{ "format": "recallweave-deck/1", "title": "Reading data and evaluating evidence", "attribution": "Original questions, explanations and fictional examples by the HAMON estate. Statistical definitions and study-design principles were checked against OpenStax, Introductory Statistics 2e, sections 1.2, 1.4 and 2.5 (Barbara Illowsky and Susan Dean). No textbook question, example dataset or passage is reproduced. References and independent derivations are in courses/reading-data-and-evidence.md.", "license": "Original course text and fictional examples: CC BY 4.0. The cited reference textbook has its own license; see the course guide.", "concepts": [ "Rates and denominators", "Summaries and spread", "Comparisons and context", "Study design" ], "items": [ { "id": "rates-1", "concept": "Rates and denominators", "prerequisites": [], "prompt": "At Library A, 24 of 80 workshop participants finished a project. At Library B, 30 of 120 finished. Which library has the higher observed completion percentage?", "options": [ "Both: 30%, despite different group sizes.", "B: 30%, compared with A: 25%.", "A: 30%, compared with B: 25%.", "B, because six more participants finished." ], "answer": 2, "explanation": "Use each library's own participant count: 24/80 = 0.30 and 30/120 = 0.25. B has more completions but a lower completion percentage. These are descriptive results for these groups, not proof that one workshop caused better outcomes.", "transfer": "An announcement compares 45 successes with 36 successes. What two additional counts would you request before comparing success rates?" }, { "id": "rates-2", "concept": "Rates and denominators", "prerequisites": [], "prompt": "A club's participation rate rises from 40% to 50%. Which statement correctly separates the percentage-point change from the relative percentage increase?", "options": [ "10 percentage points; a 25% relative increase.", "10 percentage points; a 10% relative increase.", "25 percentage points; a 10% relative increase.", "25 percentage points; a 25% relative increase." ], "answer": 0, "explanation": "The rate changes by 50% - 40% = 10 percentage points. Relative to the original 40%, the increase is (50 - 40)/40 = 0.25, or 25%. A percentage-point difference and a relative percentage change use different comparisons.", "transfer": "A rate falls from 20% to 15%. State the percentage-point decrease and the relative percentage decrease, naming the original-rate denominator." }, { "id": "rates-3", "concept": "Rates and denominators", "prerequisites": [], "prompt": "Service Cedar reports 3 late deliveries, and Service Elm reports 6. No total delivery counts are given. What can these counts alone establish about their late-delivery rates?", "options": [ "Cedar's rate is half Elm's because its late count is half as large.", "Elm's rate is higher because it has three more late deliveries.", "The rates are equal because both services have some late deliveries.", "The rates cannot be compared without the total deliveries for each service." ], "answer": 3, "explanation": "A late-delivery rate divides late deliveries by all deliveries for that service. For example, 3/10 exceeds 6/100, whereas 3/100 is below 6/10. Both examples match the reported late counts. The counts alone therefore do not determine the rate ordering.", "transfer": "Construct two possible pairs of total deliveries that give opposite rate rankings while retaining late counts of 3 and 6." }, { "id": "summary-1", "concept": "Summaries and spread", "prerequisites": [], "prompt": "Five fictional waiting times, in minutes, are 4, 5, 5, 6 and 30. What are their arithmetic mean and median?", "options": [ "Mean 5 minutes; median 10 minutes.", "Mean 10 minutes; median 5 minutes.", "Mean 10 minutes; median 6 minutes.", "Mean 6 minutes; median 5 minutes." ], "answer": 1, "explanation": "The sum is 50 minutes, so the arithmetic mean is 50/5 = 10 minutes. The values are already ordered, and the third of five values is 5, so the median is 5 minutes. The long wait raises the mean without changing which observation occupies the middle.", "transfer": "If you had to describe both the usual wait and the long delay, what information would you report beyond a single average?" }, { "id": "summary-2", "concept": "Summaries and spread", "prerequisites": [], "prompt": "In the ordered waiting times 4, 5, 5, 6 and 30 minutes, replace only 30 with 90. What happens to the mean and median?", "options": [ "The mean rises to 22 minutes; the median stays at 5 minutes.", "The mean stays at 10 minutes; the median rises to 22 minutes.", "The mean rises to 22 minutes; the median rises to 17 minutes.", "The mean stays at 10 minutes; the median stays at 5 minutes." ], "answer": 0, "explanation": "Increasing one value by 60 raises the five-value sum from 50 to 110. The new mean is 110/5 = 22, an increase of 12 minutes. The ordered middle value is still 5. This example shows why changing an extreme value can affect the mean more than the median.", "transfer": "Change only the largest of seven ordered values without moving it below another value. Which middle observation determines the median before and after?" }, { "id": "summary-3", "concept": "Summaries and spread", "prerequisites": [], "prompt": "Twelve students read an arithmetic mean of 5 pages each. Three other students read an arithmetic mean of 20 pages each. What is the arithmetic mean across all 15 students?", "options": [ "5 pages per student.", "12.5 pages per student.", "8 pages per student.", "20 pages per student." ], "answer": 2, "explanation": "The first group reads 12 × 5 = 60 pages in total; the second reads 3 × 20 = 60. Across 15 students, the mean is (60 + 60)/15 = 8 pages. Averaging the two group means to get 12.5 would incorrectly give each group the same weight despite different sizes.", "transfer": "When is the unweighted arithmetic mean of two group means equal to the overall mean across all individuals? Give one condition that makes it valid." }, { "id": "context-1", "concept": "Comparisons and context", "prerequisites": [ "Rates and denominators", "Summaries and spread" ], "prompt": "On the same 100-point test scale, Group A's mean moves from 40 before a workshop to 60 after it. Group B's mean moves from 70 to 80. What are the observed increases in group means?", "options": [ "A: 10 points; B: 20 points.", "A: 20 points; B: 10 points.", "A: 20 points; B: 20 points.", "A: 40 points; B: 70 points." ], "answer": 1, "explanation": "Subtract each group's own starting mean: A increases by 60 - 40 = 20 points, and B by 80 - 70 = 10. B's higher final mean is a different comparison. These before-and-after means alone do not establish what would have happened without the workshops.", "transfer": "Write separate sentences describing the final-score comparison and the change-score comparison. What evidence is still missing for a causal claim?" }, { "id": "context-2", "concept": "Comparisons and context", "prerequisites": [ "Rates and denominators", "Summaries and spread" ], "prompt": "Two methods are used by beginners and experienced participants. Method A succeeds for 20 of 80 beginners and 18 of 20 experienced participants. Method B succeeds for 2 of 10 beginners and 72 of 90 experienced participants. Which statement matches these counts?", "options": [ "A has the higher success rate overall and within each experience group.", "B has the higher success rate overall and within each experience group.", "The methods have equal success rates within both experience groups.", "A is higher within each experience group; B is higher when all participants are pooled." ], "answer": 3, "explanation": "For beginners, A is 20/80 = 25% and B is 2/10 = 20%. For experienced participants, A is 18/20 = 90% and B is 72/90 = 80%. Pooled rates reverse: A is 38/100 = 38%, while B is 74/100 = 74%. B's group contains a much larger share of experienced participants. Different group mixtures can reverse an aggregate comparison; none of these counts alone establishes a causal method effect.", "transfer": "If both methods were summarized using an equal 50% weight for beginners and experienced participants, what rate would each method receive? Why must the weighting rule be stated?" }, { "id": "context-3", "concept": "Comparisons and context", "prerequisites": [ "Summaries and spread" ], "prompt": "One group records the values 10, 10, 10 and 10. Another records 0, 0, 20 and 20 in the same units. Which comparison is correct?", "options": [ "Both their means and their individual observed values are equal.", "The second group's mean is larger, but their ranges are equal.", "Their means are equal, but the second group's range is larger.", "The first group's mean is larger because none of its values are zero." ], "answer": 2, "explanation": "Both sums are 40, and both groups have four values, so both means are 10. The first range is 10 - 10 = 0; the second is 20 - 0 = 20. Identical means can hide different distributions. A center summary does not by itself describe variation.", "transfer": "Create a third four-value group with mean 10 and a range between 0 and 20. Check both claims directly." }, { "id": "design-1", "concept": "Study design", "prerequisites": [ "Comparisons and context" ], "prompt": "A newsletter invites readers to reply voluntarily about a new bus timetable. Of the 200 people who reply, 180 say it is useful. What does the calculated 90% directly describe?", "options": [ "The share of all city residents who find the timetable useful.", "The share of these respondents who say the timetable is useful.", "The share of nonrespondents who would find the timetable useful.", "The chance that a different voluntary poll will also report exactly 90%." ], "answer": 1, "explanation": "The observed fraction is 180/200 = 90% of the people who replied. The invitation did not randomly sample all residents, and choosing to respond may relate to the opinion being measured. More replies from the same voluntary process do not guarantee that its respondents represent everyone.", "transfer": "Consider an unweighted voluntary-response poll. Name its target population, the people invited and the people who responded. If the recruitment method or any group is unstated, say what is missing. Which group does its reported respondent percentage directly describe?" }, { "id": "design-2", "concept": "Study design", "prerequisites": [ "Comparisons and context" ], "prompt": "Eighty volunteers are randomly assigned, 40 each, to interface A or B. They perform the same task, and completion time is recorded for everyone. What does random assignment principally help accomplish?", "options": [ "Make the volunteers a random sample of all possible interface users.", "Ensure every baseline trait is exactly balanced in this particular run.", "Ensure that any difference in task time cannot arise through chance variation.", "Prevent baseline traits from systematically deciding the assigned interface." ], "answer": 3, "explanation": "For this random split, interface allocation is independent of participants' baseline traits by design. It helps avoid systematic allocation differences, but a finite random split can still be imbalanced by chance. It neither turns volunteers into a representative random sample nor eliminates chance variation from the assignment. Study conduct and measurement still matter.", "transfer": "Explain the difference between randomly selecting people to join a study and randomly assigning enrolled people to its comparison groups." }, { "id": "design-3", "concept": "Study design", "prerequisites": [ "Comparisons and context" ], "prompt": "Students choose whether to join a study group. Those who join average 75 on a test; those who do not average 65. No earlier achievement or other differences are measured. Which conclusion is supported by this design alone?", "options": [ "The participants scored higher here, but the comparison alone does not establish that joining caused the difference.", "Repeating this voluntary comparison with more students would remove all confounding.", "The lack of random assignment proves that study groups cannot affect scores.", "Joining the study group raises every student's score by exactly 10 points." ], "answer": 0, "explanation": "The observed difference in group means is 10 points. Self-selection could also separate students by earlier preparation, motivation, available time or other factors. The comparison records an association; it does not identify the effect of joining. It also does not prove that joining has no effect. A stronger design would address alternative explanations rather than only enlarge this comparison.", "transfer": "Propose one change to the study that would make the causal question more informative, and state one uncertainty that could still remain." } ] }