Applications of Graphical Tools
Applications of Graphical Tools
When to use a logarithmic scale on a line graph?
The logarithmic scale can be used where there is a large range of data to be portrayed on the graph and there is the need for not compressing down the small values into the bottom of the graph. Another reason for using logarithmic scale could be where there is time series data.
2. How does a logarithmic scale graph represent growth occurring at a constant rate? At an increasing rate?At a decreasing rate?
Logarithmic scale graph representing a constant growth rate shows the equal absolute change in log y against x it depicts the proportionate change in the two variables. When plotted on the graph we get a straight line with the   constant slope and moreover it passes through the origin. Below is a graphical example showing the growth rate occurring at a constant rate:
Secondly, the log scale representing growth at an increasing rate shows the varying change of variable y over a particular period of time. It shows an increasing change in the growth of y in each year and the growth rate is not merely upward sloping. Lastly, the log scale representing growth at a decreasing rate shows the change in the growth of y at a decreasing trend and graphically the slope is downward sloping.
3) What (mis-)interpretation is common, when a line graph that should have a log scale is drawn without a log scale?
The common misinterpretation is the relationship between the variables in the X-axis and Y-axis since when log scale has been used student might think that there is a linear relationship.
Data Graphing Assignment
1) The data file USPOP.XLS contains data on the population of the United States, according to each ecennial census since the first one in 1790. You are to use these data for the following three graphs. First, do a graph showing how population grows over time. What does the graph (appear) to tell us?
Below graph show that the population initially was growing at a low rate in the year 1790 1830 and later at an increasing rate.
b) Since population grows exponentially, we know that we should really do a logscale graph of these data. Draw one. What does this graph to tell us?
The graph shows that there is a linearly relationship between the growth of the population over
the time period. This shows that the population increases with time.
c) For the third graph, you will show how the growth rate (rather than the population) has grown over time. Begin by computing the percent growth rate for each decade of the data. Thus, for example, between 1790 and 1800 population grew from 3,929,214 to 5,308,483. Hence the growth rate is(5 308 483 – 3 929 214)/3 929 214 = 0.351or 35.1 percent. (Note that you will have one less data point for growth rate than for population, since we can`t yet compute a growth rate for the 2010 to 2020 decade.) Graph how growth rate has changed over time. How does this fit with your interpretation of the first two graphs?
This shows that the rate of growth was higher in the initial years as compared to the later years. Even though there was the increasing growth of the population, the growth rate was high at the initial time than end years.
"How to Display Data Badly," By Howard Wainer
Howards Wainer’s book focuses on the appropriate display of figures in a graphical representation. He begins by bringing to us the history of data representation and how, different scholars have strived to improve it for years. To takes us through the journey of transformation of graphs and other data representation methods. To date, few people have mastered the effectiveness of creating graphs to the required standards. Wainer notes that, most of the graphs created are either shallow in information contain a lot of unnecessary data. He notes that this method of data display, leave viewers or the users of the data uninformed as they find it difficult to interpret its contents. The gives a brief information on the aim of a good data graphic.
The is divided into two major sections:
Good data representation
Bad data representation
Bad Representation of data
As indicated in the book, excellent data graphics display data vividly and accurately. If the intention of a display is to pass out information, the less data shown in the display the better the bad it is. The data provided should be sufficient enough to supply the users of the data with the much need information. Wainer goes ahead to provide rules for constructing data representation displays.
Rule 1: Display as few data as feasible. In other words, the data density should be minimal. Various arguments suggest that high data density does not have an implication in the quality of a graphic, nor does a low density one mean the quality is bad it gives a reflection of the efficiency of the conveyance of information. Wainer observes that, if the accuracy and clarity are kept constant, we may prefer more information to less. Graphs are effective in conveying a large amount of data using less space.
Rule 2: Keep the Data-Ink ratio at a minimal
Howard shows us that it is advisable to hide some data. This can be done in a couple of ways: a). hiding information in the grid
b). hiding information in the scale
Rule 3: Ignore the Visual Image Altogether
It is stated in the book that, if the information is ordered as well as if the visual image has an innate order, an unpleasant display will emerge if the relationship is shuffled.
Rule 4: the order of display matters
Another rule is that of utilizing length as the visual image when the area is what is recognized. These graphs tend to have a low density.
Rule 5: displaying out of Context data
The view of the graph can be modified by carefully selecting the interval shown. For instance, a precipitous drop can disappear if a starting date is chosen right after the drop.
Rule 6: modify scales in Mid-Axis
This technique can make a distinction look diminutive as well make exponential alterations seem linear.
Good Data Display
According to Wainer, a good data display should have accurate, clear and less but sufficient information for the user of it to make appropriate conclusions and calculations.
Examples of Bad Graphs
The graph above is bad since its data is hard to interpret. According the rules learnt, it is good practice to display data that contains less information but also be easy to understand. This one follows the first rule but ignores the latter. Less information leaves blank spaces which are hard to fill and derive conclusions.
The plot in fig. 4 above is simple and clear but lacks some information. The data provided does not show the rise of private education institutions in the scale.
Figure 6 above makes it hard to interpret data due to misrepresentation of data. It can be observed that the bar labeled 18 is shorter that bar labeled 14. This causes confusion when trying to interpret the data provided.
Wainer, H. (1984). How to display data badly. The American Statistician, 38(2), 137-147.