The following rules for graphs are enforced in physics 1100 labs done in Pivot. (Refer to the other rules for graphs page for rules to use in the in person class.) Each rule will have an example showing a bad graphs (and what exactly makes it bad), and the corrected (good) version of that same graph.
Include a meaningful title on the graph
A graph should be understood by looking at it, even if the reader is not sure what you are doing. A meaningful title allows anybody looking at the graph to understand what they are looking at.
Bad graph example
This graph title says nothing about what is being plotted. It is not descriptive about the type of experiment that was conducted.
If a title isn’t entered into Pivot, it will default to a meaningless title. In the graph settings, be sure to enter a title in the “Graph Title” section.
Good graph example
Here is the same graph with a meaningful title. It clearly explains the experiment that was performed, and the variables that are included in the experimental data. (The title even includes the control variable, which in this case is the mass of the cart!)
Label both axes and include units
The information on a graph should be scientifically meaningful. If it is not clear what is being plotted, then the graph is not meaningful. If units are not included in your graph, then it’s unclear exactly what you are plotting. Remember that units are just as important as the quantities that they describe!
Bad graph example
This graph has no unit on the vertical axis, and in addition is not particularly clear about what time is being measured. The horizontal axis is similarly labeled without a unit.
Good graph example
This graph shows the corrected version. The vertical axis is more clearly labeled as the period of oscillation with a unit of seconds. The horizontal axis now includes the unit used to measure the angle.
Note that if you clearly include the variable and its unit in the Pivot data table, that data should automatically populate in the axis label when you create the graph.
Include the origin in your graph
At times, data may appear to be fluctuating: it may appear noisy, or perhaps as an increasing or decreasing value. However, when compared to the value 0, it’s possible the data is not changing to a meaningful extent (typically, we will consider a variation that’s more than 10% of the average to be a meaningful change).
In Pivot, be sure under “View Options” that you select “Include Origin” on every graph.
Bad graph example
This graph shows velocity data that appears to be increasing a significant amount over time.
Good graph example
This graph plots the same data and includes the origin. It’s now much more clear that the increase in velocity values does not represent a significant change.
Clearly show all data points and don’t play connect-the-dots
A scientific graph is used to show a relationship between independent and dependent variables. All of the information on the graph should be meaningful. Drawing lines between each data point, like the child’s game of connect-the-dots, is not scientifically meaningful. It does not allow us to understand the true relationship between the independent and dependent variables.
This typically occurs in Pivot if you select “line graph” instead of “scatter graph.”
Bad graph example
Note how there is a line that connects the data points. That connect-the-dot line does not add any meaningful information to this graph. In addition, the connect-the-dot line hides each of the individual data points, which should be clearly visible on the graph.
Good graph example
This is the same data plotted as a scatter plot (so all of the data points are clearly visible), and includes a fit line that adequately represents all of the data points in the graph.
Use the correct type of fit line
If the data is linear, use a linear fit line. If the data is not linear, use the correct type of fit line. The fit line helps us to see through any variations in the data that could be caused by inaccurate lab procedures or calculations. If the wrong type of fit line is used, then it is not scientifically meaningful. In addition, the fit line can be used to interpolate and extrapolate data. The wrong type of fit line will lead to incorrect interpolations and extrapolations.
If there are no fit lines that adequately fit the data, then do not include a fit line in your graph. Also, there will be a few occasions where the lab instructs you about exactly what type of fit line to use, so be sure to read instructions carefully!
Bad graph example
This graph uses a linear fit on data that is not linear. The data is actually a square root relationship.
Good graph example
This graph uses the correct type of fit line for the data. Notice how it makes a smooth curve through the data.
If there are two sets of data, there should be two fit lines
Why? Remember, the point of a fit line is for us to interpret the relationship between independent and dependent variables, and for us to interpolate and extrapolate data. If the fit line is not correct, then it is not going to help us in our pursuit of science.
Usually the “one fit line for two sets of data” is an issue with how the data is entered into Pivot. Include each data set in its own column in the data table. Then, under “Vertical Axis,” select “Add Columns” to add another set of data to the graph.
Bad graph example
This graph shows two sets of data, but only has one fit line. Note that the fit line does not adequately represent either set of data.
Good graph example
This graph has two sets of data, and one fit line for each.
Use the correct type of graph
Variables can be qualitative (they use descriptive language, and not a numerical value, to describe the value) or quantitative (they use a numerical value to describe the value). When the independent variable is qualitative, a bar graph must be used. When the independent variable is quantitative, a scatter plot must be used.
Qualitative I.V.: bad graph
This is a scatter graph used to plot qualitative data. A bar graph should have been used instead. Because the I.V. is qualitative, and does not use numbers, the ordering of the values on the horizontal axis is meaningless. There is no trend that can be deduced by looking at the data points in this graph.
Qualitative I.V.: good graph
Here is the same data plotted as a bar graph. This is how qualitative data should be graphed in this class.
Quantitative I.V.: bad graph
This is qualitative data because the I.V. can be represented as a numerical value. It does not make sense to plot this as a bar graph.
Quantitative I.V.: good graph
This data is now represented in a scatter plot. A fit line can be included with the data that can be used to analyze the relationship between the I.V. and D.V.
Unless otherwise mentioned, use the horizontal axis to plot the independent variable and the vertical axis to plot the dependent variable
Most of the time, we want to understand the relationship between the independent and dependent variables. Therefore we usually plot the I.V. on the horizontal axis, and see how the vertical axis value (D.V.) changes. There are going to be a couple of exceptions to this rule. One of which is if we can swap the I.V. and D.V. in order to calculate the slope of a graph to get a meaningful quantity such as mass or resistance. These situations will be clearly indicated in the instructional text in Pivot.
Bad graph example
This graph meant to show how the current through a lightbulb changes when voltage changes. The I.V. is voltage and the D.V. is current. However, if we plot the data this way, the slope of the graph is not meaningful.
The instructions of this graph in Pivot would clearly indicate that current should be plotted on the horizontal axis and voltage on the vertical axis.
(Note that this graph has no fit line; none of the fit line options adequately represent this data.)
Good graph example
This is the same graph with the I.V. plotted on the vertical axis and D.V. plotted on the horizontal axis. In this graph, the slope of the graph represents the resistance of the lightbulb. This provides a scientifically meaningful quantity that we can use the graph to get information about.
Don’t just include (0,0) as a data point
Don’t just include (0,0) in your data unless it was a data point that you collected.
Bad graph example
This data includes (0,0) for all sets of data. It makes the data appear to be linear. Notice that it doesn’t necessarily “look wrong”, but it is wrong. It would imply that it took zero seconds for an object to move a space of about half a meter!
Good graph example
This data does not include (0,0) as data points, because they are not data points! It’s also more clear from this data that the relationship between independent and dependent variables is not linear.
Pay attention to your data and ask yourself if it makes sense
It’s always a good idea to do a “smell test” on your data. Does it look like it makes sense? Does the shape of the data appear consistent with what you expect? Sometimes just looking at a graph can help you to see if you made an error somewhere in your calculations or measurements. If you’re not sure, ask your professor for help or clarification.
Each of these bad examples is based on a submission I’ve seen from a student. Identifying information has been removed from the graph.
Bad graph example
In this plot, the data forms a vertical line. Vertical lines almost never happen in real life. If you see a vertical line, ask yourself if something is incorrect. The student accidentally plotted time on the horizontal axis, even though it is labeled as mass.
Bad graph example
Ask yourself if it makes sense that most of the data is between 0 and 3 seconds, until the length changes to 1.65 meters, and then the data suddenly jumps to a time greater than 60 seconds. It’s unlikely that data is going to have such a huge fluctuation like this.
Bad graph example
Here is another example of the same bad graph as the one above. Does it make sense for acceleration to be almost -3000 m/s^2 and then immediately jump up to zero? No. That data point should be deleted. The relationship that all of the other data points have cannot be deduced because the outlier data point is preventing our ability to see any trends on this graph.