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Lesson plan Grade 11 Careers & CTE

Did Tallowdean's Washer Rebate Save Water? A Study Design Lesson

A 60-minute grade 11 careers lesson in which students act as a conservation analyst, estimating rebate savings with a comparison group and sorting study designs.

Objectives

  1. Students will calculate mean and percent reduction in water use for a rebate group and a comparison group.
  2. Students will estimate program savings by subtracting the comparison group's change from the rebate group's change.
  3. Students will classify sample surveys, experiments, and observational studies and explain the role of randomization in each.

Vocabulary

Key words: comparison group, observational study, randomization, self-selection, cost of saved water

Teacher overview

Utilities spend substantial sums on conservation rebates, and someone has to report whether that spending produced measurable savings. The report is primarily a statistics problem, because participating households differ from non-participating households in ways that have nothing to do with the rebate. This lesson has students act as the conservation analyst for the fictional Tallowdean Municipal Water, computing savings two ways and then sorting three proposed follow-up studies by design. The misconception this lesson corrects is reading the participants' before-and-after drop as the program's effect; the same summer brought drought messaging to everyone, so part of the drop would have happened without a single rebate check.

Procedure

Hook (5 min): Write on the board that the fictional Tallowdean utility's rebate households cut their water use by about 10 percent after the program, and ask whether that settles the question of whether the rebate worked. Take three responses. If nobody raises the possibility that other households also cut back, prompt with the question of what the rest of the town was doing that same summer.

Direct instruction (12 min): Introduce the comparison-group idea. Explain that an analyst subtracts the change in a group that did not receive the rebate from the change in the group that did, and that the remainder is the estimate attributed to the program. Then name the three study types students will classify later. A sample survey asks a randomly chosen subset of a population about itself. An experiment assigns a treatment to units, ideally at random, and compares outcomes. An observational study compares groups that formed themselves. Emphasize that only the experiment can randomize who gets the treatment, and that this is what lets it support a causal claim.

Guided practice (15 min): Distribute the handout. Complete items 1 through 4 as a class, checking that students divide the reduction by the before value rather than the after value when computing percent reduction. Formative check: poll the class on whether the comparison group's 3.0 percent reduction should be subtracted from or added to the rebate group's figure, and do not proceed until at least four-fifths answer "subtracted." If fewer do, redraw the two before-and-after bars on the board and label the gap.

Independent work (20 min): Students complete items 5 through 12 in pairs. Circulate and listen for pairs who classify the smart controller trial as an observational study because the households volunteered; steer them to the distinction that volunteers were then assigned at random, which is what makes it an experiment even though the volunteer pool is not representative.

Closure and exit ticket (8 min): Ask two pairs to read their answers to item 11 aloud, then have every student write a one-sentence exit response naming which figure they would print in the fictional utility's annual report and why. Collect the cards and sort them into those citing the comparison-group estimate and those citing the raw participant drop, which gives a quick read on whether the main idea landed.

Did Tallowdean's Washer Rebate Save Water? A Study Design Lesson — Grade 11 Careers & CTE
Name: ____________________________ Date: ______________

Student Handout

The fictional Tallowdean Municipal Water offered a $200 rebate toward a high-efficiency clothes washer. Forty households took the rebate. The analyst pulled meter records for those 40 households and for 40 non-participating households in the same neighborhoods, comparing the same three summer months before and after the program.

Group Households Mean monthly use before (gal) Mean monthly use after (gal)
Rebate participants 40 7,600 6,850
Non-participants 40 7,500 7,275

The analyst is also weighing three follow-up studies for next year:

  • Study 1: mail a questionnaire to 500 randomly selected customers asking whether they changed their outdoor watering habits this summer.
  • Study 2: recruit 100 volunteer households, assign half at random to receive a smart irrigation controller and half to receive nothing, and compare their metered use next summer.
  • Study 3: compare the metered use of households that chose the washer rebate with the metered use of households that did not.
  1. Find the mean monthly reduction, in gallons, for the rebate participants.
  2. Find that reduction as a percent of the participants' before value. Round to the nearest tenth of a percent.
  3. Find the mean monthly reduction, in gallons, for the non-participants.
  4. Find that reduction as a percent of the non-participants' before value. Round to the nearest tenth of a percent.
  5. Estimate the monthly savings per household attributable to the rebate by subtracting the non-participants' reduction from the participants' reduction.
  6. Using your answer from item 5, find the total gallons saved by all 40 rebate households over 12 months.
  7. The utility paid $200 to each of the 40 households. Using your answer from item 6, find the first-year cost of saved water in dollars per 1,000 gallons. Round to the nearest cent.
  8. Classify Study 1 as a sample survey, an experiment, or an observational study.
  9. Classify Study 2 as a sample survey, an experiment, or an observational study.
  10. Classify Study 3 as a sample survey, an experiment, or an observational study.
  11. The utility's newsletter editor wants to publish the percent from item 2 as the program's result. Write three or four sentences advising the editor, naming which figure you would publish and what the other figure actually measures.
  12. Explain in two or three sentences what randomization accomplishes in Study 2 that it cannot accomplish in Study 3.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 750 gallons per month.
    7,600 gallons minus 6,850 gallons equals 750 gallons per household per month.
  2. Answer: 9.9 percent.
    750 divided by 7,600 equals 0.098684, which rounds to 9.9 percent.
  3. Answer: 225 gallons per month.
    7,500 gallons minus 7,275 gallons equals 225 gallons per household per month.
  4. Answer: 3.0 percent.
    225 divided by 7,500 equals 0.03, or 3.0 percent.
  5. Answer: 525 gallons per household per month.
    750 gallons minus 225 gallons equals 525 gallons. The 225 gallons the non-participants saved represents whatever the whole neighborhood was responding to that summer, so subtracting it leaves the part plausibly attributable to the rebate.
  6. Answer: 252,000 gallons.
    525 gallons times 12 months equals 6,300 gallons per household per year, and 6,300 times 40 households equals 252,000 gallons.
  7. Answer: $31.75 per 1,000 gallons.
    The program paid 40 times $200, or $8,000. The savings of 252,000 gallons is 252 thousand-gallon units. Then $8,000 divided by 252 equals $31.746, which rounds to $31.75 per 1,000 gallons for the first year. Because the washers keep saving after year one, the analyst would normally spread the cost across the appliance's expected life instead.
  8. Answer: Sample survey.
    Study 1 draws a random subset of the customer population and asks its members to report on themselves. Nothing is assigned and no treatment is applied, so it estimates what customers say about their own behavior, not what any program caused.
  9. Answer: Experiment.
    Study 2 assigns the controller at random among the volunteers, which makes it an experiment. The volunteer pool is not a random sample of all customers, so the result generalizes cautiously, but the random assignment within that pool is what supports a causal comparison.
  10. Answer: Observational study.
    Households in Study 3 sorted themselves into rebate takers and non-takers. The analyst observes two groups that already existed rather than assigning anyone, so any difference may reflect who chooses rebates rather than what the rebate does.
  11. Answer: Publish the comparison-group estimate rather than the 9.9 percent figure.
    The 9.9 percent measures how much participating households changed, which includes drought messaging, weather, and rate changes that reached everybody. The non-participants dropped 3.0 percent with no rebate at all, which is a direct measurement of that background change. Reporting 525 gallons per household per month, or roughly 6.9 percent of the before value, tells readers what the rebate itself appears to have bought. The 9.9 percent figure can still appear in the report as long as it is labeled as the participants' total change rather than the program's effect.
  12. Answer: Random assignment makes the two groups comparable before the treatment, which self-selection cannot do.
    In Study 2 the coin flip decides who gets a controller, so the two groups start out alike in the ways that matter and in the ways nobody thought to measure. In Study 3 the households decided for themselves, and the ones who pursued a rebate are likely already more attentive to their water use, so part of any measured difference belongs to that attentiveness rather than to the washer.

Differentiation

Support

Give students the two percent reductions from the fictional program already computed so they can begin the subtraction in item 5, and supply a two-bar diagram showing the before and after means for each group with the two drops shaded, which makes the subtraction in item 5 visible rather than abstract.

Extension

Ask students to recompute the fictional program's cost of saved water assuming each washer keeps saving at the same rate for 11 years, then explain in writing why utilities commonly report cost of saved water over an appliance's life rather than over its first year.

ELL supports

Pre-teach "comparison group," "self-selection," "randomization," and "attributable" with a two-column diagram showing how households enter each group in Study 2 and in Study 3. Provide the sentence frame "Study ___ is a ___ because the households were ___" for items 8 through 10.