# Stats at Uni vs A Levels (Maths)

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#1
What is the statistics like in a mathematics and statistics degree compared to the stats you do in single maths at A Level?
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1 year ago
#2
(Original post by jt1284)
What is the statistics like in a mathematics and statistics degree compared to the stats you do in single maths at A Level?
Wildly different ...

There is more to being a statistician than calculating basic probabilities and the confidence intervals by hand.

On top of all the extensive theory in statistics, you learn how to apply it in practice hence programming is an important aspect which is completely absent in A-Level maths.
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#3
(Original post by RDKGames)
Wildly different ...

There is more to being a statistician than calculating basic probabilities and the confidence intervals by hand.

On top of all the extensive theory in statistics, you learn how to apply it in practice hence programming is an important aspect which is completely absent in A-Level maths.
How could I go about establishing whether or not I'd enjoy uni stats?
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1 year ago
#4
(Original post by jt1284)
How could I go about establishing whether or not I'd enjoy uni stats?
Do you enjoy stats now?

If so, then you will more or less enjoy it to begin with at university.

The coding part really depends. If you put in the effort at the time (or even before uni), then you will be good at it and perhaps even enjoy it.

For the theory in stats after the initial introductory courses, it is hard to say. I can recommend a book to you which you can look at if you wish, then decide for yourself whether the content ahead looks interesting to you (albeit alien at this current moment in time).
Last edited by RDKGames; 1 year ago
0
1 year ago
#5
(Original post by jt1284)
What is the statistics like in a mathematics and statistics degree compared to the stats you do in single maths at A Level?
Here's a typical Maths and Stats degree: https://courses.leeds.ac.uk/4627/mat...statistics-bsc

You will meet more distributions and learn new hypothesis tests.

The amount of computation varies enormously and RDKGames's example is not typical of all courses. Talk to your teacher about what the modules might include.
0
1 year ago
#6
(Original post by jt1284)
What is the statistics like in a mathematics and statistics degree compared to the stats you do in single maths at A Level?
These are some of the things you’ll study, roughly in the order that you’ll come across them.

(i) A hefty dose of elementary probability theory. By “elementary” I mean not involving measure theory (see below). For example, you’ll get to know all the standard probability distributions, and how to manipulate them algebraically.

(ii) When you draw a sample from an underlying population, and then calculate a statistic from that sample (i.e. any function of that sample, such as the mean, median, or maximum value), then, in theory, you can do that over and over again, leading to the statistic itself having a probability distribution (called the “sampling distribution” of the statistic). Having covered elementary probability theory, you’ll learn how to deduce the analytic form of the sampling distribution of a statistic, if you know the probability distribution of the underlying population.

(iii) At school, you’ve been introduced to a number of important statistics, such as the mean and median. But why are they important? At university, you’ll learn what it means for a statistic to be a “good” statistic that makes the most efficient use of the data available to you, and you’ll learn how to find these “good” statistics in various situations.

(iv) You’ll be introduced to a whole new approach to statistics called “Likelihood theory”. Take a probability distribution that’s a function of some parameter, and consider it as a function of that parameter. It turns out that if you maximize the function with respect to that parameter conditional on some observed data, you end up with a whole load of “good” statistical estimators.

(v) You’ll be introduced to statistical inference where you make no assumption about the underlying probability distribution of the population from which you’re drawing samples. This is called “non-parametric” statistics.

(vi) Hopefully you’ll get an introduction to Bayesian statistics. This used Bayes’ theorem to allow you to make probability statements about quantities that in ordinary (“frequentist”) statistics you consider to be fixed, but possibly unknown, parameters.

(vii) You will, I hope, be immersed in the modern field of computationally intensive statistics, where you use the ability to draw vast numbers of random samples from underlying distributions to do almost everything numerically rather than analytically.

(viii) You will introduced to rigorous (rather than elementary) probability theory, involving measure theory. This will open up the field stochastic processes (such as Brownian motion), with its myriad number of modern applications, all the way from financial mathematics, to biological modelling of diffusion processes.

But we’re now getting close to the boundary with graduate studies, so I’ll stop there!
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