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Introduction to Data Science: Overview

Course Overview

Goals

Introduction to Data Science (IDS) is designed to introduce you - through hands-on activities - to the exciting opportunities available at the intersection of data analysis, computing, and mathematics. Data are everywhere, and this curriculum will help prepare you to live in a world of data. The curriculum focuses on practical applications of data analysis to give you concrete and applicable skills. Instead of using small, tailored, curated data sets as in a traditional statistics curriculum, this curriculum engages you in the wider world of data that fall into the "Big Data" that are relevant to your life. In contrast to the traditional formula-based approach, in IDS statistical inference is taught algorithmically, using modern randomization and simulation techniques. You will learn to find and communicate meaning in data, and to think critically about arguments based on data.

Standards

The standards used for the IDS curriculum are based on the High School Probability and Statistics Mathematics Common Core State Standards (CCSS-M) and the Standards for Mathematical Practice (SMP). Standards addressed are outlined in detail in the Scope and Sequence section. The Computer Science Teacher’s Association (CSTA) K-12 Computer Science Standards were also consulted and incorporated. Applied Computational Thinking Standards (ACT) outline the application of Data Science concepts using technology.

Hardware

An ideal laboratory environment has a 1:1 computer-to-student ratio. Your computer can be Apple, PC, or Chromebook, depending upon availability. Internet access is required for the use of RStudio on an external server.

Software

Ideally, your computer should have a modern, updated web browser installed (such as Firefox or Google Chrome). This will allow you to access RStudio from an external server, and to perform searches and make use of a variety of websites and Internet tools. RStudio is available at https://tools.idsucla.org. The IDS team will provide the remainder of the software used in the IDS curriculum, available at https://tools.idsucla.org. This software includes the IDS UCLA app, which is deployed for Android and iOS smartphones and tablets, as well as through the web browser on a desktop or laptop computer. The app allows you to collect the Participatory Sensing data that is a motivational foundation for the course. In addition to the app, you will use the IDS software to access and manipulate their Participatory Sensing data and to author your own campaigns.

Prerequisites

It is recommended that you successfully complete a first-year Algebra course prior to taking IDS. This will provide you with the background you'll need to learn about data science and statistics through this challenging and innovative curriculum. No previous statistics or computer science courses are required to take this course.

Assignments & Homework

IDS work will take place as much as possible during class time. Lessons are designed for a 50-60 minute class period. Classes on block schedule will need to complete two lessons; however, the teacher will decide where to stop in each lesson. You will be given computer-based assignments to be completed during class time, as well as open-ended assignments to be completed on your own. If you miss lab time, you will need to find a time to complete the assignment outside of class. As discussed in the software section above, you can use an Internet-enabled computer to do make-up work.

You will be expected to have both a calculator and your Data Science (IDS) Journal - a notebook where you will record your notes, work on small assignments, and sketch plots - on hand daily. Teachers may choose to check IDS journals and other assignments in the curriculum for credit. You will also be assigned oral presentations, Practicums, and End of Unit Projects.

Overview of Instructional Topics

The purpose of IDS is to introduce you to something called "dynamic data analysis". The four major components of this curriculum are based on the following standards, the Common Core State Standards High School - Statistics and Probability, which are explained in greater detail below:

  • I. Interpreting Categorical and Quantitative Data
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  • II. Making Inferences and Justifying Conclusions
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  • III. Conditional Probability and the Rules of Probability
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  • IV. Using Probability to Make Decisions
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IDS will emphasize the use of statistics and computation as tools for creative work, and as a means of telling stories with data. Seen in this way, its content will also prepare you to "read" and think critically about existing data stories. Ultimately, this course will be about how we discern good stories from bad through a practice that involves compiling evidence from one or more sources, a process which often requires hands-on examination of one or more data sets.

Through IDS you will learn about tools, techniques, and principles for reasoning about the world with data. It will present a process that is iterative and authentically inquiry-based, comparing multiple "views" of one or more data sets. These views are the result of some kind of computation, producing numerical summaries or graphical displays, the interpretation of which relies on a special kind of computation known as "simulation" to describe the uncertainty in each view. This kind of reasoning is exploratory and investigatory, sometimes framed as hypothesis evaluation, and sometimes as hypothesis generation.

Interpreting Categorical and Quantitative Data

A handful of data interpretations are standard. Some, including summaries of shape, center, and spread of one or more variables in a data set - as well as graphical displays like histograms and scatterplots - are standard in the sense that they provide interpretable information in a number of research contexts. They are portable from one set of data to the next, and the rules for their use are simple; and yet our interpretation of data is rarely “standard.” Data have no natural look - even a spreadsheet or a table of numbers embeds within it a certain representational strategy. We construct multiple views of data in an attempt to uncover stories about the world.

In addition to numerical data, this course will consider time, location, text, and image as data types, and will examine views that uncover patterns or stories. Throughout the course, simulation will be used to calibrate our interpretation of a view, or of a numerical or graphical summary, so that we understand what “story-less” data (i.e., pure noise, no association) look like.

In addition to summaries and simple graphics, you will engage in a modeling practice aligned with the CCSS mathematical practices in order to learn how statistical analyses can explain and describe real-world phenomena. You will practice fitting and evaluating standard mathematical and statistical models, such as the least-squares regression line, and you will learn the concept of modeling as you design and implement probabilistic simulations in order to test and compare hypothetical chance processes to real-world data.

Making Inferences and Justifying Conclusions

Data are becoming increasingly plentiful, supported by a host of new "publication" techniques or services. Post-Web 2.0, data are interoperable (they flow out of one service and into another), helping us easily build a detailed data version of many phenomena in the world. Reasoning with data, then, starts with the sources and the mechanics of this flow. Which sources do we trust? How do data from different organizations compare? What stories have been told previously with these data, and by whom?

This course answers these questions, in part, by using the tools and techniques already mentioned. The ability to read and critique published stories and visualizations are additions to these tools and techniques. Finally, you will also learn to formulate questions, identify existing data sets, and evaluate how the new stories stack up against the old. To support this cycle of inquiry, you will examine the basic publication mechanisms for data and develop a set of questions to ask of any data source - computation meets critical thinking. In some cases, data will exhibit special structures that can be used to aid in inference. The simulation techniques for calibrating different views of a data set take on new life when some form of random process was followed to generate the data. Polls, for example, rely on random samples of the population, and clinical trials randomly assign patients to treatment and control groups. A simulation strategy that repeats these random mechanisms can be used to assess uncertainty in the data, assigning a margin of error to poll results, or identifying new drugs that have a "significant" effect on some health outcome.

In many cases, data will not possess this kind of special origin story. A census, for example, is meant to be a comprehensive list of a population, and we can reason in a very direct way from the data. In other cases, no formal principle was applied, perhaps being a sample "of convenience." The techniques for telling stories from these kinds of data will also rely on a mix of simulation and subsetting. Finally, this course will introduce Participatory Sensing as a technique for collecting data. The idea of a data collection campaign will be introduced as a means of formalizing a question to be addressed with data. Campaigns will be informed by research and data analysis, and will build on, augment, or challenge existing sources. The "culture" behind the existing sources and the summaries or views they promote will be part of the classroom discussions.

It is worth noting that everything described so far depends on computation, using a piece of statistical software on a computer. You will learn simple programming tools for accessing data, creating views or fitting models, and then assessing their importance via simulation. Computation becomes a medium through which you will learn about data. The more expressive the language, the more elaborate the stories we can tell.

Probability

Since simulation is our main tool for reasoning with data, interpreting the output of simulations requires understanding some basic rules of probability. First and foremost, this course will discuss the ways in which a computer can generate random phenomena. For example, how does a computer toss a coin? You'll first use simple probability calculations to describe what you expect to see from random phenomena, then you will compare your results to simulations. The point is to both rehearse these basic calculations and to make a formal tie between simulation and theory in simple cases.

In that vein, this course will motivate the relationship between frequency and probability. You will essentially be simulating independent trials and creating summaries of those simulations. In turn, you should understand that the frequency with which an event occurs in a series of independent simulations tends to the probability for that event as the number of simulations gets large (the Law of Large Numbers, a topic that is often taught in introductory statistics courses).

From here you will simulate a variety of random processes to aid in formal statistical inference when some random mechanism was applied as part of the data design. In short, probability becomes a sort of ruler for assessing the importance of any story we might tell. In this approach to probability, a combination of direct mathematical calculation and computer simulations will be used in order to give you a good sense of the underlying statistical concepts.

Topic Outline

This outline describes only the scope of the course; the sequence is described in each unit.

I. Interpreting Data

A. Types of data

B. Numerical and graphical summaries

  1. Measures of center and spread, boxplots

  2. Bar plots

  3. Histograms

  4. Scatterplots

  5. Graphical summaries of multivariate data

C. Simulation and visual inference

  1. Side-by-side bar plots and association

  2. Scatterplots

D. Models

  1. Linear models

  2. k-means

  3. Smoothing

  4. Learning and tree-based models

II. Making Inferences and Justifying Conclusions

A. Aggregating data

  1. Identification of sources

  2. Mechanics of Web 2.0

  3. Comparison of sources

B. Data with special structures

  1. Random sampling

  2. Random assignment and A/B testing

  3. Simulation-based inference

C. Participatory Sensing

  1. Designing a campaign

  2. Participation as a data collection strategy

III. Probability

A. Computers and randomness

  1. Web services

  2. Pseudo-random numbers (optional)

B. Frequency and probability

C. Probability calculations

IV. Algebra in RStudio

  1. Vectors

  2. Algorithms

  3. Functions

  4. Evaluating and fitting models to data

  5. Graphical representations of multivariate data

  6. Numerical summaries of distributions and interpreting in context