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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.

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

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Descriptive Statistics

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

Lesson

Measures of central tendency for ungrouped data.

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Measures of central tendency for grouped data.

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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.

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Continuous random variables and probability density.

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

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What's the correct distribution?

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Hypothesis Testing

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

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

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

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

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Estimation

Estimators, standard error and confidence intervals.

Estimating means, standard deviations etc from numerical data.

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How uncertain is my estimate?

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

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Regression and Correlation

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

The least-squares curve of best fit.

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The correlation coefficient; significance of correlation.

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Rank correlation (Spearman's version); significance.

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Rank correlation (Kendall's version); significance.

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