An experiment ends in a table or a graph. Reading it well is a skill of its own. It starts before you look at the shape of the line, and it uses the mean you already know.
Key idea
Read the title, the axes and their units first, then the trend. Compare groups by their means and their spread. Two things that change together show a correlation; only a controlled experiment can show that one causes the other.
- Title and axes. What was measured, in what units, and over what range? Does the y-axis start at zero?
- Trend. Does the dependent variable go up, go down, rise and level off, or peak?
- Spread. Error bars show how much the trials varied. When the bars of two groups overlap a lot, the difference between their means may be chance.
Worked example: The mean of trials
Three trials of an enzyme reaction made 12, 15 and 18 mL of oxygen. What is the mean?
- Add the trials: $12 + 15 + 18 = 45$ mL.
- Divide by the number of trials: $45 \div 3 = 15$ mL.
Answer: $15$ mL
Worked example: Do the means really differ?
Plants in light grew a mean of 24 cm (error bar ± 2 cm). Plants in shade grew 15 cm (± 3 cm). Is the difference likely to be real?
- The light group runs from $24 - 2 = 22$ to $24 + 2 = 26$ cm.
- The shade group runs from $15 - 3 = 12$ to $15 + 3 = 18$ cm.
- The ranges do not overlap ($18 < 22$), so chance alone is an unlikely explanation.
Answer: Yes: the error bars do not overlap.
Why it works
A trend can be made to look large or small just by the scale. A y-axis that runs from 90 to 100 makes a change from 92 to 96 look huge. That is why the axes come first. And a correlation can come from a third factor: towns that sell more ice cream also have more sunburns, but both rise because of sunny weather. Neither causes the other.
Common mistake
Reading the trend before checking the axes and units, or treating a correlation as cause and effect. Before you conclude "X causes Y," ask two things: was X changed on purpose with everything else held constant, and could a third factor drive both?