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 [...]
Every sprint needs a track. This checklist is our track. The Fair Comparison Checklist (COMPARABLE) is meant to provide you a quick way to break down a comparison and critique it. As we go through the course, the categories presented here will have more meaning. For now, we want to introduce the checklist, and, if [...]
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 [...]
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 [...]
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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 [...]
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So what do we mean when we say something like “Asthma has risen?” The naive answer is that “More people have asthma.” But what exactly are we counting? What has gone up? We can measure asthma in a number of ways: Emergency room visits A survey where we ask people about asthma medication New diagnoses [...]
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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 [...]
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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 [...]
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Thinking about Randomness Randomness (and probability) is one of the more difficult things to understand. In this course we do not go into nearly the detail that most statistics courses go into on randomness. Instead, we are going to try to get across a few main points. The point we want to get across here [...]
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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 [...]
One of the most common comparison controls we use is controlling for population, both when looking at something societal (percentage of people out of work) and at experimental results (percentage of people experiencing a positive outcome). Percentages and Natural Frequencies Take for example this list of the top 15 countries in terms of number of [...]
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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 [...]
Lessons:
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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, [...]
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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 [...]
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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.” [...]
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 [...]
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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 [...]
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 [...]
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 [...]
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 [...]
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 [...]
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 [...]
(BEWARE! FOR GUESSTIMATION ONLY! BRUTALLY ROUNDED!) 20 billion: Number of chickens in world 7 billion: Population of World (humans) 4 billion: Population of Asia (2010) 3 billion: Population of the World, 1960 1 billion: Population of China, Population of the world in 1800, Population of Africa, number of cattle in world (2010) 600 million: Population of Europe [...]