Speed feedback signs on residential streets

Use the given information to respond to parts A, B, C, D, E, and F. Label any subparts (e.g., i and ii) that may be present.

1. A.

   i. Identify the experimental units in the study.

   ii. Identify the explanatory variable and the response variable in the study.

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   Score part A

   • 1 point Identifies the experimental units as the 24 residential street segments selected for the study.Earns it: "the 24 street segments"; "the residential street segments selected for the study"Does not: "the drivers" (the signs are assigned to segments, not to drivers); "the 300 street segments" (those make up the population; only 24 segments are in the study); "the feedback signs" (the sign is the treatment, not the unit)
   • 1 point Identifies the explanatory variable as whether a segment has a feedback sign, and the response variable as the speed of the vehicles on the segment (the mean speed over the four weeks). Both variables must be identified correctly.Earns it: "Explanatory: sign or no sign. Response: mean speed of vehicles on the segment."; "Explanatory: whether the segment gets a feedback sign. Response: vehicle speeds recorded on the segment."Does not: "Explanatory: the street segments. Response: speed." (the segments are the units, not a variable); "Explanatory: speed. Response: the sign." (the variables are reversed); "Response: whether drivers slow down" (vague; the measured response is the mean speed)

   Model response

   i. The experimental units are the 24 randomly selected residential street segments.

   ii. The explanatory variable is whether a segment has a feedback sign (sign or no sign). The response variable is the mean speed of the vehicles recorded on the segment over the four weeks.

2. B.

   Describe how the engineers could randomly assign the feedback signs to 12 of the 24 selected segments using a completely randomized design.

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   Score part B

   • 1 point Describes a random mechanism that gives signs to exactly 12 different segments and leaves the other 12 without signs, in enough detail that someone else could carry it out. A method that draws random numbers must say what happens to repeated numbers.Earns it: "Number the segments 1 to 24. Use a random number generator to choose 12 different integers from 1 to 24, ignoring repeats. Those segments get signs and the rest do not."; "Write the 24 segment names on identical slips, mix them in a bag, and draw 12 slips without replacement. Those segments get signs."Does not: "Randomly choose 12 segments to get signs." (no random mechanism is described); "Flip a coin for each segment, heads gets a sign." (does not guarantee 12 segments in each group); "Use a random number generator to pick 12 numbers from 1 to 24." (repeats are not addressed, so fewer than 12 segments might be chosen)

   Model response

   Number the 24 segments from 1 to 24. Use a random number generator to produce integers from 1 to 24, ignoring repeats, until 12 different numbers have been chosen. Install feedback signs on the 12 segments with those numbers, and leave the other 12 segments without signs.

3. C.

   The engineers notice that 8 of the 24 selected segments are within two blocks of a school, where drivers tend to slow down even without a sign.

   i. Describe an experimental design that accounts for whether a segment is near a school, including how the signs would be assigned.

   ii. Explain why the design you described in (i) would be better for this study than a completely randomized design.

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   Score part C

   • 1 point Describes a randomized block design with blocks formed by school proximity (the 8 segments near a school and the 16 other segments) and with signs randomly assigned within each block, such as 4 of the 8 near-school segments and 8 of the 16 other segments. A matched pairs design that pairs segments with the same school proximity and randomly assigns the sign within each pair also earns the point.Earns it: "Block by school: 8 near-school segments and 16 others. Randomly pick 4 of the 8 and 8 of the 16 to get signs."; "Randomized block design with near-school segments as one block and the rest as the other; within each block, randomly assign half of the segments to get a sign."Does not: "Block by whether the segment is near a school." (does not say that signs are randomly assigned within each block); "Put signs on the 8 segments near schools and 4 others." (no random assignment, and school proximity is then mixed up with the sign); "Stratify the segments by school." (stratifying is a sampling method, and no assignment of signs is described)
   • 1 point Explains that being near a school affects vehicle speeds, so blocking compares segments with and without signs among similar segments. The response must connect the benefit to school proximity: blocking separates the variation in speed caused by school proximity from the effect of the signs, giving a more precise comparison, or it prevents a chance imbalance of near-school segments between the two groups.Earns it: "Speeds near schools are lower anyway. Blocking keeps that variation out of the comparison of sign and no sign, so the effect of the signs is estimated more precisely."; "With complete randomization, most of the near-school segments could end up with signs by chance, making the signs look better than they are. Blocking prevents that."Does not: "Blocking reduces bias." (vague; does not connect to school proximity or to variation in speed); "Blocking lets the engineers generalize to more streets." (generalization comes from random selection, not blocking)

   Model response

   i. Use a randomized block design. Put the 8 segments near a school in one block and the other 16 segments in a second block. Within the school block, randomly choose 4 segments to get signs, for example by drawing 4 of 8 numbered slips from a bag. Within the other block, randomly choose 8 of the 16 segments to get signs the same way. The remaining segments get no sign.

   ii. Speeds are likely to be lower near schools with or without a sign. With complete randomization, chance could put most of the near-school segments in the sign group and make the signs look more effective than they are. Blocking compares sign and no sign within similar segments, so the variation in speed due to school proximity is separated from the effect of the signs, which gives a more precise comparison.

4. D.

   Explain why the engineers can generalize the results of their study to all 300 residential street segments in Harlow with a 25 mph speed limit.

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   Score part D

   • 1 point Explains that the 24 segments in the study were randomly selected from all 300 segments, so they are likely to be representative of all 300 segments.Earns it: "The 24 segments were randomly selected from the 300, so they should represent all 300 segments."Does not: "Because the signs were randomly assigned." (random assignment supports cause and effect, not generalization to a population); "Because 24 segments is a large enough sample." (sample size does not make a sample representative)

   Model response

   The engineers used a random number generator to choose the 24 segments from all 300 residential segments with a 25 mph limit. Because the segments in the study were randomly selected, they should be representative of all 300 segments.

5. E.

   Instead of random assignment, a city council member suggests putting the 12 signs on the selected segments where residents have complained the most about speeding. Explain why this plan would make it difficult to conclude that the signs caused any difference in mean speeds.

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   Score part E

   • 1 point Explains that the segments with the most complaints may differ from the other segments in ways that affect speed (for example, drivers may already go faster on them), so a difference in mean speeds could be caused by those differences rather than by the signs. The response must connect the nonrandom placement of the signs to an alternative explanation for a difference in speeds.Earns it: "Complaints probably come from streets where drivers already speed, like wide, straight streets. Then the type of street, not the sign, could explain a difference in mean speeds."Does not: "That plan is biased." (does not explain how the placement would affect the comparison); "Residents who did not complain would be upset." (not a statistical reason); "There would not be enough segments in each group." (both groups still have 12 segments)

   Model response

   The segments with the most complaints are probably the ones where drivers already go fastest, such as wide, straight streets with through traffic. If only those segments get signs, the type of street is mixed up with the sign, so a difference in mean speeds could be caused by the type of street rather than the signs. Random assignment would spread these streets across both groups.

6. F.

   Determine a valid investigative question for the engineers' study. Ensure all three components of a valid investigative question are included in your response.

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   Score part F

   • 1 point First component: identifies the variables of interest as whether a segment has a feedback sign and the speed of the vehicles on the segment.Earns it: "feedback sign or no sign, and vehicle speed"; "whether a segment has a sign and the mean speed of vehicles on it"Does not: "signs" (the speed variable is missing); "speed" (the sign variable is missing)
   • 1 point Second component: identifies the parameter as the mean speed and the direction of the comparison as lower for segments with a sign than for segments without a sign.Earns it: "the mean speed is lower for segments with a sign than for segments without a sign"Does not: "speeds are lower with a sign" (no parameter; the question should be about mean speed); "mean speeds are different with and without a sign" (the engineers want to know whether signs reduce speeds, so the direction is lower); "mean speeds are equal" (this describes no effect, not the question being investigated)
   • 1 point Third component: identifies the population as all residential street segments in Harlow with a 25 mph speed limit and states the conclusion as cause and effect, for example by asking whether installing a sign causes lower mean speeds.Earns it: "Does installing a sign cause lower mean speeds on Harlow's residential segments with a 25 mph limit?"Does not: "all streets in Harlow" (includes streets that are not residential 25 mph segments); "the 24 segments in the study" (that is the sample, not the population); "Is a sign associated with lower mean speeds on Harlow's 25 mph residential segments?" (random assignment allows a cause-and-effect question, and the response does not ask one)

   Model response

   Does installing a radar speed feedback sign cause the mean speed of vehicles on Harlow's residential street segments with a 25 mph speed limit to be lower than the mean speed on those segments without a sign?

Your score: 0 of 10. Each point is earned on its own, the way the exam scores it.