Lecture 3

Expressions

DATA 8

Summer 2017

Slides created by John DeNero (denero@berkeley.edu) and Sam Lau (samlau95@berkeley.edu)

Announcements

Review: Cause & Effect

Comparison

• Group by some treatment and measure some outcome
• Simplest setting: a treatment group and a control group
• If the outcome differs between these two groups, �that's evidence of an association (or relation)
• E.g., the top-tier chocolate eaters died of heart disease at a lower rate (12%) than chocolate abstainers (17%)
• If the two groups are similar in all ways but the treatment, �a difference in the outcome is also evidence of causality

Confounding

• If the treatment and control groups have systematic differences other than the treatment itself, then it might be difficult to identify a causal link
• When these systematic differences lead researchers astray, they are called confounding factors
• Such differences are often present in observational studies
• Observational study: the researcher does not choose which subjects receive the treatment
• Controlled experiment: the researcher designs a procedure for selecting the treatment and control groups

Randomize!

• When subjects are split up randomly, it's unlikely that there will be systematic differences between the groups
• And it's possible to account for the chance of a difference
• Therefore, randomized controlled experiments are the most reliable way to establish causal relations

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Expressions

Programming Languages

• Python is popular both for data science & �general software development
• Mastering the language fundamentals is critical
• Learn through practice, not by reading or listening
• Follow along: data8.haas.berkeley.edu

(Demo)

Arithmetic Operators

Example: Slopes

Much better

(Demo)

Numbers

(Demo)

Ints and Floats

Python has two real number types

• int: an integer of any size
• float: a number with an optional fractional part

An int never has a decimal point; a float always does

A float might be printed using scientific notation

Three limitations of float values:

• They have limited size (but the limit is huge)
• They have limited precision of 15-16 decimal places
• After arithmetic, the final decimal few places can be wrong

Discussion Question

Rank the results of the following expressions in order from least to greatest

1. 3 * 10 ** 10
2. 10 * 3 ** 10
3. (10 * 3) ** 10
4. 10 / 3 / 10
5. 10 / (3 / 10)

• 30000000000
• 590490
• 590490000000000
• 0.33333333333333337
• 33.333333333333336

Names

Assignment Statements

• Statements don't have a value; they perform an action
• An assignment statement changes the meaning of the name to the left of the = symbol
• The name is bound to a value (not an equation)

more_than_1 = 2 + 3

(Demo)

Exponential Growth

Growth Rate

• The rate of increase per unit time
• After one time unit, a quantity x growing at rate g will be

x * (1 + g)

• After t time units, a quantity x growing at rate g will be

x * (1 + g) ** t

• If after and before are measurements of the same quantity taken t time units apart, then the growth rate is

(after/before) ** (1/t) - 1

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(Demo)

Ebola Epidemic, Sept. 2014

"It's spreading and growing exponentially," President Obama said.

"This is a disease outbreak that is advancing in an exponential fashion," said Dr. David Nabarro, who is heading the U.N.'s effort against Ebola.

A Frightening Curve: �How Fast Is The Ebola Outbreak Growing?

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http://www.npr.org/sections/goatsandsoda/2014/09/18/349341606/why-the-math-of-the-ebola-epidemic-is-so-scary

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