Writing Results sections right

A common task is writing a lab report (often in APA style) that consists of an Introduction, Method, Results, and Discussion section.  Good Introductions and Discussion sections are very hard to write, and really take a lifetime of practice.  Method and Results sections, by contrast, are more formulaic and therefore are easier to master - and yet, when my students make their first attempt at these sections, they make a number of common rookie mistakes.  Today I'd like to focus on the Results section.

1.  Just say it, don't tell me you're going to say it

"After collecting the data, the Control group averaged 124.5 correct."

As I've posted before, there is no need to state the obvious.  Of course you got this average "after collecting the data."  This problem shows up any number of ways.  "Our results indicated that the control group did worse that the experimental group" is another popular one.  Just kill the extra words.

2.  Results are not significant or insignificant, but certain comparisons might be

I can't count the number of times a student has written some version of "Our results were insignificant," though the number would probably be proportional to the number of hairs that used to be in my head that are now ripped out of my head and collecting on the floor around my desk chair.


When we run statistical tests, we are assessing whether some difference between groups, or some relationship between variables, or some other kind of comparison, is likely (or not likely) to have occurred by chance alone.  We use the (perhaps unfortunate) term "statistical significance" to indicate when the data are not likely to have occurred by chance alone. 

Imagine I have two groups, a Control and an Experimental group, and I have conducted a t-test which resulted in a non-significant p-value.  That "result" - that the Control and Experimental groups don't differ, may be important.  It may be reliable.  It may be replicable.  To say "Our results were insignificant" is, therefore, potentially misleading, and it's definitely vague.

The right way to describe the t-test would be: "The difference between the Control and Experimental groups was not significant (t(18) = 0.563, p = 0.58)."  When describing a statistical result, always describe what your statistics is testing.  It's a t-test, so it's testing whether a difference between two groups is a reliable difference.  You aren't testing a "result" - you're testing a difference.

Likewise "Our ANOVA was not significant" and "Our correlation was significant" aren't very informative.  "There was no main effect of temperature on our measure of aggressiveness" and "Level of anxiety was significantly correlated with blood pressure readings," on the other hand, correctly describe the statistical results.

3.  Figures and statistical tests should match

There's an art to making figures, but it's an important art.  Figures are usually the heart of a Results section, so much so that I make my figures first and build the text of the Results around the key figures.

Students often don't know what to graph, but the recipe for making a graph is actually quite simple.  Your hypothesis is a prediction about how some independent variable will affect some dependent variable.  ("We hypothesized that reaction time in a visual search task will increase as a function of carbon dioxide levels.")  Your design was based on the hypothesis.  ("We tested people in 4 conditions: the atmospheric carbon dioxide level in the testing room was set at 0.04%, 0.08%, 0.16%, or 0.32%.")  Your statistical analysis is based on your design.  ("We conducted a one-way ANOVA on reaction times with carbon dioxide level as a between-subjects factor.")  Your key figure - it should be obvious - will have the dependent variable on the vertical axis ("Average reaction time, ms") and the independent variable on the horizontal axis (the four carbon dioxide level groups).

Students sometimes seem to get overwhelmed with what to do once they've got a spreadsheet full of data.  The cure for this is to plan your graphs before you start your experiment.  If you have a good experimental design, the graphs you'll need in your report should be obvious from the very beginning.

3a.  Figures are figures, tables are tables

Every year I get a student or two who refers me to "Table 1" when he or she really wants me to look at "Figure 1".  I don't know why.

3b.  Refer to figures early and often, but parenthetically

Frequently students will refer to figures at the end of the Results almost like an afterthought.  "The data are graphed in Figure 1."  As soon as the figure is relevant - as soon as looking at the figure would help a reader understand what you're saying - it should be referenced in the text.  Whenever I can, I try to refer to the first Results figure at the end of the first sentence of my Results section.  "Somewhat consistent with our expectation, reaction times were longer at the highest carbon dioxide level, but were relatively equivalent at the three lower levels (see Figure 1)."  Notice that I refer to the figure at the end of that sentence - the text should not just refer to the figure, it should also describe the pattern of the data that the figure graphically represents.  Don't just say "The relationship of reaction time to carbon dioxide level is shown in Figure 1."  Tell the reader what the data were and refer to the figure parenthetically so they can also see the data pattern for themselves.

4.  Inferential statistics aren't data - statistics assess the reliability of patterns in the data

Students have a way of losing their data when they start doing inferential statistics like ANOVA and t-test.  Imagine a Results section that starts out like this:  "An ANOVA indicated that there was a significant main effect (F(3,36) = 5.797, p = 0.002)."  That's a terrible first sentence, because I have no idea what actually happened in the experiment, I only know what happened after the experiment when my student was studying a computer printout from his or her statistics program.  Better would be:

"Somewhat consistent with our expectation, reaction times were longer at the highest carbon dioxide level, but were relatively equivalent at the three lower levels (see Figure 1).  An ANOVA indicated that the main effect of carbon dioxide level on reaction times was significant (F(3,36) = 5.797, p = 0.002).  A post-hoc test (Tukey-HSD) indicated that the differences between the highest carbon dioxide group and the other 3 groups was significant (all p-values < 0.05) but that the 3 other groups did not differ from one another."  All the statistics are dutifully included, but I also now know what was measured (reaction time), what was manipulated (carbon dioxide levels), and what the pattern of the data was (one group's reaction times were higher than the other three).

5.  Units are always important

This should go without saying, but if a number has a unit, always report the unit.  "The control group averaged 375.6" is wrong.  "The control group averaged 375.6 ms" is much better.

6.  A final bit of advice

Ideally, your Results section should be perfectly understandable if every figure and statistic was removed.  Figures and statistics are super-important - you'd never really want to remove them - but the point is that you shouldn't "lead" with them either.  Your Results section isn't really about figures, F-values, and p-values; it's really about what happened to your subjects.  Some of them scored high.  Some scored low.  Some were fast, some were slow.  Your reader must have a clear picture of the pattern of the data, and this usually requires you to use plain, every day language.

Wherever you can, stick the stats and the references to figures in parentheses, and then make sure your sentences still make sense without the parentheses.  Sometimes you won't be able to do this, but you might put your statistics or figure descriptions in a separate sentence, and then verify that your paragraphs make sense without those sentences.  Yes, you need the statistics.  You need the figures.  But these do not replace a description of the pattern of data obtained in your experiment.