Science Practice: Experimental Design and Error Analysis
Good experimental design changes one variable at a time while holding others constant, so any change in outcome can be traced to a single cause. Error analysis then tells you how much the uncertainty in your measurements limits how much you can trust that outcome.
Every experiment needs three roles sorted out before you touch any equipment: the independent variable (the one thing you deliberately change), the dependent variable (what you measure as a result), and the controlled variables (everything else, held fixed so it can't sneak in and cause the change you're seeing). If you change two things at once, say the acid concentration and the temperature, and the reaction rate goes up, you cannot tell which change caused it. The data might look perfectly smooth and clean, but the conclusion is worthless because it's not isolating a cause.
Designing a real comparison, like testing which of two unknown acids is stronger, means setting up identical conditions, same concentration, same volume, same temperature, same indicator, and changing only which acid is used. You'd measure something that tracks acid strength directly, such as pH, conductivity, or the volume of base needed to reach an equivalence point in a titration. Every other condition across your two trials must match, or the comparison is contaminated.
Once data is collected, error analysis asks how much the unavoidable uncertainty in each measurement limits your conclusion. Percent errors from independent measurements roughly add when those measurements are multiplied or divided together, so small errors in mass and volume both show up, combined, in a calculated molarity. This matters most when the propagated uncertainty is bigger than the effect you're trying to detect: if your measured difference between two trials is smaller than your error bars, you cannot claim a real difference exists, no matter how the averages compare.
Key terms
- Independent variable
- The single factor the experimenter deliberately and intentionally changes between trials.
- Controlled variable
- Any factor held constant across trials so it cannot explain the observed change.
- Systematic error
- A consistent, repeatable bias, often from a miscalibrated instrument, that skews all readings in the same direction.
- Random error
- Unpredictable fluctuation in measurements, such as small variations in reading a scale, that scatters data in both directions.
- Propagated error
- The combined uncertainty in a calculated result that comes from the uncertainties in each measurement used to compute it.
Watch it explained
- How it worksHow do you decide which variable to control, which to change, and which to measure?
- How it worksWalk me through designing an experiment to compare the strength of two unknown acids.
- Worked exampleFind how a 2 percent error in a mass measurement propagates through to the final molarity.
- Common mistakeWhy isn't every disagreement between your result and the accepted value called human error?
- Going furtherWhat changes about a conclusion when the uncertainty is larger than the effect you measured?
Check yourself
End of topic.