How do I know which type of graph to use?  Follow this key…

1. Is the data a percent that sums to 100%?

a.     If yes…………………………………………………………………………………..Pie chart

b.    If no……………………………………………………………………………………Go to #2

2.     Are both your manipulated and responding variables quantitative? 

a.     If no…………………………………………………………………………………..Bar graph

b.    If yes …………………………………………………………………………………Go to #3

3.     Are your manipulated variable levels continuous or clumped into groups?

a.     Continuous…………………………………………………………………………..Scatter plot/line

b.    Clumped …………………………………………………………………………….Histogram

Graphing Conventions

For graphs to be understood there are some conventions that need to be learned.

Determine the manipulated and responding variables.  In an experiment the experimenter will set up a set of conditions, it may be a range of temperatures or pH values, or, more common, the experimenter may choose to observe the experiment proceeding at set intervals of time (seconds, days or even years). These are the manipulated variables and always go on the horizontal axis (x—axis). The effect of the experimenter varying the manipulated variable is measured as the responding variable (the part of the experiment under observation), this is always plotted on the vertical axis (y—axis or ordinate).

Note the units of measurement for each of the variables.  Non- metric units such as Fahrenheit (°F) should be avoided in science.  It is important to indicate to your audience in what unit you are actually measuring your variables. The units of measurement are presented behind the label of the axis, e.g. Temperature (°C)

The proportions of the axes.  The area enclosed by the axes should be roughly square and not disproportionately exaggerated.

Mark the quantities on both axes and. number them at regular intervals.  Your axis intervals do not have to be the same on the x and y axis and they do not have to always start at the origin with a value of 0.

Giving the graph a title.  The graph must have a title which should contain a brief description of what is being investigated. Other information which may go in the title, if available, includes: the date, place and name of experimenter or collector of the data. If there is more than one graph a reference number or letter is required. For example:

“Fig 2:  A graph showing the change in testis weight throughout the year in the brown rat (Rattus rattus)”  IS BETTER THAN... “A graph of testis weight against time” which is insufficient.  Underline or use bold type for your title it makes it stand out and is easier to find on the page. 

Plotting more than one graph on a set of axes.  Sometimes two or three sets of data (though rarely more) are plotted within the same set of axes. You must distinguish between them by using different symbols (X, Ο, 􀀀, ∇ etc) or lines (…………., ________, -----------, etc). Use a key by the side of the graph which explains the symbols or lines. Do not write on the graph itself though labels and arrows may be useful.  You may wish to plot data from two different responding variables together on one graph but the values may be so different you have to use two different scales. One axis can be placed on each side of the graph.   However, the situation gets too confusing if more variables are treated in this way on one graph.

Graphing in Excel 2003

1. Enter your data on a spread sheet.  Put your manipulated variable data in the A column and your responding variable data in the B column.

2. Choose which type of graph you need to make.  Note:  If you are looking to find a trend in the data (say a trend over time), you would want to have a scatter plot.  To draw a curve of the data, highlight the data and click the chart wizard icon (looks like a bar graph in the tool bar) and select “XY scatter”.  Do not select “line”; this is a recipe for disaster!

3. The options are then followed in sequence which allows you to set up some of the basic features of the graph: (a) whether or not you want to include a grid, (b) whether or not you need a key, (c) entering your title and the labels on the axes.

4. Finally you have to decide if you want the graph in its own file or as an insert on the spread sheet.  The insert on the spread sheet is probably the most useful as it permits you to easily cut and paste the graph into a document and you can see the data at the same time as the graph.

5. Once you have the graph insert you can continue to work on it.

You can pull it out to the size you want. 

Click on its frame and you can set the size of the lettering, the type of font.

Click on the area inside the axes and you can set the background color.  White is best.

Changing the scale of the axes can be useful. Click on the axis that you want to alter.

Click on a block of text to make any changes.

You can change the color of the curve and the style of the data points by clicking the line.

6. If you drew a scatter plot, you can add a best fit line and calculate the slope of the line:

Click on “chart” on the toolbar.

Click on “add trendline.”  Choose the “linear” option.

7. Your graph may now be cut and pasted into your document!

Graphing Standard Deviation & Range

On a bar graph, histogram or line graph, plot the mean.  Make a smaller horizontal mark at the value of the mean -1 SE.  Make another mark at the value of the mean + 1 SE.  Draw a +/- 1 SD error bar by connecting those marks with a vertical line or making a rectangle around the mean.  We often plot the range as well.  Make a dot on the graph or the highest data points used in calculating the mean.  Make another for the lowest data point.  Connect them with a vertical line. 

Graphing Standard Deviation in Excel 2003

1. First calculate the means (by clicking at the “formula” icon in the toolbar, and selecting “average”) and the standard deviation (select “standard deviation” in the “formula” menu) of each of your samples. 

2. Then you can plot the mean for each sample using a bar graph.  To do this, click on the “Chart wizard” icon in the toolbar, choose the “column” graph type, and click next.  Select the means of the two samples as the data you want to plot); click next. 

3. You will have the option of adding a title, axes labels, etc.; do so if you wish, and next, and click finish in the last window. 

4. Once you have plotted the means, you can add error bars with the standard deviation of your samples.  This will give you an idea of the variability of your data.  To do this, right-click once on one of the columns.  This will open a menu; select “Format data series,” and go to the “Y error bars” window.  Click the red arrows in the custom error amount (lower part of window); this will shrink the window.  Select the cells where the standard deviations of your two samples are (select them both at the same time), and click the red arrow again.  You will have to this twice, once for the + and once for the – error bars.  Click “OK.”  This will modify your graph.

Using error bars to determine if populations differ

If error bars of samples from two populations overlap:

There is a chance that the true means of the 2 populations fall somewhere in the region of overlap.  So the true population means could be the same.  By the conventions of statistics, we must conclude that the samples do not support the hypothesis of a difference between the 2 populations.  Of course, there is a chance that the true population means do not fall in the region of overlap and this conclusion may be wrong.  The greater the overlap, the greater the chance that the populations are the same--and the less likely our conclusion is wrong.

If error bars of samples from two populations don't overlap:

In this course, we will conclude the samples support the hypothesis of a difference between the 2 populations.  But since true population means can fall outside the error bars, there is a chance this conclusion is wrong.  The more separated the error bars, the more the chance that the populations are different.  If the error bars touch there is about an 84% chance that the two populations are different and a 16% chance they are the same.  So there is a 16% chance (1 in 6 such situations) that we will conclude the populations are different when they really aren't.  We usually require 95% chance of difference before concluding populations are different.   You can always to a T-test to find out whether the difference is significance for sure!!