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.
