Tag: mathematics
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T testing – a worked example
A simple one-sample T-test This variant on hypothesis testing is used when you have limitations, specifically: The population standard deviation (σ) is unknown and your sample size (n) is <30 The fundamentals The formula is a variant of what we’ve seen thus far, where x̄ = your sample mean, μ = a hypothesized population mean,…
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Proportion testing
Using everything we’ve learned so far about the central limit theorem, the z-score, and hypothesis testing, we can now also perform proportion testing! There are just a few new concepts to add into the mix: The preliminary terrors – notation & terminology p = the proportion of items that falls into H0 q = the…
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Hypothesis testing basics
A simple example of hypothesis testing is where we know what “normal” is, and we want to evaluate whether some sample conforms to our understanding of “normal”, or is so unusual that it’s indicative of an actual shift in behaviour or pattern. Make your hypothesis statement If I…(do this to an independent variable)….then (this will…
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Preliminary terrors of statistics
The “preliminary terrors“, of course, being the notation as Silvanus P. Thompson so aptly described them :). Pronunciation μ sounds like “mew” σ sounds like “sigma” x̄ sounds like “x-bar” The population So we can think of this as the complete set of “things”, whatever the “things” are that are under consideration – for example…
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Populations and samples
Populations We can think of the population as the complete set of “things”, whatever the “things” are that are under consideration – for example if we’re interested in studying the height of men in South Africa, then the population would be all adult men in South Africa. A population can be described by parameters. Here’s…
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Central limit theorem – a worked example
Remember our formal definition: The CLT states that, provided enough samples are taken, the sample distribution of the sample mean will be normally distributed, regardless of the population distribution. In mathematical terms we say therefore that the sample mean is equal to the population mean: With enough samples this also happens – the sample standard deviation…
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Bayes theorem – a worked example
So I found this quite a mind-bender, although I believe this is part and parcel of the typical high-school maths syllabus now! Here is my stab at understanding the theorem and how it relates to a real-life example… Problem wording: Jane witnessed a robbery in which a car was involved. It is known that 1…
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Calculus made easy (really)
For some reason I didn’t expect someone writing in 1910 to have such a wonderful sense of humour – most books from this time seemed…
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The “Nigel Molesworth” method
When I was growing up my Dad was my best mathematics tutor! I would come home from school feeling rather…
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