Statistics is about learning from data and the role that variability plays in drawing conclusions
from data.
— Roxy Peck, Statistics: Learning From Data
Just because someone quotes you a statistic or shows you a graph, it doesn’t mean it’s
relevant to the point they’re trying to make. It’s the job of all of us to make sure we
get the information that matters, and to ignore the information that doesn’t.
— Daniel J. Levitin, A Field Guide to Lies: Critical Thinking in the Information Age
Be wary, though, of the way news media use the word “significant,” because to statisticians it doesn’t mean “noteworthy.” In statistics, the word “significant” means that the results passed mathematical tests such as t-tests, chi-square tests, regression, and principal components analysis (there are hundreds). Statistical significance tests quantify how easily pure chance can explain the results. With a very large number of observations, even small differences that are trivial in magnitude can be beyond what our models of change and randomness can explain. These tests don’t know what’s noteworthy and what’s not—that’s a human judgment.
— Daniel J. Levitin, A Field Guide to Lies: Critical Thinking in the Information Age
Quantitative reasoning empowers
people by giving them tools to think
for themselves, to ask intelligent
questions of experts, and to
confront authority confidently.
— Lynn Steen, Mathematics and Democracy (2001)
The Normal Probability Distribution
Definition:
If a continuous random variable has a probability distribution with a graph that is symmetric
and bell-shaped, and it can be described by the function equation
\[
f(x)=\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{1}{2}(\frac{x-\mu}{\sigma})^2} \quad\quad -\infty \leq x \leq \infty\]
then we say it has a normal distribution.