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... Continue Reading →

# 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... Continue Reading →

# 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... Continue Reading →

# Central limit theorem – a worked example

Formal definition: Provided enough samples are taken, the sample distribution of the sample mean will be normally distributed, regardless of the population. Basically: With enough samples this also happens: Which ultimately allows us to calculate the Z-score: And using a Z-table, this allows us to find the probability of a value being <= x Here is... Continue Reading →

# 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... Continue Reading →

# 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...

# The “Nigel Molesworth” method

When I was growing up my Dad was my best mathematics tutor! I would come home from school feeling rather...