Stats symbol

Does anyone know what this symbol is within statistics?

Does anyone know what this symbol is within statistics?

Does anyone know what this symbol is within statistics?

In this context, Φ (the capital Greek letter phi) is about probabilities of the Z or N(0, 1) distribution. Φ(a) = P(Z < a), that is, Φ(a) is the probability that the N(0, 1) distribution is less than a. Φ^-1 is the inverse function, so if a = Φ^-1(p), then a is the value such that P(Z < a) = p.

It is still a part of the current A Level, but it used to have much more prominence in the previous version of the course.

Inverse cumulative. So when z=-0.5244, that corresponds to a 0.3 probability.

In my course we glossed over it and used a calculator

Now that the course requirement is to have a calculator that can do normal probabilities for you, it does tend to get overlooked. For the old course, there was no expectation that students would have calculators that could do this, and the usual way to answer any normal probability question was to standardise and use tables, so people were using the N(0, 1) table all the time, and Φ was a bit of a bigger deal!