores, respectively.

Error bar chart

a graphical representation of the mean of a set of observations that includes the 95% confidence interval of the mean. The mean is usually represented as a circle, square or rectangle at the value of the mean (or a bar extending to the value of the mean). The confidence interval is represented by a line protruding from the mean (upwards, downwards or both) to a short horizontal line representing the limits of the confidence interval. Error bars can be drawn using the standard error or standard deviation instead of the 95% confidence interval.

Regression line

a line of a scatterplot representing the regression model of the relationship between the two variables plotted.

Density plot

similar to a histogram except that rather than having a summary bar representing the frequency of scores, it shows each individual score as a dot. They can be useful for looking at the shape of a distribution of scores.

Chartjunk

superfluous material that distracts from the data being displayed on a graph