Mathematics
Grade 11
15 min
Experiment design
Experiment design
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1
Introduction & Learning Objectives
Learning Objectives
Distinguish between an observational study and a controlled experiment.
Identify explanatory, response, and potential confounding variables in a given scenario.
Explain the three core principles of experimental design: control, randomization, and replication.
Describe and differentiate between completely randomized, block, and matched pairs designs.
Identify potential sources of bias in an experimental setup.
Design a simple, valid experiment to test a hypothesis.
Does a new fertilizer *really* make plants grow taller? 🌱 How can we design a fair test to prove it without being fooled by other factors like sunlight or soil type?
This tutorial introduces the fundamental principles of experiment design. You will learn how to structure scientific studies to...
2
Key Concepts & Vocabulary
TermDefinitionExample
Observational Study vs. ExperimentIn an observational study, we observe subjects and measure variables of interest without assigning treatments. In an experiment, we deliberately impose a treatment on subjects to measure their responses.Observing the health of people who choose to drink coffee vs. those who don't is an observational study. Randomly assigning people to drink coffee or not and then measuring their health is an experiment.
Explanatory & Response VariablesThe explanatory variable (or factor) is what we manipulate or believe explains changes in another variable. The response variable is the outcome we measure to see the effect of the treatment.In a study testing a new fertilizer, the type of fertilizer (new vs. old) is the explanatory variable, a...
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Core Formulas
The Three Principles of Experimental Design
1. Control 2. Randomize 3. Replicate
These are the three pillars of a valid experiment. Control for lurking variables by comparing two or more treatments. Randomize the assignment of subjects to treatments to spread out confounding factors. Replicate the experiment on many subjects to reduce chance variation in the results.
Margin of Error Approximation
E \approx \frac{1}{\sqrt{n}}
This formula provides a rough estimate for the margin of error (E) in a simple random sample, where 'n' is the sample size. It demonstrates the principle of replication: as the number of subjects (n) increases, the margin of error decreases, making your results more reliable.
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Challenging
How do the three principles of experimental design (control, randomization, replication) work together to establish a cause-and-effect relationship?
A.Control creates a large sample, randomization makes it representative, and replication ensures blinding.
B.Control isolates the treatment effect, randomization minimizes confounding, and replication ensures reliability.
C.Control ensures blinding, randomization creates a baseline, and replication reduces the placebo effect.
D.Control minimizes bias, randomization increases sample size, and replication allows for a baseline comparison.
Challenging
A researcher is testing two different types of fertilizer on a new species of plant. The experimental field has a known moisture gradient, being wetter on the east side and drier on the west. To get the most accurate results, which design is superior to a completely randomized design and why?
A.double-blind study, because it will eliminate the moisture's effect on the researcher.
B.matched pairs design, pairing each plant with itself.
C.block design, using vertical strips of land (e.g., East, Center, West) as blocks, to control for the moisture variable.
D.completely randomized design is still best because it is the simplest to implement.
Challenging
In a year-long study of a new diet pill, researchers conduct a double-blind, placebo-controlled experiment. They find a statistically significant weight loss in the treatment group. However, their data shows that 50% of the placebo group dropped out of the study, compared to only 10% of the treatment group. How does this high, differential dropout rate (attrition) most likely bias the conclusion?
A.It has no effect on the conclusion because the study was double-blind.
B.It likely underestimates the pill's true effect because many successful placebo users left.
C.It likely overestimates the pill's true effect because the people who remained in the placebo group might be those for whom the placebo had no effect, making the group's average worse.
D.It invalidates the study entirely, meaning no conclusion can be drawn whatsoever.
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