For general advice on how not to design misleading graphs, have a look at this Wikipedia page that covers a broad spectrum of scenarios. You may also be interested in the book "How to lie with statistics" -- originally published in 1954, it is very popular and still in print. Because I don't know what your exact use-case is, I'll rely on a contrived example to discuss some scenarios and their impact on the user. For line graphs, the slope of the graph will be a deciding factor in the user's interpretation of the data. The question comes in when deciding by how much to boost the perceived slope of the line, by scaling the y-axis.
Example: Your company installs smart temperature sensors for a number of industries, from pathology labs that store blood samples, to industrial freezers for supermarkets. They also sell off-the-shelf thermometers for people interested in tracking the weather on their home PCs. You are tasked with designing the interface for graphing these temperatures on screen. Users may even want to compare temperature from different sensors, or from different time periods. I will stick to degrees celsius going forward.
Home thermometer in moderate climate
Assuming no air conditioning is present, and the thermometer is installed indoors, the user can expect to see cycles of gradual increase and decrease of temperatures, depending on the time of day (in summer, maybe min: 15C, max: 30C)
- Is the user interested in data above and below zero? Not if this is a normal summer's day, or a very unusual weather phenomenon. It will be interesting if we compare against winter's temperatures though. But for single series, no, only above zero.
- Is the user interested in minor fluctuations, such as going from 25.05C to 25.1C? In general, no.
- Suggestion: Scale the axis to encompass the expected range of the data, not worrying too much about minor fluctuations. Active range should show gradual slopes.
Industrial freezer
Each freezer has a dedicated temperature range depending on the type of food it is keeping cool. There is a margin of error allowed, but not much. If it becomes too hot, the food may spoil. If it becomes too cold, the food may be damaged and the energy bill will skyrocket.
Is the user interested in data above and below zero? Yes, since this is the target operational range of the freezer. The user may actually want to subdivide this into different target areas (5C to -5C, -5C to -15C, -15C and colder) when they monitor different sensors at the same time, each for a different type of food. Here it may be important to look beyond the single sensor's target range, and include the other target ranges too (unless if you want to dedicate a graph to each sensor).
Is the user interested in minor fluctuations? It may be interesting, if only to point out that there might be fluctuations in power supply, or ageing equipment that needs to be serviced/replaced.
Suggestion: Focus on the active range of the freezer to highlight slight changes, but flexible to allow comparisons with other sensors if need be. Expect to see lots of flat lines, maybe slight slope changes to indicate slowly degrading performance.
Pathology lab
Specialised freezing equipment, that needs to maintain critical cooling range in order not to compromise biological samples (min -31C, max -30C).
- Is the user interested in data above and below zero? Not really. The user is only interested in a very specific tight range of values below zero, where even minor fluctuations may trigger alarms.
- Is the user interested in minor fluctuations? Yes, this is the most important reason for graphing the data.
- Suggestion: Scale the graph to highlight fluctuations to allow users to take appropriate counter measures as soon as possible. Users should react to major slope changes.
So, as you see, this will be highly dependent on your use-case.
For academic research, you may be interested to read the following two papers:
Review of Graph Comprehension Research: Implications for Instruction (2002) looks at how students interpret graphs, and why they struggle. They consider visual (perception) reasons as well as domain knowledge (what do the students know about the underlying data, and how does this influence their expectations/reading of the graph).
Sizing the Horizon: The Effects of Chart Size and Layering on the Graphical Perception of Time Series Visualizations (2009) compares horizon graphs to line graphs, and tests users' ability to estimate variance (value differences) in data.
