# A Sampling Story

I’m going to assume no one reading this piece has any idea what a statistic is, so I thought we could start at the beginning. Every great story starts at the beginning, so why shouldn’t we? I don’t want to delve into linear regression or stochastic processes right off the bat, that would be like throwing a 4 year old into the deep end at their first swimming lesson. Consider this chapter to be almost like a prologue.

When you were in school, can you remember what your first notable encounter with statistics involved? I remember mine. My 5th class teacher sent me into the junior infants class with a survey, asking students what they had for their breakfast that morning. There were 4 options: (a) Coco Pops, (b) Cornflakes, (c) Weetabix and (d) Other. The 20-ish four year olds coloured in their chosen box and I was sent on my merry way back to my own class.

However, I now critique the process of 10 year old me trotting to the infants class and carrying out that survey. Why, you ask? Well, one of the most important aspects of surveying correctly is avoiding bias at all cost. We never want to influence the results we collect. I may have lingered in the classroom, pacing up and down, checking what the students were answering. Of course I was very young myself, so I didn’t know any better, but who is to say that my impatient hovering didn’t influence the students? Or sitting next to their friends, being able to see what each other's answers, didn’t change their response? Ensuring anti-bias and neutrality when surveying is essential.

I learned quite a few things from that adventure to the youngest class in the school. One was that four year olds eat an ALARMING amount of Coco Pops. The second was that I conducted my first ever survey and it was one of many methods of collecting statistics. When starting the lesson, I didn’t want to waste my time surveying each student in the junior cycle, so my teacher put the classroom numbers into a hat, closed his eyes and picked a number out. Little did I know that this is the most basic form of sampling.

Sampling is a critical part of statistics. We wouldn’t be able to play with statistics without it. Although it might be fun, it’s physically impossible to gather information on an entire population. Instead, we choose a smaller subset of the population and take a closer look at the information there. Sampling allows us to gather pieces of data effectively and efficiently and we can analyse the data to make assumptions on what is happening throughout the wider population. The data collected from these samples can also be denoted as “observations”, one piece of data = one observation. It does what it says on the tin - it OBSERVES.

There are a few basic sampling methods and they go as follows:

Random sampling : a personal favourite of mine. Gives an equal chance to each item in the population of being picked for the sample. Your standard “pull it out of a hat” method. Quick and stress-free.

Stratified Sampling : picking a stratum (it just means subset) of the target population but all the members of that group have one or more common attributes. Fun fact - sampling error* is lower in comparison to random sampling! Time-consuming, but accurate.

Systematic Sampling: this involves picking every ‘Nth’ name from a list, e.g. every third person on the list. Easy-peasy to carry out. Can result in some error.

*sampling error = errors that occur while sampling...

There are MANY more sampling methods and no doubt these processes will continue to develop and evolve as new technology advances. How you pick your sampling method is completely up to you. Are you looking for a faster method? A more accurate method? A bit of

both? Consider what exactly you are collecting data on and decide what you value most in a sampling method.

Statistics are important but we can’t have statistics without gathering the data. We cannot gather the data without sampling. By equivalence, sampling = important. Q. E. D. Don't you agree?

*My name is Saoirse Trought and I am a 3rd year Mathematical Sciences student at University College Cork, Ireland. Besides my obvious interest in all things maths, I happen to be fluent as Gaeilge. I enjoy sailing (although I am extremely accident prone), staycation-ing and attempting to run UCC MathSoc. I'm looking forward to combining some of these interests with statistics and seeing where it takes us!*