Chapter 1
Key Ideas
Terms: Data (Quantitative vs. Qualitative), Discrete vs. Continuous Data, Statistics, Population, Census, Sample, Parameter, Statistic,
Observational Study vs. Experiment
Bias: Voluntary Response, Small Samples, Misleading Graphs/Percentages, Loaded Questions, Nonresponse, Missing Data,
Correlation vs. Causality, Self-Interest, Precision, Partial Pictures
Obs. Studies: Cross-Sectional Study, Retrospective (Case-Control) Study, Prospective (Cohort) Study
Experiments: Confounding Variables, Single/Double Blind, Blocking, Randomization, Replication
Sampling: Convenience, Simple Random, Stratified, Cluster, Systematic, Multistage, Sampling vs. Nonsampling Error
Section 1-1: Overview
Why Statistics?
Before beginning the study of statistics, it is important to understand why it is even needed in the first place. We need statistics
because we want to know something about the world, but because of random processes, we can only make educated guesses. For
example, let’s say you want to start a new organization on campus, but you are not sure how much of the student body would even be
interested in it. You ask some people who live on your residence hall floor, and they seem to be excited about it. However, when you
ask some people in your classes, they don’t like the idea. It would be great if you could find a way to ask everyone on campus if they
would be interested in your organization. Unfortunately, this would take too much time. This is where statistics comes in. Even
though you can’t know for sure what percentage of the population likes your idea, you could find a way to get a small group of people
together who represent most of the variation in the student body (in terms of race, gender, sexual orientation, economic status, political
affiliation, etc.). Then this group of people should be a rough microcosm of the entire campus, and their responses to your questions
should generally match the campus as well. This is how statistics is used. We want to know something about the world that is either
too difficult or impossible to observe. Therefore, we use logical thinking and mathematical principles (often it’s common sense) to
make an educated guess about what the true value is. The good thing about statistics is that we can even quantify how accurate and
precise that measurement is (e.g. margin of error in polling). Since statistics is not tied to any one application, it is used in any
situation where something is uncertain (business, medicine, aeronautics, physics, politics, athletics, weather forecasting, and so forth).
Here is some basic terminology we’ll be using in class:
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Population – The entire group you want to know something about (like the entire student body above)
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Sample – The group you use to infer something about the population (the representative group you chose in the example above)
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Data – Collected observations from a study, experiment, etc. (the yes/no responses from the students in the sample)
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Census – Collection of data from everyone/everything in the population (usually hard to do or impossible)
Section 1-2: Types of Data
More terminology:
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Parameter – A value measuring some trait of the population (the percent of all students on campus who like your idea)
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Statistic – A value measuring some trait of the sample (the percent of students in your smaller sample who like your idea)
A note about the word “data”: A lot of people don’t realize it, but data is plural for datum. So although people often say things like
“the data shows that…”, they should really be saying “the data show that…”. Just thought you’d like to know.
Data comes in two flavors: Quantitative and Qualitative.
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Quantitative data is in number form… this is also sometimes called measurement data.
Examples: Height, Weight, Age (Years), Die Roll on a 6-sided die, Distance (miles), Shoe Size, etc.
It can also be subdivided into two sub-classes:
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Discrete – Numbers that aren’t densely packed together (you can separate all the possible response values and count them)
Examples: Age (Years), Die Roll, Shoe Size
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Continuous (Numerical) – Numbers that can be very close to each other (there are infinitely many possible response values)
Examples: Height, Weight, Distance (miles)
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As a general rule of thumb, you can think of continuous data as data that can have decimal places, whereas discrete data do
not (except for maybe .5 on the end in the shoe size example, since they run in half sizes too).
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Qualitative data (also called Categorical or Attribute data) can be separated into different categories and don’t use numbers.
Examples: Grade (A, B, C, D, F), Gender (M, F, Other), Economic Class (Lower, Middle, Upper), etc.
You can probably already see that it can be difficult to stick some variables into certain data types without knowing the context. If
you take something like “Age,” it could actually be in any of these groups. If Age is measured in years, but decimals are allowed (e.g.
someone could be 14.236 years old), then it is continuous. If it is rounded off, then it is discrete. Furthermore, if you are doing a
study on infants, say, and you only consider Age 0 (newborn) and 1 (one year old), then it could be thought of as qualitative data,
since you have 2 categories. The point here is that these are just labels for data, and nothing is set in stone. You can use whatever
terms you want to describe the data as long as you can make an argument for why the data should fall into that group.
