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# Statistics and Probability (Metric)

## Class Details

Tom Baker

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.

Lesson

Using tree diagrams to calculate probabilities of combined events.

Lesson

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

Lesson

### Descriptive Statistics

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

Lesson

Measures of central tendency for ungrouped data.

Lesson

Measures of central tendency for grouped data.

Lesson
Lesson

Measures of dispersion for ungrouped and grouped data.

Lesson

### Probability Distributions

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

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

Lesson

Events that occur randomly but at a steady rate.

Lesson

Continuous random variables and probability density.

Lesson

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

Lesson

What's the correct distribution?

Lesson

### Hypothesis Testing

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

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

Lesson

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

Lesson

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

Lesson

### Estimation

Estimators, standard error and confidence intervals.

Estimating means, standard deviations etc from numerical data.

Lesson

How uncertain is my estimate?

Lesson

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

Lesson

### Regression and Correlation

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

The least-squares curve of best fit.

Lesson

The correlation coefficient; significance of correlation.

Lesson

Rank correlation (Spearman's version); significance.

Lesson

Rank correlation (Kendall's version); significance.

Lesson
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