Statistics
Data about a group vary from one individual to the next. How do you collect them, describe them, and say what they show without claiming more than they can support?
Where you are 7 inside
What this area is about
Statistics is the study of data that vary: how to gather, summarize and picture them, and how to reason from a sample to a population with an honest measure of uncertainty. The conclusions hold only as far as the way the data were collected allows.
How these fit together
Starting out. Data and variables asks a statistical question, records individuals and variables, and counts categories in tables.
Describing data. Data displays picture data, from bar graphs to box plots and scatter plots, and center and spread summarize them with numbers such as the mean, median, IQR and standard deviation.
Collecting well. Sampling and study design says when a sample speaks for its population and when a study can show cause and effect.
Models. Distributions replace a histogram with a smooth curve, above all the normal curve N(\mu, \sigma), and describe how a statistic varies from sample to sample.
Two variables. Bivariate data measures association with r and fits a line \hat{y} = a + bx, without by itself showing cause.
Conclusions. Statistical inference turns a sample into confidence intervals and hypothesis tests about \mu, p or a slope \beta.
A path through it
Data and variables come first. Data displays and center and spread interleave next, then distributions, then bivariate data, then inference. Sampling and study design runs alongside: it can start right after data and variables, random sampling comes before sampling distributions, and its experiments lessons draw on confounding and on hypothesis tests.
Next, in probability: joint and marginal probability.