Experimental Design — Design an experiment conceptually: controls, precision vs accuracy - Chemistry 2

SECTION 1

Historical Context & Motivation

Science did not always rely on carefully structured experiments. For centuries, observations about nature were recorded informally, and conclusions were drawn without any systematic attempt to isolate the cause of an effect. The idea that an experiment should include controls — setups that keep everything the same except the one factor under study — took hundreds of years to develop. Without controls, early researchers often confused correlation with causation, leading to unreliable results and medical treatments that were no better than guesswork.

Similarly, the distinction between precision (how close repeated measurements are to each other) and accuracy (how close a measurement is to the true value) only became important once instruments improved enough to reveal the difference. Understanding this distinction is critical in chemistry, where tiny measurement errors can change the identity of an unknown substance or the yield of a reaction.

1747 • James Lind's Scurvy Trial

Scottish naval surgeon James Lind conducted one of the first controlled clinical experiments. He divided twelve sailors with scurvy into six pairs and gave each pair a different treatment. The pair who received citrus fruit recovered, demonstrating the power of a controlled comparison.

1882 • Koch's Postulates

Robert Koch formalized rules for proving that a specific microbe causes a specific disease. His postulates required isolating the variable (the microbe), re-introducing it to a healthy host, and observing whether the disease developed — a classic controlled experiment framework.

1926 • Fisher's Statistical Methods

Ronald Fisher published methods for designing agricultural experiments using randomization and replication. His work showed that repeating trials and analyzing variation were essential to distinguishing real effects from random noise — the mathematical foundation of precision and accuracy.

1948 • First Randomized Controlled Trial

The British Medical Research Council tested streptomycin against tuberculosis using random assignment and a control group. This landmark study established the randomized controlled trial (RCT) as the gold standard in experimental design.

These milestones reveal a central question that every scientist still faces today: How do you design an experiment that produces results you can actually trust? The answer lies in understanding variables, controls, and the twin concepts of precision and accuracy — the building blocks of every reliable chemistry experiment.

SECTION 2

Core Principles & Definitions

Before you can design a sound experiment, you need to understand five foundational concepts. Each one plays a specific role in making sure your results are meaningful and repeatable.

Independent Variable

The single factor the experimenter deliberately changes between trials. In a reaction-rate experiment, this might be the temperature of the solution. A well-designed experiment changes only one independent variable at a time.

Dependent Variable

The outcome you measure or observe in response to the independent variable. If you change temperature, the dependent variable might be the time it takes for a precipitate to form. This is the data you collect.

Controlled Variables (Constants)

All other factors that must stay the same across every trial — concentration, volume, type of container, stirring rate, etc. If these vary, you cannot tell whether the independent variable or a controlled variable caused the observed change.

Control Group

A baseline trial where the independent variable is either absent or set at a standard value. The control group provides a reference point so you can see whether the experimental treatment actually had an effect.

Precision vs. Accuracy

Precision describes how closely repeated measurements cluster together (reproducibility). Accuracy describes how close those measurements are to the accepted or true value. You can be precise without being accurate and vice versa.

✦

KEY TAKEAWAY

Think of an experiment like testing whether a new basketball has better bounce. The independent variable is the ball type (new vs. old). The dependent variable is the bounce height. Controlled variables include dropping from the same height, on the same surface, with the same inflation pressure. The control group is the old ball you already know about. If you measure the bounce ten times and get 87 cm, 86 cm, 87 cm, 88 cm … that is precise. If the true bounce is 87 cm, those measurements are also accurate.

SECTION 3

Visual Explanation — Precision vs. Accuracy Target Diagrams

The classic way to visualize precision versus accuracy is with target diagrams. Each target represents a set of measurements, and each dot represents an individual data point. The bullseye at the center represents the true or accepted value.

Four target diagrams showing all combinations of precision and accuracy. The red dot at the center of each target is the true value. Notice that the ideal result (bottom right) has data points that are both tightly clustered (precise) and centered on the bullseye (accurate).

Look at the second target from the left — the violet dots are tightly grouped, meaning the measurements are precise. However, the cluster is far from the bullseye, so the measurements are not accurate. This situation typically results from a systematic error — a consistent flaw in your instrument or technique that shifts every reading the same way. In contrast, the third target (amber dots) shows data scattered widely around the bullseye. The average of those measurements may be close to the true value, but individual readings are unreliable. This reflects high random error. The goal in every chemistry experiment is to minimize both types of error so your data looks like the green target on the far right.

SECTION 4

Mathematical Framework — Quantifying Precision & Accuracy

While experimental design is primarily conceptual, you often need to put numbers to precision and accuracy. Chemistry uses two straightforward calculations: percent error to quantify accuracy, and standard deviation or range to quantify precision.

PERCENT ERROR (ACCURACY)

% Error = |Experimental Value − Accepted Value| ÷ Accepted Value × 100%

The vertical bars indicate absolute value — you ignore the sign of the difference. A lower percent error means greater accuracy. A percent error of 0% would mean a perfect measurement.

RANGE (SIMPLE PRECISION MEASURE)

Range = Highest Value − Lowest Value

The range is the simplest way to express the spread of your data. A smaller range means your measurements are more tightly clustered, indicating higher precision.

MEAN (AVERAGE)

x̄ = (x₁ + x₂ + x₃ + … + xₙ) ÷ n

The mean (x̄) is the sum of all measured values divided by the number of measurements (n). You compare the mean to the accepted value when calculating percent error, and you use it to assess whether your data set is accurate overall.

⚠

Why Both Matter

Imagine you measure the density of aluminum five times and get 2.70, 2.71, 2.69, 2.70, and 2.70 g/cm³. The accepted density of aluminum is 2.70 g/cm³. Your range is only 0.02 g/cm³ (high precision) and your mean matches the accepted value (high accuracy). Now imagine a different student gets 3.10, 3.11, 3.10, 3.09, 3.10 g/cm³ — very precise (range = 0.02), but the mean of 3.10 g/cm³ is far from the true value. That student has a systematic error — perhaps a miscalibrated balance.

SECTION 5

Detailed Breakdown — Types of Controls & Variables

A well-designed experiment isolates the effect of the independent variable by carefully managing everything else. There are several types of controls used in chemistry experiments, and understanding when each applies is essential for designing trustworthy investigations.

Side-by-side comparison of a control group and an experimental group. The only difference between the two groups is the temperature (the independent variable highlighted in green). All other factors — volume, mass, stirring, and container type — are controlled variables that remain identical in both groups.

In the diagram above, notice how a positive control could also be included — a trial where you already know the outcome (for instance, dissolving the sugar at 80 °C, where you know from prior data it dissolves quickly). A positive control confirms that your experimental setup is working. A negative control is a trial where no effect is expected (perhaps placing sugar in an empty, dry beaker at 25 °C with no water). If the negative control shows a change, something is wrong with the experiment. Together, these controls bracket your results and give you confidence that the independent variable — and nothing else — is causing the effect.

Type of Control	Purpose	Example (Sugar Dissolution)
Control Group	Provides a baseline for comparison; independent variable at standard value	Sugar in 200 mL water at 25 °C (room temperature)
Positive Control	Confirms the experiment can detect an effect when one should exist	Sugar in 200 mL water at 80 °C — sugar should dissolve very quickly
Negative Control	Confirms no effect occurs when the independent variable is absent	Sugar placed in a dry beaker with no water — sugar should not dissolve
Controlled Variables	Factors held constant so they cannot confound results	Volume of water, mass of sugar, grain size, stirring rate, beaker type

Types of controls used in a well-designed chemistry experiment

SECTION 6

Worked Example — Designing and Evaluating an Experiment

A student wants to determine whether the concentration of hydrochloric acid (HCl) affects the rate of reaction with magnesium (Mg) ribbon. She also needs to evaluate whether her data are precise and accurate. Let's walk through the experimental design and data analysis step by step.

Designing and Evaluating an HCl + Mg Experiment

1
Step 1 — Identify Variables

The student identifies the independent variable as the concentration of HCl (0.5 M, 1.0 M, 1.5 M, 2.0 M). The dependent variable is the time (in seconds) for the Mg ribbon to completely dissolve. Controlled variables include: length of Mg ribbon (3.0 cm), volume of HCl (50.0 mL), temperature (25 °C), and using the same brand of Mg ribbon.

Independent: [HCl]; Dependent: dissolution time; Constants: Mg length, HCl volume, temperature, ribbon brand
2
Step 2 — Set Up Controls

The control group uses 0.5 M HCl as the baseline. A positive control could use 2.0 M HCl with a very short piece of Mg (known to react quickly). A negative control could place Mg ribbon in 50.0 mL of distilled water — no reaction should occur because water alone does not dissolve Mg at room temperature.

Control: 0.5 M HCl; Positive: 2.0 M HCl + small Mg; Negative: Mg in pure water
3
Step 3 — Collect Data with Replication

The student runs three trials at each concentration and records the dissolution times. At 1.0 M HCl, she records 42 s, 44 s, and 43 s. The accepted value from published data is 43 s for these exact conditions.

Three trials at 1.0 M: 42 s, 44 s, 43 s; Accepted value: 43 s
4
Step 4 — Evaluate Precision

Range = 44 s − 42 s = 2 s. The measurements are tightly clustered with a spread of only 2 seconds, indicating high precision.

Range = 2 s → High precision
5
Step 5 — Evaluate Accuracy

Mean = (42 + 44 + 43) ÷ 3 = 43.0 s. Percent error = |43.0 − 43| ÷ 43 × 100% = 0%. The data are both precise and accurate — the ideal outcome.

Mean = 43.0 s; % Error = 0.0% → High accuracy

SECTION 7

Strengths, Limitations & Types of Error

No experiment is perfect. Understanding the types of errors that can affect your results — and how to reduce them — is a hallmark of good scientific thinking. Errors fall into two broad categories, and each has a different effect on precision and accuracy.

Feature	Random Error	Systematic Error
Definition	Unpredictable fluctuations that vary from trial to trial	Consistent bias that shifts all measurements in the same direction
Affects	Precision	Accuracy
Examples	Reading a meniscus slightly differently each time; small temperature fluctuations in the room	A balance that reads 0.05 g too high; consistently reading the meniscus from above instead of at eye level
How to Reduce	Increase the number of trials and average the results	Calibrate instruments; improve technique; use proper controls
Can It Be Eliminated?	Reduced but never fully eliminated	Can often be identified and corrected with calibration or a positive control

Comparison of random error and systematic error

✦

KEY TAKEAWAY

Think of random error like the natural wobble in your hand when you try to hit a dartboard — it makes your throws scatter around the bullseye. Systematic error is like a crooked dartboard that has been mounted three inches to the left — every single throw will miss to the left no matter how steady your hand is. Fixing the wobble (random error) requires practice and repetition. Fixing the crooked mount (systematic error) requires identifying and correcting the source of the bias.

SECTION 8

Connection to Advanced Experimental Techniques

The principles you have learned here — controls, precision, and accuracy — form the foundation for more sophisticated experimental methods you will encounter in AP Chemistry, college-level courses, and professional research. The table below highlights how these basic ideas evolve.

Concept in This Lesson	Advanced Extension
Control group (one standard condition)	Randomized controlled trials (RCTs) with blinding; placebo controls in pharmacology
One independent variable at a time	Factorial designs that vary multiple factors simultaneously and analyze interactions (e.g., ANOVA)
Range as a measure of precision	Standard deviation, confidence intervals, and propagation of uncertainty calculations
Percent error for accuracy	Statistical hypothesis testing (t-tests, chi-squared tests) to determine if differences are statistically significant
Identifying systematic error by comparing to accepted values	Calibration curves, certified reference materials (CRMs), and inter-laboratory comparisons

How high school experimental design concepts extend to advanced methods

As you move into more advanced chemistry, you will also encounter significant figures as a way to communicate the precision of a measurement, and uncertainty analysis as a formal method for propagating errors through calculations. These tools build directly on the concepts of precision and accuracy explored in this lesson. The key idea to carry forward is this: a result is only as good as the experiment that produced it, and sound experimental design is the first step toward trustworthy science.

SECTION 9

Practice Problems

Question 1: CONCEPTUAL

A student measures the boiling point of water three times and records 101.2 °C, 101.3 °C, and 101.1 °C. The accepted boiling point at standard pressure is 100.0 °C. Are these measurements precise, accurate, both, or neither? Explain your reasoning.

Show answer

The measurements are precise but not accurate. They are precise because the range is only 0.2 °C (101.3 − 101.1), meaning the values are tightly clustered. However, the mean of the three values is 101.2 °C, which is 1.2 °C above the accepted value of 100.0 °C, giving a percent error of 1.2%. This pattern — consistent readings that are consistently off from the true value — suggests a systematic error, such as a miscalibrated thermometer that reads about 1.2 °C too high.

Question 2: BASIC CALCULATION

A student titrates a vinegar sample and determines its acetic acid concentration to be 0.842 M. The accepted value is 0.833 M. Calculate the percent error of this measurement.

Show answer

Use the percent error formula: % Error = |Experimental − Accepted| ÷ Accepted × 100%. Substituting: % Error = |0.842 − 0.833| ÷ 0.833 × 100% = 0.009 ÷ 0.833 × 100% = 1.08%. This is a relatively small percent error, indicating good accuracy. The measurement is about 1.08% higher than the accepted value, which is within an acceptable range for a typical student titration.

Question 3: INTERMEDIATE

A chemistry class is testing whether the type of metal affects the amount of hydrogen gas produced when the metal reacts with hydrochloric acid. Student A proposes using 5.0 g of zinc in 100 mL of 1.0 M HCl, and 5.0 g of magnesium in 100 mL of 2.0 M HCl. Identify the flaw in this experimental design and explain how to correct it.

Show answer

The flaw is that two variables are being changed simultaneously: the type of metal (independent variable) and the concentration of HCl. Since the zinc trial uses 1.0 M HCl while the magnesium trial uses 2.0 M HCl, the student cannot determine whether any difference in hydrogen production is caused by the metal type or by the different acid concentration. This is a failure to control variables. To fix this, the student should use the same concentration of HCl (e.g., 1.0 M) for both metals. Additionally, using equal moles rather than equal masses might be a more chemically meaningful comparison, since 5.0 g of zinc (≈ 0.077 mol) and 5.0 g of magnesium (≈ 0.206 mol) contain very different numbers of atoms.

Question 4: APPLIED

You are hired by a water-testing company to determine whether a new pH meter is suitable for field use. You measure the pH of a certified buffer solution (true pH = 7.00) ten times and obtain these values: 6.98, 7.01, 6.99, 7.00, 7.02, 6.97, 7.01, 6.99, 7.00, 7.03. Calculate the mean, range, and percent error. Then state whether the meter is precise, accurate, both, or neither, and whether it is suitable for field use.

Show answer

Mean = (6.98 + 7.01 + 6.99 + 7.00 + 7.02 + 6.97 + 7.01 + 6.99 + 7.00 + 7.03) ÷ 10 = 70.00 ÷ 10 = 7.000. Range = 7.03 − 6.97 = 0.06. Percent error = |7.000 − 7.00| ÷ 7.00 × 100% = 0.00%. The range of 0.06 pH units is small, indicating high precision. The mean matches the accepted value exactly, giving 0% error and high accuracy. The meter is both precise and accurate, making it suitable for field use. In practice, you would also want to test it with additional buffer solutions at other pH values (e.g., pH 4.00 and pH 10.00) to confirm accuracy across the full range.

Question 5: CRITICAL THINKING

Two students each design an experiment to test whether surface area affects the rate at which an antacid tablet dissolves in water. Student X crushes one tablet into a fine powder and drops it into 200 mL of water at 25 °C, then uses a whole tablet in a separate 200 mL beaker at 25 °C. She runs one trial for each. Student Y uses whole, halved, quartered, and crushed tablets — each in 200 mL of water at 25 °C — and runs five trials for each condition. Compare the two designs. Which is stronger and why? Discuss variables, controls, precision, and accuracy in your answer.

Show answer

Student Y's design is significantly stronger for several reasons. First, Student Y tests four levels of the independent variable (whole, halved, quartered, crushed), which reveals a trend rather than just a two-point comparison. This makes it easier to draw a meaningful conclusion about the relationship between surface area and dissolution rate. Second, Student Y runs five trials at each condition, which allows her to assess precision by calculating the range or standard deviation of each data set and to reduce the impact of random error by averaging. Student X runs only one trial per condition, so there is no way to evaluate precision — a single data point could be an outlier. Third, both students hold temperature and volume constant, which is good, but Student Y's design provides a more complete picture. One limitation both students share is that neither mentions a negative control (e.g., a beaker of water with no tablet). Overall, Student Y's experiment is far more reliable because it incorporates replication, multiple levels of the independent variable, and the ability to distinguish between random variation and a genuine effect.

SUMMARY

Lesson Summary

Summary

A well-designed experiment starts by identifying the independent variable (the one factor you change), the dependent variable (the outcome you measure), and all controlled variables (factors held constant). The control group provides a baseline, while positive and negative controls confirm that the experimental setup is functioning correctly and that no unintended effects are occurring.

Precision refers to the closeness of repeated measurements to each other (low spread), while accuracy refers to closeness to the true value. Random errors reduce precision and can be minimized by running multiple trials and averaging. Systematic errors reduce accuracy and must be identified and corrected through calibration and careful technique. Use percent error to quantify accuracy and range (or standard deviation) to quantify precision. Together, these tools allow you to evaluate and communicate how reliable your experimental results truly are.