Graphical Analysis and Display of Data
there are relationships between data values. Key terms a graph consists of two axes called the x-axis (horizontal) and y-axis (vertical). Categorical data. But it is often useful to represent the relation in a two-dimensional graph. is a simple relationship between the two variables, it is readily observable once the This method of representation is called the Cartesian coordinate system or plane. Scatterplot. ▫ The most useful graph for displaying the relationship between two a graphical representation that includes both of these variables. Such a.
Graphs are a common method to visually illustrate relationships in the data. The purpose of a graph is to present data that are too numerous or complicated to be described adequately in the text and in less space. Do not, however, use graphs for small amounts of data that could be conveyed succinctly in a sentence. Likewise, do not reiterate the data in the text since it defeats the purpose of using a graph. If the data shows pronounced trends or reveals relations between variables, a graph should be used.
The Effective Use of Graphs
If the data doesn't show any significant trend in the evidence, a graph is not the figure of choice. A basic requirement for a graph is that it is clear and readable.
This is determined not only by the font size and symbols but by the type of graph itself. It is important to provide a clear and descriptive legend for each graph.
Graphs may have several parts, depending on their format: For most purposes, design a graph so that the vertical axis ordinate, Y axis represents the dependent variable and the horizontal axis abscissa, X axis represents the independent variable.
Hence, time is always on the X axis. Plotting symbols need to be distinct, legible, and provide good contrast between the figure in the foreground and the background. Open and closed circles provide the best contrast and are more effective than the combination of open circles and open squares. If the independent and dependent variables are numeric, use line diagrams or scattergrams; if only the dependent variable is numeric, use bar graphs; for proportions, use bar graphs or pie charts.
Graphical methods in Statistics | Health Knowledge
These are briefly described below. A scattergram is used to show the relationship between two variables and whether their values change in a consistent way, such as analyzing the relationship between the concentration levels of two different proteins.
The values of both variables for each individual are represented by a point on the plot. The individual values can be read from the plot and an idea of the relationship between the variables across individuals is obtained.
Even if the plot is not used in the final presentation, it may highlight outliers and will help to indicate the appropriate form of analysis to use. For example, the plot below comes from a study from the BMJ, looking at the association between age and ear length.
They found a weak positive association, meaning higher values of 'age' are associated with higher values of 'ear length' the article was published in the Christmas edition, where more light-hearted articles are encouraged. Why do old men have big ears? Alternatively, the same variable may be measured in a matched pair of individuals.
Any 'pairing' that is inherent because of the way in which the data was collected should be retained in both displaying and analysing the data. Line diagrams are often used whereas a scatterplot is generally more appropriate.
Milliner et al, Results of long-term treatment with orthophosphate and pyridoxine in patients with primary hyperoxaluria, New England Journal of Medicine,;Vol ,No. Measurements were made of calcium oxalate inhibition in 12 patients, pre and post treatment.Linear Equations: Graphical Representation of Linear Equation in Two Variable - Class 9th - 05/14
The authors displayed the data as a line-plot. The values for each patient are shown pre and post treatment and are joined by lines to show the within person pairing of the measurements.
Inhibition of the formation of calcium oxalate crystals during treatment with orthophosphate and pyridoxine in 12 patients with primary hyperoxaluria.
The line plot shows that all individuals have values that rise during treatment. One individual shows a very large increase from about 25 pre-treatment to about during treatment as illustrated by the steeply rising diagonal line.
The same data is presented below as a scatterplot: The line of equality no change in values pre to during treatment is shown as a dashed line on the display. All points lie above the line of equality showing that values rose for each individual. Whilst the same information is given by the two displays, the scatterplot uses only one point to represent each individual compared to 2 points and a line for the line diagram. The line diagram may be confusing to assess if there are changes in various directions, the scatterplot with the line of equality superimposed if necessary is easier to interpret.
No information is lost, the display clearly shows the relationship between the variables and also highlights possible outliers. A histogram for all the 98 birth weights in the Simpson data is shown in Figure 2. The area of each histogram block is proportional to the number of subjects in the particular birth-weight category concentration group.
Thus, the total area in the histogram blocks represents the total number of volunteers. Relative frequency histograms, where the y-axis shows the proportion of the observations in each bin rather than an absolute number, allow comparison between histograms made up of different numbers of observations which may be useful when studies are compared.
Figure 2 Histogram of birth weight of 98 babies data from Simpson The choice of the number of intervals is important.
Too few intervals and much important information may be smoothed out; too many intervals and the underlying shape will be obscured by a mass of confusing detail.
It is usual to choose between 5 and 15 intervals, but the correct choice will be based partly on a subjective impression of the resulting histogram.
Graphs of Two Variable Functions
Histograms with bins of unequal interval length can be constructed but they are usually best avoided. Advantages of histograms include the ability to visualise the shape of the frequency distribution and to demonstrate central tendency. However, because data are grouped into intervals, exact values of each observation cannot be determined.
- Choosing the Best Graph Type
- Graphical methods in Statistics
- Graphs of Two Variable Functions
Box-Whisker Plot If the number of points is large, a Dot plot can be replaced by a box-whisker plot which is more compact than the corresponding histogram. Such a plot is illustrated in Figure 3 for the birth weight and type of delivery from Simpson Figure 3 Box-Whisker plot of birth weight of babies by method of delivery data from Simpson, The 'whiskers' in the diagram indicate the minimum and maximum values of the variable under consideration.