• Although this lesson analyzes the same data as a prior lesson (Lesson 4.A.3), the materials are designed without presuming that students have seen the prior lesson. So, instructors can use this lesson even if they haven’t used the prior lesson. However, instructors who have used the prior lesson with their students can save time in class by only briefly covering the Identifying Matched Pairs section, since the same material was also covered in the prior lesson.
• The large majority of climate scientists report that climate change is real and currently happening. However, rather than beginning the lesson with that final conclusion, it’s more powerful to allow students to openly analyze the argument and data from State of Fear. This provides them the opportunity to apply principles of statistical reasoning to identify the “cherry-picked” data in the book. Then, later in the lesson, students get the opportunity to see evidence of warming from a more representative sample of temperature stations across the globe.
• Since students previously analyzed these data using a confidence interval, it can be powerful to use the repeated context to highlight the different questions answered by confidence intervals and hypothesis tests. A confidence interval identifies an interval of plausible values for the true mean difference, while a hypothesis test evaluates whether there is convincing evidence that the true mean difference isn’t 0. The discussion at the end of the lesson provides an opportunity to connect the two approaches and show how their conclusions are consistent.

First, download this lesson's Handout Key and read through its Discussion Question section. Then, check out our model discussion norms and the additional background notes below.

• Encourage students to move beyond simply stating that the two conclusions “agree” and explain why they agree. In particular, it may help to have students informally look at the dotplot of sampled temperature differences once more. Ask students: “Just based on this dotplot and the sample mean, would you have guessed that the confidence interval would be entirely above zero? Why or why not? Would you have guessed that the null hypothesis would be rejected? Why or why not?” This return to the raw data and reasoning from baseline statistics will help build the conceptual connection between confidence intervals and hypothesis tests.

• The data in this lesson come from NASA’s GISS surface temperature data set. Specifically, we utilize the "Adjusted cleaned" dataset from NASA, which they describe as "adjusted data after removal of some outliers and duplicate records.“ Michael Crichton appears to use the unadjusted and uncleaned data in the chart displayed in State of Fear, but the patterns at Punta Arenas and other areas are largely the same.
• NASA’s GISS Surface Temperature Analysis (GISTEMP) provides NASA’s own estimates of changes in global surface temperature using data from weather stations and other sources around the world. Estimating global temperature change can be complex, as temperature patterns can vary by location, elevation, measurement instrument, and other characteristics. GISTEMP therefore uses temperature anomalies and methods designed to account for uneven geographic coverage and other sources of variation. NASA publicly documents its data, methodology, and uncertainty estimates. For additional background, see NASA’s GISTEMP website.
• State of Fear provides a useful example of how cherry-picking can occur without fabricating or incorrectly reporting data. The Punta Arenas temperatures shown in the book are real, but the station does not appear representative of the broader pattern. In the random sample used in the lesson, most stations experienced warming and the mean temperature difference was positive.

• In matched pairs data, the pairing itself contains information. Observations are paired because they share something meaningful, such as coming from the same person or location, or from individuals deliberately matched on relevant characteristics. Analyzing differences within pairs can account for some of the variation associated with those shared characteristics, allowing the analysis to focus more directly on the comparison of interest. This connects to the broader statistical idea of controlling for extraneous variables.
• Students can sometimes confuse inference for matched pairs (the mean of differences) with inference for two-samples (the difference between two means). However, inference for two-samples will be covered in a later lesson, and so the distinction doesn’t need to be broached here. The first two-sample lesson in Unit 4, Part B of the course will include practice problems that cover distinguishing between matched-pairs and two-sample scenarios.