Statistics: Experimental Design: Control Groups and Confounds Worksheet

Question 1

A researcher wants to test whether a new fertilizer increases tomato plant growth. She gives the fertilizer to 30 tomato plants and gives no fertilizer to another 30 tomato plants. After six weeks, she compares the average plant heights. Identify the treatment group, the control group, the explanatory variable, and the response variable.

Accepted Answer

The treatment group is the 30 plants that receive the new fertilizer. The control group is the 30 plants that receive no fertilizer. The explanatory variable is whether a plant receives fertilizer, and the response variable is plant height after six weeks.

Question 2

A school compares test scores from students who choose to attend an after-school tutoring program with scores from students who do not attend. The tutoring group has higher scores. Explain why this study does not prove that tutoring caused the higher scores.

Accepted Answer

This study does not prove causation because students chose whether to attend tutoring. The students who attended may have been more motivated, had more parent support, or had different prior achievement levels. These differences could confound the relationship between tutoring and test scores.

Question 3

A pharmaceutical company tests a new allergy medicine. Half of the volunteers receive the medicine, and half receive a sugar pill that looks identical. Neither the volunteers nor the doctors measuring symptoms know who received which pill. What are the control group, placebo, and blinding features in this experiment?

Accepted Answer

The control group is the group that receives the sugar pill. The placebo is the sugar pill that looks like the real medicine but has no active ingredient. The experiment is double-blind because neither the volunteers nor the doctors measuring symptoms know which treatment each person received.

Question 4

A teacher wants to know whether playing classical music during class improves quiz scores. She plays music during her first-period class but not during her fifth-period class. The first-period class scores higher. Identify one possible confounding variable and explain how it could affect the results.

Accepted Answer

One possible confounding variable is the time of day. Students in first period and fifth period may differ in alertness, schedule, or class composition. If these differences affect quiz scores, then the higher scores may not be caused by the music alone.

Question 5

A fitness app company tests whether reminder notifications increase daily step counts. It randomly assigns 500 users to receive reminders and 500 users to receive no reminders. Explain why random assignment is important in this experiment.

Accepted Answer

Random assignment is important because it helps create similar groups before the treatment begins. It reduces the chance that differences such as age, fitness level, or motivation are systematically different between the reminder and no-reminder groups.

Question 6

A study finds that people who drink more coffee also tend to report higher stress levels. The researchers conclude that coffee causes stress. Identify a possible confounding variable and explain why the conclusion may be flawed.

Accepted Answer

A possible confounding variable is job workload. People with demanding jobs may drink more coffee and also feel more stress. Because workload could be related to both coffee consumption and stress, the study cannot conclude that coffee causes stress without stronger experimental control.

Question 7

A company tests two website designs to see which leads to more purchases. Visitors are randomly sent to either Design A or Design B, and the company records whether each visitor buys something. Identify the explanatory variable, response variable, and control group, if any.

Accepted Answer

The explanatory variable is the website design shown to each visitor. The response variable is whether the visitor makes a purchase. There may not be a true control group unless one design is the current standard design used for comparison.

Question 8

A researcher tests a new study strategy by asking volunteers to use the strategy for one month, then comparing their exam scores with their scores from the previous month. Name one weakness of this design and suggest an improvement.

Accepted Answer

One weakness is that other changes over time, such as easier material or more study time, could affect exam scores. An improvement would be to randomly assign similar students to use the new strategy or continue their usual strategy during the same time period.

Question 9

A medical researcher wants to test a blood pressure drug. Patients are grouped by age category first, then randomly assigned within each age category to either the drug group or the placebo group. What type of design is this, and why might it be useful?

Accepted Answer

This is a randomized block design because patients are grouped by age category before random assignment. It is useful because age may affect blood pressure, so blocking by age helps make fairer comparisons within similar age groups.

Question 10

A gardener tests whether a new watering schedule helps flowers bloom. She gives the new schedule to plants on the sunny side of the yard and the old schedule to plants on the shady side. Explain the confounding problem.

Accepted Answer

Sunlight is confounded with the watering schedule because all plants with the new schedule are in the sunny location and all plants with the old schedule are in the shady location. If the sunny plants bloom more, it is unclear whether the cause is the watering schedule or the amount of sunlight.

Question 11

A psychologist tests whether a short meditation exercise reduces anxiety. Participants are randomly assigned to meditate for 10 minutes or sit quietly for 10 minutes. Then they complete an anxiety survey. Why is the quiet-sitting group a better control group than having no comparison group at all?

Accepted Answer

The quiet-sitting group provides a baseline for comparison and controls for the effect of taking a 10-minute break. This makes it easier to determine whether meditation itself has an effect beyond simply resting quietly.

Question 12

A nutrition study compares people who eat breakfast daily with people who skip breakfast. Breakfast eaters tend to have lower body weight. Explain why this observational study may be affected by confounding.

Accepted Answer

This observational study may be affected by confounding because breakfast habits may be related to other lifestyle factors, such as exercise, sleep, income, or overall diet quality. Those factors could also affect body weight, so breakfast alone may not be the cause.

Question 13

A researcher wants to compare two math teaching methods. Each of 20 teachers teaches one class using Method A and another similar class using Method B. The order of methods is randomly chosen for each teacher. Explain why this matched design may be helpful.

Accepted Answer

This matched design is helpful because each teacher serves as a match for themselves across the two methods. It reduces the effect of teacher differences, such as teaching style or experience, because both methods are tested with the same teacher.

Question 14

A sleep researcher studies whether a blue-light filter improves sleep. Participants are randomly assigned to use either a real blue-light filter or an app that looks the same but does not change the screen color. Participants do not know which app they have. Identify the placebo and explain its purpose.

Accepted Answer

The placebo is the app that looks like a blue-light filter but does not actually change the screen color. Its purpose is to control for the placebo effect, so researchers can compare the real filter against the effect of believing that a sleep-improving app is being used.

Question 15

Design a simple randomized experiment to test whether drinking a sports drink before a workout improves running endurance compared with drinking water. Include the treatment group, control group, random assignment, and response variable.

Accepted Answer

A good design would randomly assign runners to drink either the sports drink or water before a workout. The treatment group would drink the sports drink, and the control group would drink water. The response variable could be the time each runner can run at a set pace or the distance completed before stopping.

Statistics: Experimental Design: Control Groups and Confounds

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