Concepts

Null hypothesis

A default hypothesis that a quantity to be measured is zero (null).

• The null hypothesis is true if data values are drawn from the hypothesized distribution.

p-value

The probability of obtaining observed, or more extreme, results when the null hypothesis is true.

• The probability that an observed difference could have just occurred by chance.
• A p-value near zero provides evidence against the null hypothesis.

t-test

A t-test automatically tests the null hypothesis that the mean value of the data is zero.

• T-tests assume:
  • The distribution is normal
  • The distribution remains fixed

Example

Example:

• A random sample of 5 customers spent $10.24, $12.31, $9.38, $14.03, and $11.72.
• Predict how much the next 100 customers will spend.

x = c(10.24, 12.31, 9.38, 14.03, 11.72)
t.test(x)

OSEMN data science framework

• Obtain — gather data from relevant sources
• Scrub — clean data to formats that machine understands
• Explore — Find significant patterns and trends using statistical methods
• Model — Construct models to predict and forecast
• iNterpret — put the results into good use

Simpson’s Paradox

• A phenomenon in which a trend appears in several groups of data but disappears or reverses when the groups are combined.

Lessons:

• What is true for a population may be false for each subpopulation.
• Many proportions and differences of proportions can only be interpreted clearly in the context of multiple causally relevant variables (multivariate models).