1.01 Cases, variables and levels of measurement

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En provenance du cours de University of Amsterdam

Basic Statistics

1789 notes

University of Amsterdam

Basic Statistics

1789 notes

Cours 3 sur 5 dans Specialization Methods and Statistics in Social Sciences

Understanding statistics is essential to understand research in the social and behavioral sciences. In this course you will learn the basics of statistics; not just how to calculate them, but also how to evaluate them. This course will also prepare you for the next course in the specialization - the course Inferential Statistics. In the first part of the course we will discuss methods of descriptive statistics. You will learn what cases and variables are and how you can compute measures of central tendency (mean, median and mode) and dispersion (standard deviation and variance). Next, we discuss how to assess relationships between variables, and we introduce the concepts correlation and regression. The second part of the course is concerned with the basics of probability: calculating probabilities, probability distributions and sampling distributions. You need to know about these things in order to understand how inferential statistics work. The third part of the course consists of an introduction to methods of inferential statistics - methods that help us decide whether the patterns we see in our data are strong enough to draw conclusions about the underlying population we are interested in. We will discuss confidence intervals and significance tests. You will not only learn about all these statistical concepts, you will also be trained to calculate and generate these statistics yourself using freely available statistical software.

À partir de la leçon

Exploring Data

In this first module, we’ll introduce the basic concepts of descriptive statistics. We’ll talk about cases and variables, and we’ll explain how you can order them in a so-called data matrix. We’ll discuss various levels of measurement and we’ll show you how you can present your data by means of tables and graphs. We’ll also introduce measures of central tendency (like mode, median and mean) and dispersion (like range, interquartile range, variance and standard deviation). We’ll not only tell you how to interpret them; we’ll also explain how you can compute them. Finally, we’ll tell you more about z-scores. In this module we’ll only discuss situations in which we analyze one single variable. This is what we call univariate analysis. In the next module we will also introduce studies in which more variables are involved.

1.01 Cases, variables and levels of measurement7:32

1.02 Data matrix and frequency table6:08

1.03 Graphs and shapes of distributions7:21

Rencontrer les enseignants

Matthijs Rooduijn
Dr.
Department of Political Science
Emiel van Loon
Assistant Professor
Institute for Biodiversity and Ecosystem Dynamics

Imagine you're very, very interested in football.

You know. That sport some of us like to call soccer.

You are the person who wants to know all the details,

like how many goals were scored by some player?

How many games were won by a particular team?

Or how many penalties were stopped in a certain football competition.

In this video, I will explain how improving your knowledge of statistics

could make you a real expert in football or any other kind of sport.

The number of scored goal, won games, and stopped penalties are all pieces of

information that can be thought of in terms of variables and cases.

Variables are features of something or someone.

And cases are that something or someone.

Let me be a little bit more specific.

Imagine you are interested in some characteristics of football players

belonging to your favorite team.

Of every single player, you want to know his or her body weight, hair color,

age, and the total number of goals scored during the most recent competition.

All these player characteristic are variables.

The players themselves are cases.

Another example, it could be the case that you are not so

much interested in the features of individual players, but

in the features of the teams these individuals play for.

For instance, you might want to know about every Spanish team and

which city it is based.

What the main colors of the shirts are and

how many goals the team scored in the last year.

These features are variables again.

However, the cases here are not individual football players but

the teams these individuals play for.

In a study, cases can thus be many different things.

They can be individual football players and football teams.

But they can also be, for instance, companies, schools or even countries.

Every characteristic of a case can be called a variable,

as long as it meets one essential criterion.

It needs to vary.

What does that mean?

Let's go back to the example, with teams as cases, and

look at the variable, city where the team is based.

You focus on every Spanish team, so there will be many different cities.

One team comes from Barcelona, and other teams come from, for

instance, Madrid, Valencia, or Sevilla.

We have, in other words, variation.

Let's now focus on another characteristic, not the city but

the country where the team is based.

For every single team, this will be Spain.

The teams are after all Spanish teams.

This means that there is no variation here.

Not a single team will be from another country than Spain.

For this reason, we call this characteristic not a variable, but

a constant.

You can probably imagine that we can have many, many different kinds of variables,

representing strongly divergent characteristics.

For this reason, and also for other reasons that I will discuss later.

It is of essential importance to distinguish different levels

of measurement.

The most simple level of measurement is the nominal level.

A nominal variable is made up of various categories that differ from each other.

There is no order, however.

This means that it's not possible to argue that one category is better or

worse, or more, or less than another.

An example is the nationality of the football players.

The various categories, for instance Spanish, French, or

Mexican differ from each other, but there is no ranking order.

Another example is the gender of the football players or

the city the football teams come from.

The second level of measurement is the ordinal level.

There is not only the difference between the categories of the variable,

there is also an order.

And example is the order in a football competition.

You know who is the winner.

You know who came second, and third, etc., etc.

However, by looking at the order,

you don't know anything about the differences between the categories.

You don't know, for example, how much the number one was better than the number two.

Both nominal and ordinal levels can be called categorical variables.

The next level of measurement is the interval level.

With interval variables, we have different categories and

an order, but also similar intervals between the categories.

An example is the age of a football player.

We can say that a player of 18 years old differs from a player of 16 years old,

in terms of his or her age.

In addition, we can say that this player is older.

But we can also say that in terms of age,

the difference between a 18 year old player and a 16 year old player,

is similar to the difference between a 14 year old player and a 12 year old player.

The final level of measurement is the ratio level.

It is similar to the interval level but has, in addition, a meaningful zero point.

An example is a player's body height, measured in centimeters.

There are differences between the categories.

There is an order, there are similar intervals, and

we have a meaningful zero point.

A height of zero centimeters means that there is no height at all.

Note that we cannot say that age has a meaningful zero point,

because an age of zero does not mean that there is no age.

Age therefore is an interval variable.

Interval and ratio variables are what we call quantitative variables.

Because the categories are represented by numerical values.

Quantitative variables can also be distinguished in discrete and

continuous variables.

A variable is discrete if it's possible categories form a set of separate numbers.

For instance, the number of goals scored by a football player.

A player can score, for instance, one goal or two goals, but not 1.21 goals.

A variable is continuous if the possible values of the variable form an interval.

An example is again, the height of a player.

Someone can be 170 centimeters, 171 centimeters tall.

But also for instance, 170.2461 centimeters tall.

We don't have a set of separate numbers, but an infinite region of values.

Why is it so important to distinguish these various levels of measurement?

Well, because the methods we employ to analyze data

depend on the level on which the variables are measured.

However, in practice the distinction sometimes get blurred.

For instance, for many statistical analyzes,

the differences between the interval and ratio level are not that important.

Moreover, many statisticians argue that if you have an ordinal variable

measured on a scale with ten categories or

even more, you are allowed to analyze this variable as if it were quantitative.

An example is a survey question that asks,

on a scale from zero to 10 how good would you say player X is?

Formally, this is an ordinal variable but in practice you are allowed to cheat and

to treat it as if it were a quantitative one.

To conclude, how does all this information make you a better expert in football?

Well, thinking about players, teams, and

competitions in terms of cases, variables, and the levels of measurement of these

variables makes your knowledge about football more structured.

To become even more of an expert, do not hesitate and watch the next videos, too.

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