AP Stats 1.13 Experimental DesignAP Stats 1.13 Experimental Design

APS TAT ISTICS · UNIT1B

Experimental Design

Topics 1.13A and 1.13B

In one sentence: a well-designed experiment compares treatments, randomly assigns units, replicates, and controls extraneous variables, and you pick a design (completely randomized, block, matched pairs) to make the treatment effect easy to see.

1.13A The four principles

Principle Meaning Missing looks like

Comparison At least two treatment groups (a control group for

baseline)

Everyone gets the wrap, no one to

compare

Random

assignment

Units go to treatments by chance Students choose their own app

Replication More than one unit per treatment One jet with winglets vs one without Direct control Hold extraneous variables the same for all units All Fertilizer A pots in the sun, B in the shade

Trap. Random assignment balances what you cannot control, but it does not make groups identical, and it does not make the sample representative.

Control, placebo, placebo effect

Control group: set aside for comparison. It may get a placebo or no treatment. Placebo: inactive treatment that looks and feels real.

Placebo effect = (average response to placebo) − (average response to no treatment). If pain drops 1.8 with placebo and 0.6 with nothing, the placebo effect is 1.2.

Blinding

Single-blind: participants or the people who interact with and measure them do not know the assignments.

Double-blind: neither participants nor the people who interact with or measure them know. What matters is who interacts with or measures the participants. An analyst who never meets anyone may know the assignments and it is still double-blind.

To isolate the chemical effect, compare real vs placebo. Real vs no treatment mixes the chemical effect with the placebo effect.

1.13B Three designs

Design How it works Purpose

Completely

randomized

Treatments assigned to all units completely at random

(groups need not be equal)

Simplest, fine when units are alike

Randomized

block

Sort units into blocks of similar units (by a variable

related to the response), then randomly assign within

each block, so every treatment is in every block

Separates variation due to the

blocking variable, so comparisons

are more precise

Matched pairs A block design with exactly 2 treatments. Either pair

similar units and randomize within the pair, or give each

unit both treatments in random order

Each unit is its own comparison

Block when you assign treatments, stratify when you sample. A block is not a treatment group. Analyzing matched pairs: use the difference within each pair or subject. Why randomize order: it balances order effects such as fatigue or warm-up.

Conclusions

Random assignment → can conclude the treatment caused a significant difference.

Random selection → can generalize to the population. Most experiments use volunteers, so results apply only to units similar to the volunteers.

Writing a random assignment (FRQ)

1. Number the units 1 to N.

2. Use a random number generator for integers 1 to N, ignoring repeats, until you have n unique numbers. Those get treatment 1.

3. For three groups, pick the next n for treatment 2, and the rest get treatment 3. Worked examples

1. Cafés and cold brew. 40 volunteer cafés, café size affects ratings. Completely randomized could be thrown off by size differences. Block by size (20 large, 20 small), randomize half to 18 hours and half to 12 hours within each block. Cause and effect holds, but generalize only to cafés like the volunteers. 2. Weighted vest, 14 athletes. Each sprints with and without the vest, coin flip for order. Advantage over two groups of 7: athlete-to-athlete speed differences are removed.

3. VR balance game, 60 volunteers. Participants know their treatment, so not double-blind, but therapists giving the stability test can be kept unaware: single-blind.

Practice

1. Airline puts winglets on one jet and compares to one unmodified jet. Which principle is missing? 2. Inactive pill: average reduction 2.0. No treatment: 0.5. New drug: 3.4. Estimate the placebo effect.

3. Cherry drink 14 min, look-alike drink 9, no drink 2. Estimate the chemical effect and the placebo effect.

4. A cyclist rides the same hill at two tire pressures, coin flip for order. Name the design. 5. Tomato plants are sorted into greenhouse and outdoor groups, then watering schedules are randomly assigned within each. Name the design.

6. Why block vineyard vines by slope before choosing a trellis?

7. 24 students do a puzzle with music and one in silence, coin flip for order. How should the data be analyzed?

8. 50 volunteers are randomly assigned two stretching routines. Who can the results be generalized to? Answer key

1. Replication (one unit per treatment).

2. 2.0 − 0.5 = 1.5 points.

3. Chemical effect: 14 − 9 = 5 minutes. Placebo effect: 9 − 2 = 7 minutes.

4. Matched pairs (each unit gets both treatments, order randomized).

5. Randomized block (blocks are greenhouse and outdoor).

6. So differences in sun exposure do not obscure the trellis comparison.

7. Use the difference between the two times for each student.

8. Members similar to those who volunteered. Random assignment still allows cause and effect.