Posts By: admin


Activity: Replot NASA Graph

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Using data from Wolfram Alpha or some other source, replot the NASA graph here either: 1. Controlling for inflation, 2. Tracking expenditure as a percentage of GDP, or 3. Tracking expenditure as a percentage of government spending. Defend your choice, and note any differences in the shape of the graph that result.

death penalty

Activity: Death Penalty Poll

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First, read How to Construct a Bogus Survey. Second, consider this poll from The Washington Post’s website. Walk through what would happen if you set up the poll in various different ways. Be ridiculous where it helps. For the moment, ignore issues of non-response and response bias. Name at least one strength and one weakness […]

Stat Lit Chart of the Day

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Stat Lit Chart of the Day This chart could mean that the more education you get, the more you drink. What is another explanation for the increase in average annual expenditures on alcohol?


Chapter One Introduction

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A Note to Instructors We’ve broken this text up into chapters. In our estimation, each chapter could take one to two weeks depending on how much time in your class is dedicated to other activities and needs. A four-hour, twice-a-week-class with no other content or class-time obligations should be able to do a chapter a […]


Why We Compare

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Which intersection in town is the most dangerous? How much more expensive will college be if I graduate a year late?  Which product line has given our business the best overall return in the past two years?  At what rate is global temperature rising? How expensive was the most recent election compared to previous elections? […]


The Ten Minute Statistical Sprint

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Much of college is about the marathon – the 20-page term paper, the semester-long project. This course is not about marathons. This course is about sprinting. It’s about the 10 minute brainstorming session. It’s about speed chess. What we hope you will develop by the end of this course is the ability to critique a […]


How to Memorize Anything (A Detour)

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Let’s take a brief detour, since we asked you to memorize the above checklist, and since we will be asking you to memorize other things as well. A little instruction here can make your life easier, not just in this class, but in all your classes. Memorization is a lost art. Most students memorize by […]


The Golden Rule: Compare Like to Like When Possible, and Account for Things When Not

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This section deals with the following elements of the COMPARABLE framework: C: Were appropriate comparison groups chosen? Was like compared to like? A1: Which factors were accounted for/controlled for (population, inflation, income) and which were not?  There are many rules that apply to making fair comparisons, but there is one rule that leads, in one […]


Why Comparing Averages Is Just a Starting Point

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This section deals primarily with the following elements of the COMPARABLE framework: E:  What is the story of the edges? What is the story of the center? How are they different and what does that mean?  THE STORY OF THE CENTER We’ve been looking at various comparisons, in many cases using what statisticians call measures […]


Activities to Reinforce: “The Golden Rule”

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The following questions can be answered in one to two sentences. While a variety of answers might make sense, there are right and wrong answers here. Think carefully about your answers. Write down your answers and bring them to class. We will review your answers either in class or in a net-mediated peer instruction activity. […]


Activities to Reinforce: “Why Comparing Averages is Just a Starting Point”

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Remember — questions will not only test the previous chapter. They will test all previous content (In this case everything from the golden rule, to subpopulations, to averages, to distributions). Figuring out which concept to apply to each problem is often the crucial skill, so we don’t indicate which concept comes into play. In some cases […]


Chapter Two Introduction

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  After completing chapter one, you have the basics of the COMPARABLE framework. Week Two will introduce you to time-based comparisons, term definition, the art of performing mental experiments, and the many uses of percentages.


Thinking Hypothetically About Numbers

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This section deals primarily with the following elements of the COMPARABLE framework: M: Do a mental experiment. In the process of writing this book, I’ve come to the conclusion that one of the most important parts of any comparer’s toolkit is hypothetical thinking. Hypothetical thinking comes in many forms, but the key skill is gaining […]


Longitudinal vs. Cross-sectional Approaches

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This section deals primarily with the following elements of the COMPARABLE framework: L: Would the comparison benefit from a longitudinal/cross-sectional analysis? B: Were base rates considered? Were relative and absolute increases considered? P: Were the pictorial/graphical representations fair and unbiased? Did they help illustrate the data or were they eye-candy? Note to instructors: We are […]


Percentages, the Swiss Army Knife of Comparison

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One of the quickest ways to become a smart consumer of statistics is to translate raw numbers into percentages, and raw increases into percentage gain. Percentages are not just an alternate way to present a statistic. They can give you a broader sense of the relative size of the statistic you are looking at. They […]


Activities Following “Percentages, the Swiss Army Knife of Comparison”

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Questions: 1. Rick Santorum, a candidate for the 2012 Republican nomination, claimed that “62 percent of kids who go into college with a faith commitment leave without it.” [Source:] What is being explicitly compared here? Is it a longitudinal or cross-sectional comparison? If 62 percent is the “part”, what is the “whole”? 2. Of […]


Beware the Base Rate

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Does the sign above tell you whether you are more likely to drown if you are not wearing a life jacket? Think about it a bit. Derek Bruff,  the mathematician who took this picture, points out the sign doesn’t tell you anything unless you know what percentage of people wear lifejackets on the lake. Imagine […]


Weighted Means & Standardization

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  You probably already know about and have used weighted means — they are one of the most popular ways for professors to calculate grades. For example, if quizzes are going to be 30% of the grade and the midterm + final is going to be 70% of the grade then if your grades look […]


Displaying Percentages Graphically

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    Displaying Simple Part-Whole Relationships When percentages are part of a common whole, the usual way to display them is a pie chart. The pie chart has its share of problems as a graphical representation of data (particularly when people go all 3D on them), but the one thing a pie chart does is […]


Base Rate, Revisited

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The following insight is an old saw of research on statistical intuition by now, but was revolutionary when Kahneman & Tversky came up with it in the early 70s. It is a good explanation of what goes wrong when we think about prediction. As you consider the next question, please assume that Steve was selected […]

Critical Thinking is Part Intelligence, Part Attitude

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Critical Thinking is about more than intelligence: Even after controlling for differences in cognitive ability, reasoning performance correlated with degree of open-mindedness and epistemic flexibility (cultivating reflectiveness rather than impulsivity, seeking and processing information that disconfirms one’s belief, being willing to change one’s beliefs in the face of contradictory evidence). Further, these dispositions tended to […]


Activity: Effect Sizes and Mind-Mapping

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Example from A Theory-Based Meta-Analysis of Research on Instruction by RJ Marzano: The next two techniques displayed in Table 7.2 employed the information processing function of idea representation.  Techniques that provided students with metacognitive strategies for using visual memory had an effect size of 1.04, indicating a percentile gain of 35 points.  Presumably, these strategies help […]


A Note About Why Practice Matters

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From A. N. Whitehead’s An Introduction to Mathematics, some insight into why practice is important: “It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending […]

Specificity and Sensitivity, Visual Explanation

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This is a great walk-through of the issues of sensitivity and specificity in medical test design and interpretation. It is a good supplement to the explanations in this text. Everyone that gets medical tests done or will get medical tests done (which, let’s face it, is everyone) should be familiar with these principles, but it’s often hard […]


Associations and Mechanism: How Visa Predicts Divorce

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How Visa Predicts Divorce From TDB: Hunch then looks for statistical correlations between the information that all of its users provide, revealing fascinating links between people’s seemingly unrelated preferences. For instance, Hunch has revealed that people who enjoy dancing are more apt to want to buy a Mac, that people who like The Count on […]


Activity Following “Stocks, Inflows, and Outflows”

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1. Consider the following issue: 17.1. A major controversy has occurred about apparent contradictions in biostatistical data as researchers try to convince Congress to allocate more funds for intramural and extramural investigations supported by the NIH. Citing improved survival rates for conditions such as cervical cancer, breast cancer, and leukemia, clinicians claim we are “winning […]


Gas Prices and Cyclical Patterns

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When things have a seasonal cycle, it’s often difficult to make direct comparisons. Ideally you compare to last year this time, or the ten year average of this time last year, but what people really want is a sense of how high it will go. This article does a decent job with that — look, […]

Title Page

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Making Fair Comparisons: An Approach to Quantitative Literacy Written by: Mike Caulfield Editors & Contributors: Becca Berkey, Elli Caldwell This work is heavily influenced by the work of Milo Schield, Neil Lutsky, and Nathan Grawe. The questions we ask here are questions they ask, although the presentation and focus of this text is someone different. This […]


Distribution of Risk: J-Curves

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My new favorite term from epidemiology: J-Curve. Distribution matters, even with something as shades-of-grey as risk. For instance, yhere’s a lot of things that increase your mortality in a more-or-less linear way. The more you smoke, the greater your all-cause mortality risk, for example. This isn’t to say you increase your chance of death by […]

Lifecycle Analysis: CFL vs. Incandescent Mercury Pollution

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From Lifecycle impact analyses, like the one shown above, are invaluable tools in making fair comparisons.  It’s easy, for example, to get hung up on the small amount of mercury in a CFL bulb, a percentage of which can escape into the environment if the bulb is crushed in a landfill. But the biggest contributor […]

Mental Experiments and the Mancovery

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This is the new story out — it’s a mancovery! From Bloomberg: Men, who lost more than twice as many jobs as women during the worst economic slump since the Great Depression, have landed 88 percent of the non-farm jobs created since the recession ended in June 2009. The share of men saying the economy […]

Mind the Edges: Unemployment by College Major

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In the COMPARABLE framework the “E” is for “Edges”, and part of the “question of edges” is whether there are significant subpopulations. In the case of unemployment of recent college grads, the answer is yes: The center would tell you only that the average unemployment for college grads is about 9%. But the lowest rates […]

Longitudinal Analysis: SIDS and Prone Sleeping in Norway

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This is an amazing chart — sad in one way, but uplifting in another, because it shows how stats-informed public policy can make a difference. The chart represents the incidence of SIDS (“crib death”) in Norway plotted out against the rise and fall of parents that put their children to sleep on their stomach. (Which […]

Farm Share of Food Dollar and Subgroups

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As we say in the COMPARABLE checklist, the story is often somewhere in the edges. Take this chart of the proportion of a food dollar which goes to the farmer vs. post-farm activities. At first it seems to show declining farm revenue as the the market bill (which includes everything from transportation to preparation) climbs: […]


Surrogate Outcomes

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In medicine, researchers often rely on surrogate outcomes (also called surrogate endpoints). Take, for example, something like heart health. We know that a good ratio of good cholesterol to bad cholesterol is a predictor of heart health and increased longevity. So we come up with a pill that changes that ratio for the better. And […]

Activity Following “Surrogate Outcomes”

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Focused question: While “surrogate outcomes” and “clinical outcomes” are terms generally used in medicine, the same concept can be applied to a wide range of disciplines. Come up with the equivalent of a “surrogate outcome” and its corresponding “clinically meaningful outcome” for each of the following disciplines: Education Economics/Economy Politics  


Activity: New Housing Starts Graph

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The following graph is from Architect Magazine. The caption reads: “The construction boom of the 2000s often cited as the reason for the boom in housing prices doesn’t break precedent—or break records. At a time when U.S. population growth was slower, the 1970s saw two housing booms that produced more housing starts than the 2000s. The high […]


Standard Things Controlled For in Sociology, Medicine, Politics, Psychology & Economics

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When making comparisons between countries, climates, people, or anything else there are differences which can make a fair comparison difficult. Some disciplines talk about lurking variables, some talk about confounders — for the moment we are just going to talk about this stuff as the “things your comparison might need to account or control for.” […]


Questions: Student Loan Debt Surpasses Credit Card Debt

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Read the following comparison: Consumers now owe more on their student loans than their credit cards. Americans owe some $826.5 billion in revolving credit, according to June 2010 figures from the Federal Reserve. (Most of revolving credit is credit-card debt.) Student loans outstanding today — both federal and private — total some $829.785 billion, according to Mark […]


Mental Experiment: Undocumented Immigrants in the University of California System

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Dream Act rally in Washington, D.C.   From the June 9 edition of Fox News’ The O’Reilly Factor: CARLSON: So, at University of California schools — just to get this in. O’REILLY: Right. CARLSON: In 2009, about 35 percent of the in-state tuition people or students were illegals. O’REILLY: Really? That’s an interesting stat, Carlson. [Fox News, The […]


Glossary: Median Household Income

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  Adapted from Wikipedia; see Wikipedia for references and additional explanation. Please note that some of this definition may be specific to the U.S. The median household income is commonly used to generate data about geographic areas and divides households into two equal segments with the first half of households earning less than the median […]

Glossary: Median Income (U.S. Census)

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From the Census definition: Median income is the amount which divides the income distribution into two equal groups, half having incomes above the median, half having incomes below the median. The medians for households, families, and unrelated individuals are based on all households, families, and unrelated individuals, respectively. The medians for people are based on […]

Glossary: Race (U.S. Census Definition)

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From the U.S. Census definition: The race of individuals was identified by a question that asked for self-identification of the person’s race. Respondents were asked to select their race from a “flashcard” listing racial groups. The population is divided into five groups on the basis of race: White; Black; American Indian, Eskimo or Aleut; Asian […]

sky bacon

Relative vs. Absolute Increases

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Let’s talk about risk for a second. And in particular, lets talk about bacon. If the article above is to be believed, eating two slices of bacon daily can increase your risk of pancreatic cancer by almost 20%. So here’s a simple question — if you eat bacon daily at those levels, what is your […]


Stock vs. Flow

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Imagine a tank of water that has a pipe in and a pipe out. As water flows in, water also flows out. Ignore the flow rates on this diagram, and just think for a minute — if the water level in the tank is rising, what can we say about the inflow and outflow? The […]

Keene State Quantitative Literacy Outcomes (and Mapping Codes)

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The following tags will be used on posts to indicate the programmatic student learning outcomes they support: SLO-ADS: Apply basic methods of descriptive statistics. SLO-UAS: Use appropriate software to create charts, tables, spreadsheets. SLO-IVD: Read and interpret visually represented data. SLO-DGM: Distinguish among various types of growth models. SLO-CRP: Critically read and interpret quantitative problems. […]

Base Rate Refresher

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You Meet a Guy Named John Base rates are extremely important, but we neglect them all the time. In fact, we do worse than that, because we exaggerate the importance of data apart from base rates. In an article about the statistics of predicting marriage success, reporter Laurie Abraham gives a classic example of how we ignore […]

Guesstimating: How to Sanity Check Any Figure

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As part of our focus on doing mental experiments, we want to introduce you to the wonderful world of guesstimating. While guesstimating — the ability to guess at what a statistic might be using only information available to you — is seen by some as a trivial magic trick, in reality it is an extremely […]


Graphing Longitudinal Comparisons

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How has student borrowing for education changed over time? Here’s one look at that question, shown as a bar chart: Visually the impact is striking — but as with all comparisons we need to make sure we actually understand the terms of the comparison. First, you need to ask what is being measured. When longitudinal […]

Top and Bottom Quintile

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In the COMPARABLE framework, the “Question of Edges” is a placeholder to remind us that measures of central tendency such as mean, median, and mode are helpful, but only tell us so much. One way to get a sense of the distribution of values is to use quintiles. With quintiles, we start out by imagining […]

Predicting with Percentages (Review)

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Quick review of our idea of “representativeness”: When we hear a percentage (For example, 41% of college students are male vs. 59% female) used to advance a theory (fewer men want to go to college) we can make predictions based on assumptions (if the reason for the non-representation is lack of applicants then SAT participation […]

Cut-points and Specificity vs. Sensitivity

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a. A cut-point is any point on a continuous scale we use to define a separation between states or conditions. b. Examples: High blood pressure, Failing grades, Psychological conditions based on tests, Recessions. c. Cut-points aren’t arbitrary (usually). But they always involve some non-numerical judgment on what is important. d. In the context of comparison, […]

Percent vs. Percentiles

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a. Pretty standard – getting students to understand what the difference is between these, and when to use each. b. Example: On the retest I jumped from the 40th percentile to the 90th. What does that mean? What does that not mean?


Example: Where’d the Productivity Go?

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The hourly compensation of a typical worker grew in tandem with productivity from 1948–1973. That can be seen in Figure A, which presents both the cumulative growth in productivity per hour worked of the total economy (inclusive of the private sector, government, and nonprofit sector) since 1948 and the cumulative growth in inflation-adjusted hourly compensation for private-sector […]


Activity: Fluoridation and Decayed, Missing, and Filled Teeth

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From Promoting Oral Health:The Use of Salt Fluoridation to Prevent Dental Caries by Saskia Estupiñán-Day. This chart shows the incidence of decayed, missing, and filled teeth in children in a town that used fluoridation against a set of control towns that did not. 1. For the purposes of this graph, how was “fluoridation” defined? 2. Would this […]


Activity: Rabbits

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The settler Thomas Austin released 24 wild rabbits on his Australian farm, called Barwon Park, in 1859, and some other Australian farmers later followed his example. Rabbits are sexually mature at about six months, and they have a 31-day gestation period. Given a favorable environment, rabbits can easily increase their population fourfold in a year. […]

Question: Corporate Psychopathy

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In a widely reported study, psychologists found the following: In this study, we had a unique opportunity to examine psychopathy and its correlates in a sample of 203 corporate professionals selected by their companies to participate in management development programs. The correlates included demographic and status variables, as well as in-house 360° assessments and performance […]

corporate tax rate

Net vs. List, Effective vs. Statutory Cost

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When we are measuring the price of anything, it’s tempting to measure “list” price — that is, what the asking price of a thing is. In many cases that’s fine — the asking price for a two liter of Diet Coke is most likely the same as the selling price. So if we average what […]


Activity: Law Salaries

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The graph above shows salaries of 2006 graduates of law school as measured in 2007. 1. The study did not include people out of work. How might the graph shape change if it included people out of work? Would the median salary be lower or higher? 2. Look up the term “bimodal distribution”. Does this […]

A Sample Assignment Weighting for this Class

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To get an A or B in this class, the student must Come to class prepared and participate (20% of grade): Reading quizzes to test preparation (10%) Participation points (awarded for engaged attendance) (10%) This class relies on student participation to work. Missing more than three classes is grounds for failure. Early in the year […]


Question: Weighted Tax Average

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The above graph shows average taxes for 15 countries. Notice the difference between the straight average, and the average weighted by population (25.3 vs. 27.2). 1. Do a mental experiment to figure out the following: Does this difference between the weighted average and the straight average mean that a smaller country (or number of smaller […]


Activity: Rent vs. Mortgage Cost

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Some people say that we couldn’t have known there was a real estate bubble. But quite a few economists pointed out well before the crash that the “price/rent” ratio — that is, the average cost of owning a house/apartment divided by the average cost of renting — was well outside of historical norms. This led economist […]


Zero-day Comparisons

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Game of Thrones, Season 2 is getting illegally downloaded. A lot. In fact, it’s on track to be the most pirated show of 2012, and maybe 2011 as well: Maybe that’s interesting to you, maybe not. Here’s what’s interesting to me: notice the horizontal axis of the graph. What this represents is number of days […]

Questions Following Weighted Means and Standardization

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1. Look at the following graph: Notice the difference between the average tax weighted by population, and the average tax. Make up a set of six imaginary countries with different populations and tax rates where the weighted average tax is less than the unweighted average tax. What trends do you notice? 2. 3. A 2006 […]

Question: Predicting Marriage

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A longitudinal study with 95 newlywed couples examined the power of the Oral History Interview to predict stable marital relationships and divorce. A principal-components analysis of the interview with the couples (Time 1) identified a latent variable, perceived marital bond, that was significant in predicting which couples would remain married or divorce within the first […]


Question: Random vs. Scientific

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A recent headline: Here’s how the ACS is implemented (from Wikipedia): The ACS has an initial sample of approximately 3 million housing unit addresses and group quarters in the United States, with sample selected from all counties and county-equivalents, American Indian and Alaska Native area, and Hawaiian Homeland, and in Puerto Rico annually. Data are collected primarily by mail, with follow-ups by […]