What are Data?

welcome. My name is Andrew Bell.

I am a lecture and cognitive neuroscience at the Institute for Psychiatry,

Psychology and Neuroscience at King's College, London.

Today I'll be delivering you an introductory course to to statistics.

Now you might be wondering why a neuroscientist

will be giving a course in statistics.

Well, it is true that neuroscience and psychology were my first passions,

but I quickly learned that in order to fully appreciate these topics,

I needed a strong background in probability, statistics and mathematics.

To my surprise and great fortune,

I found that I really enjoyed these topics and they

have now become a fundamental part of my teaching activities.

I hope you have a similar experience as we go through the content.

So for those of you with some background in math or statistics,

some of what we will discuss maybe familiar but will hopefully,

nonetheless help you consolidate your understanding about statistics

and increase your enjoyment of the topic.

In this introductory course, we're gonna cover the following topics

were first going to look at different types of data and review.

Some of the terms we use to describe these data

will then look at ways we describe and summarise data and in so doing,

introduce our first type of statistic, which is descriptive statistics.

Next we'll explore inferential statistics,

which are the tools that allow us to make inferences or educated guesses

about the nature of our data and how different data sets compare.

This will lead naturally to an overview of null hypothesis, significance testing,

which is the backbone of most quantitative research.

And finally,

I'll take you through some of the most common and useful type of statistical tests.

Tests scientists such as myself use every day.

By the end of this course,

you'll be able to describe different types of data using appropriate terminology,

summarised data and be able to perform several statistical tests by hand.

Let's get started.

So regardless of what scientific discipline you are

interested in and question you are currently tackling,

they all have one thing in common.

They all begin with data.

So what? Our data?

Well, this is data,

a beloved character from a popular TV show from

the late 19 eighties to the early 19 nineties.

But data might also be a set of heart

rate measurements before and after a drug has been administered

or a set of images of the brain

of a particular patient or a list of languages spoken in

different countries or collections of favourite toys in the nursery.

In short, the term data refers to any facts, quantities, measurements,

amounts and so forth that describes something about our world.

Now we divide data into two types.

Numerical or quantitative data and categorical or qualitative data.

Numerical data are any data that deal with quantities

or amounts anything that can be measured or counted.

And we further divide numerical data into discrete data,

which is when there is a limit to how much the units can be subdivided.

For example, the number of houses on a given street.

This is a discrete quantity because it doesn't make sense,

at least for most applications to count houses

in units of less than one complete house.

Contrast that to the other type of numerical data

continuous data,

which is when the subdivisions of data points can be divided more and more.

A classic example is time.

We can always divide a period of time into smaller and smaller chunks.

One hour, 10.1 hour, 0.1 hour and so forth.

Categorical data are data that don't describe a quantity,

but rather a quality or feature of something in the world.

As with numerical data,

we further divide categorical data into two different types.

Nominal categorical data are those that don't have a natural order,

like colours or shapes or countries.

Orginal, categorical data

do have a natural order,

even though they can't be counted.

This might include something like letters of an alphabet,

days of the week, etcetera,

anything with an intrinsic structure or organisational scheme.

Now the next important distinction we make about sets of data is whether the data

set represents the entire population or just a sample of a larger data set.

Let's imagine we are interested in the average height

of all British persons aged 17 years old.

We have two options as to how we would determine the average height.

We could

measure the height of every single 17 year old in Britain,

which would take a very long time and cost a lot of money.

Or we could measure a sample

of 17 year olds and use that to extrapolate to the entire population.

The former is an example of a population level

data set because every instance of the measure of interested

interest is represented.

The latter is an example of a sample data set

where only a proportion of instances are represented.

The distinction between a population

and sample dataset has important ramifications

as to how we handle those data and make judgments about them

that introduces you to the concept of data as we deal with it

in statistics

before we go any further, let's quickly review what we've learned so far.

We've learned the difference between numerical or

quantitative data and categorical or qualitative data.

In the case of numerical data, we further subdivided into discrete and continuous,

and in the case of categorical data,

we further divided into nominal and orginal data.

We reviewed the difference between population and sample data sets,

and these are all important terms to recognise and use.

When discussing discussing statistics and data analysis

in the next segment,

we're going to look more closely at data

specifically how we summarise our data using descriptive statistics