Applied Mathematics for Science
CoreExperimental design: controls

Control Groups & Controlled Experiments

Set up a fair test by comparing a treated group against an untreated control while every other variable is held the same.

Why this matters

An experiment can only answer one question: did the thing I changed cause the result? You cannot answer that from the treated group alone, because you have nothing to compare it against. The control group is that comparison: it is treated exactly like the experimental group except it does not receive the treatment (or it receives a fake treatment called a placebo). If the two groups end differently and everything else was held the same, the treatment is the reason. Drug researchers build controls into every clinical trial so they can prove a new medicine beats a sugar pill rather than just the passage of time. Microbiologists run a positive control (a plate they know should grow) and a negative control (a plate that should stay blank) so they can trust the reading on their real sample. Agricultural scientists compare fertilized plots against untreated plots on the same soil, and quality-control technicians compare a new batch against a known-good standard. Without a control, a result is just a story; with one, it is evidence.

Standards this builds
  • NGSS · SEP-3Planning and Carrying Out Investigations: design a controlled investigation that identifies the variable being tested and holds all other variables constant so the results are interpretable.
  • NGSS · SEP-4Analyzing and Interpreting Data: compare a treatment group to a control group to decide whether an observed difference is due to the treatment.
  • Common Core · HSS-IC.B.3Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization and controls relate to each.
  • Ohio · Ohio HS Bio SPDesign and conduct scientific investigations that use controls and control variables so a cause-and-effect conclusion is justified.
  • AP · AP Bio SP 3 (Experimental Design)Identify the control group and the controlled (constant) variables in an experiment, and explain why a control is required to support a claim.
Builds on (2 levels back)inferred · high confidence
  • Independent vs dependent variable: You must name the one variable you change (independent) before you can say what the control group leaves unchanged.
  • Compare two groups fairly: The whole point of a control is a fair comparison, so students first need the idea that only one thing should differ between groups.
  • Read counts and rates from a table: Deciding whether a treatment worked means reading each group's result off a table and comparing them.

Prerequisites are inferred: pending teacher review.

Re-learn the skill with worked practice and clear examples.

Build a fair test in three moves: choose the one variable you will change (the treatment), give the control group everything except that treatment, and hold every other condition the same for both groups (the controlled variables). Then compare the two groups' results. If they differ and only the treatment differed, the treatment is the cause.

Step 1: Change exactly one thing
The experimental group and the control group should differ in only one way: the treatment. If they differ in two ways, you cannot tell which one caused the result.
Step 2: Hold everything else constant
Same light, same water amount, same temperature, same starting condition for both groups. These are the controlled variables. Keeping them equal is what makes the comparison fair.
Two groups with identical light, water, pot and soil; the only difference is the control group gets no fertilizer and the experimental group gets fertilizer
Step 3: Compare the two results
Read each group's outcome and compare. If the treated group did better and only the treatment differed, the treatment is the likely cause. If everything was equal except the treatment, that is a controlled experiment.
Practice

In a seed-sprouting study, 20 seeds get plain water (control) and 20 seeds get a fertilizer solution. The table shows how many sprouted. How many MORE seeds sprouted in the fertilizer group than in the control group?

Reviewed
GroupSeeds plantedSeeds sprouted
Control (plain water)208
Fertilizer (treatment)2015
Table: control group planted 20 seeds and 8 sprouted; fertilizer group planted 20 seeds and 15 sprouted
  1. A.3 more
  2. B.7 more
  3. C.8 more
  4. D.15 more
Show the worked solution ▾

Answer: B. 7 more

  1. Step 1: Read both counts: Control sprouted 8; fertilizer sprouted 15.
  2. Step 2: Subtract: 15 - 8 = 7 more seeds sprouted in the fertilizer group.

Why it's right: Comparing the treated group (15) to the control (8) gives 15 - 8 = 7 more sprouted seeds.

Why the others miss:
  • A: This is not the difference; 15 - 8 is not 3.
  • C: 8 is the control's count, not the difference between groups.
  • D: 15 is the fertilizer count alone; you must subtract the control.

Aligned to NGSS SEP-4: compare treatment to control · reading level ~grade 9

A group tests whether a disinfectant kills bacteria. Plate A gets disinfectant. Plate B is set up exactly the same but gets no disinfectant. Which choice correctly names the roles?

Reviewed
  1. A.Plate A is the control; Plate B is the experimental group
  2. B.Plate B is the control; Plate A is the experimental group
  3. C.Both plates are controls
  4. D.Neither plate is a control because both have bacteria
Show the worked solution ▾

Answer: B. Plate B is the control; Plate A is the experimental group

  1. Step 1: Find the treatment: The treatment being tested is the disinfectant, which is on Plate A.
  2. Step 2: Find the untreated group: Plate B gets no disinfectant, so it is the control; Plate A is the experimental group.

Why it's right: The group without the treatment is the control, so Plate B (no disinfectant) is the control and Plate A is the experimental group.

Why the others miss:
  • A: This reverses the roles; the treated plate is not the control.
  • C: The two plates have different roles, so they cannot both be controls.
  • D: Having bacteria does not disqualify a plate from being a control; the untreated plate is still the control.

Aligned to AP Bio SP 3: assign control vs experimental · reading level ~grade 9

Two plant groups are meant to test fertilizer. The control group sits by a cold north window; the fertilizer group sits on a warm heated shelf. Everything else is the same. What is the flaw in this design?

Reviewed
  1. A.Nothing is wrong; only the fertilizer differs
  2. B.Temperature was not controlled, so it could explain a difference instead of the fertilizer
  3. C.The control group should also get fertilizer
  4. D.The experiment has too many plants
Show the worked solution ▾

Answer: B. Temperature was not controlled, so it could explain a difference instead of the fertilizer

  1. Step 1: List what differs between groups: The groups differ in TWO ways: fertilizer AND temperature (cold window vs warm shelf).
  2. Step 2: Spot the uncontrolled variable: Because temperature also changed, you cannot tell whether fertilizer or warmth caused any difference. Temperature should have been a controlled variable.

Why it's right: A controlled experiment changes only the treatment; here temperature also changed, so it is an uncontrolled variable that could explain the results instead of the fertilizer.

Why the others miss:
  • A: Two things differ (fertilizer and temperature), so it is not a fair test.
  • C: If the control got fertilizer too, there would be no untreated baseline at all.
  • D: The number of plants is not the flaw; the uncontrolled temperature is.

Aligned to NGSS SEP-3: identify an uncontrolled variable · reading level ~grade 9

Where you'd see this
  • A microbiology class keeps two agar plates identical (same medium, same incubation) and applies disinfectant to only one, so any difference in bacterial growth points to the disinfectant.
  • A greenhouse team gives every tray the same light and water and changes only the fertilizer, so the harvest difference can be blamed on the fertilizer.
  • A student peer-reviews a classmate's design and catches that the two groups were kept at different temperatures, flagging temperature as uncontrolled.
Video library
Watch: control group vs experimental group
Control Group Vs Experimental Group (Easy Explanation)
Helpful Professor Explains! · 3:46
Watch: controls and controlled variables
Experimental Design
Bozeman Science · 17:53
Extension: placebos and positive vs negative controls
Introduction to experimental design | High school biology | Khan Academy
Khan Academy · 9:00
Guided notes

Fill these in as you work through the lesson.

Big idea: A controlled experiment compares an experimental group that gets the treatment against a control group that does not, while every other variable is held the same, so any difference can be traced to the treatment.
Key terms: write the meaning
  • Control group (the group with no treatment (baseline)):  
  • Experimental group (the group that gets the treatment):  
  • Controlled variable (kept the same for both groups):  
  • Confounding (two variables changed at once):  
The rule

In a controlled experiment, the   group does not get the treatment, the   group does, and every other condition is a   variable kept the same, so any difference points to the  .

Check yourself
  1. In a fertilizer plant study, name the treatment, the control group, and two variables you would keep the same. 
  2. A positive control should ____ and a negative control should ____; explain what it means if each one behaves the wrong way. 
  3. Give an example of a design where two variables change at once, and explain why its results are confounded. 
Work one example

A study gives 20 seeds plain water (control) and 20 seeds fertilizer, keeping light and water amount the same. Control: 8 sprout. Fertilizer: 15 sprout. The number of extra seeds that sprouted with fertilizer is 15 - 8 = ____ seeds, and because only the fertilizer differed, that difference can be credited to the ____.

 
Illustrated glossary

The vocabulary of this topic, shown in the way you will meet it.

Control group
The group in an experiment that does not get the treatment, used as the baseline you compare the treated group against.
Two boxes: a control group getting plain water and no fertilizer, and an experimental group getting water plus fertilizer
In context: In a fertilizer trial, the control group of plants gets plain water so the scientist can see how tall plants grow with no fertilizer at all.
Experimental group
The group that receives the treatment you are testing, so you can see what the treatment does.
In context: The experimental group of mice received the new drug, while the control group received none, and the two were compared after two weeks.
Controlled variable
A condition kept exactly the same for every group so it cannot explain any difference in the results. Also called a constant.
A list of controlled variables kept the same for both groups: light, water amount, pot size, soil type, temperature, plant age
In context: Light, water amount, pot size, and soil were controlled variables kept identical for both plant groups, so only the fertilizer differed.
Placebo
A fake treatment with no active ingredient (like a sugar pill) given to the control group so it goes through the same experience as the treated group.
In context: Half the patients got the real pill and half got a placebo, so any improvement from simply believing you took medicine happened in both groups.
Positive control
A group or sample you set up to get a known, expected result, so you can trust that the experiment is working.
In context: A well already known to contain the target gene serves as the positive control: if it does not light up, the test itself failed, not the sample.
Negative control
A group or sample with no reason to react, used to prove the setup does not give a false positive on its own.
In context: A tube of pure water is the negative control in PCR: if it shows a band, the reagents are contaminated and every result is suspect.