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# Statistics and Probability (Metric)

Learn, or revise, basic stats, probability, hypothesis testing, estimation, regression and correlation.

## Units

### Probability

The idea of probability; tree diagrams; mutual exclusion and independence.

Probability of an event consisting of equiprobable outcomes.

Using tree diagrams to calculate probabilities of combined events.

The cases $$P(A\cap B)=0$$ and $$P(A\cap B)=P(A)\,P(B)$$.

### Descriptive Statistics

Histograms; averages and measures of dispersion for ungrouped and grouped data.

Measures of central tendency for ungrouped data.

Measures of central tendency for grouped data.

Measures of dispersion for ungrouped and grouped data.

### Probability Distributions

Discrete distributions (including Binomial, Poisson); continuous distributions (including Normal).

Independent identical trials with success probability $$p$$.

Events that occur randomly but at a steady rate.

Continuous random variables and probability density.

The bell curve; using lookup tables; using percentage points.

What's the correct distribution?

### Hypothesis Testing

Null and alternative hypotheses; selecting a test; performing and interpreting a test.

Deciding on the default (null) hypothesis and the alternative hypothesis.

How is my test statistic distributed? What test should I use?

How strong is the evidence for an effect that isn't simply due to chance variation?

### Estimation

Estimators, standard error and confidence intervals.

Estimating means, standard deviations etc from numerical data.

How uncertain is my estimate?

"My estimate is almost certainly no more wrong than…"

### Regression and Correlation

Fitting a curve to data, and measuring the correlation of two quantities.

The least-squares curve of best fit.

The correlation coefficient; significance of correlation.

Rank correlation (Spearman's version); significance.

Rank correlation (Kendall's version); significance.