İSTATİSTİK I

Statistics is at the heart of understanding climate patterns and making weather forecasts. The first role of Statistics is to reduce this mass of complex data to a simpler form in order to facilitate understanding and learning from the data. This is often done by making graphical representations of the data.

It may seem that everything may be recorded and stored somewhere. But in reality - unless we somehow centralize and link all the databases in the world, and have free access to them - we can get access to only a small part of whatever data we are interested in. For example, it is impossible to ask the whole population of Turkey what their view on climate change is, whether they believe it is natural or manmade. This is where the most basic concept in Statistics comes into play: sampling from a population.

Categorical variables and data can be either nominal or ordinal.
The question about climate change, with possible responses “natural”, “manmade” or “don’t know/can’t answer” is a nominal categorical variable, as is the variable “country” - there is no ordering in the categories of these variables. By contrast, exam grade is an ordinal categorical variable, since its categories are ordered: A is better than a B, B is better than a C, and so on.

There is a subtle difference between interval-scale and ratio-scale continuous data, which is worth mentioning here. Age is an interval-scale variable: to compare two children of ages 10 and 12, we would compute the interval difference, i.e. 2 years. We would not say the 12-year old is 20% older than the 10-year old. But comparing prices or incomes, for example, we would tend to compute percentage differences, making them ratio-scale variables. A good example is the inflation rate, comparing the prices of a basket of products over time, not as a difference but as a percentage. As a general rule, most data on monetary values and those coming from physical measurements (e.g., lira, gold price, centimeters, kilograms) are ratio-scale variables.

The world today abounds in textual data. Words, SMSs, tweets, social media posts, verbal responses in questionnaires, these can all be treated as data. Some recoding will be necessary, since text is not numerical. Frequently occurring words can be counted, the lengths of sentences can be measured, the number of words used just once can be identified, and so on, in order to create quantitative variables from text. Textual data have been used, for example, in identifying the author of threatening letters, in comparing political party manifestos, in classifying respondents in a survey who give answers to open ended questions.

Medical research is a good context to understand these differences - Statistics in medical research is often called Biostatistics.

The way the sample is collected is crucial to obtaining a valid estimate, and this is an important subject which will be dealt with in this course. The main criteria for selecting a sample will be that the sample is representative of the population and that there is no or very little subjectivity in the choice of the sampling units. Sampling is not only conducted by survey researchers on human populations, but also by auditors on a company’s accounts, by agricultural researchers on different pieces of land, and by quality control inspectors on products in a factory, to name only a few examples.

In order to be able to prove that aspirin is the cause of the improvement in health, an experiment needs to be conducted where conditions are controlled between those taking aspirin and those not taking it. Such an experiment might be designed as follows, restricted to men, for example, since the effects are suspected to be different for men and women.

In order to be able to prove that aspirin is the cause of the improvement in health, an experiment needs to be conducted where conditions are controlled between those taking aspirin and those not taking it. Such an experiment might be designed as follows, restricted to men, for example, since the effects are suspected to be different for men and women.

At the start of this Introduction we asked “What is Statistics? What is Data Science? What is Analytics?” To deal with Analytics first, this is a term now used in business circles as a substitute for the word Statistics, but it really means the same thing. The word Statistics is considered by some people, especially businessmen, as a bit old-fashioned, and sometimes even difficult to pronounce! But don’t be fooled: Analytics is a fancy word for Statistics.

When it comes to Data Science, however, the term does have some different meaning. Data Science is a field that includes Statistics as well as areas such as Computer Science, Database Management and Data Visualization, for example, and has come into being mainly as a result of the spectacular growth in the amount of available data in this new information world that we live in.

Data come in the form of numbers as well as text, which is something we are discovering more and more. We live in an information world and information is the virtual gold of our society. All observations can be reduced to some numerical quantity, and there are even fields of digital philosophy and digital sociology. (Page 6)

…The key to all of the above is the phrase: “a sample of about 1000 carefully selected people”. The way the sample is collected is crucial to obtaining a valid estimate, and this is an important subject which will be dealt with in this course. The main criteria for selecting a sample will be that the sample is representative of the population and that there is no or very little subjectivity in the choice of the sampling units. Sampling is not only conducted by survey researchers on human populations, but also by auditors on a company’s accounts, by agricultural researchers on different pieces of land, and by quality control inspectors on products in a factory, to name only a few examples. (Page 7)

As also understood from the information given, the correct answer isI, II, III, IV and V.

Data come in various forms and are measured in different ways. For example, a doctor measures your blood pressure with an instrument, a survey researcher asks you a question and you give a verbal response, you go on holiday to a particular country, you are at a certain age and have a certain income, you have a grade for a completed university course, or this past week you have gone to the supermarket a certain number of times, and bought a certain basket of products, etc. Blood pressure, question response, country, age, income, course grade, number of supermarket visits and purchased products, these are all statistical variables.

As also understood from the information given, the correct answer is I, II, III, IV and V.

The easiest form of data is called categorical, or qualitative, for example data on variables “country” (e.g., the data observation might be Germany) or “question response” (e.g., believe that climate change is manmade) or “exam grade” (e.g., B). Categorical variables and data can be either nominal or ordinal. The question about climate change, with possible responses “natural”, “manmade” or “don’t know/can’t answer” is a nominal categorical variable, as is the variable “country” - there is no ordering in the categories of these variables. By contrast, exam grade is an ordinal categorical variable, since its categories are ordered: A is better than a B, B is better than a C, and so on.

Other examples of nominal categorical variables are gender, region of residence, field of study, type of transport, type of housing, etc.

Other examples of ordinal categorical variables are income group (if incomes have been categorized), an attitude question in a survey where possible responses are strongly agree/agree/disagree/strongly disagree (these categories have an order), social class (with classes usually in an inherent order), terrorist threat levels (in the UK these are low/moderate/substantial/severe/critical), etc.

The other main type of data (see Fig. 1.4) is called continuous, or quantitative, for example data on variables “blood pressure”, “age” and “income”. These are observations of variables on continuous scales, usually rounded in some convenient way. For example, although age is a continuous time variable, and we are getting older all the time by seconds, minutes and hours, someone’s age is almost always rounded to the number of years completed. There is a subtle difference between interval-scale and ratio-scale continuous data, which is worth mentioning here. Age is an interval-scale variable: to compare two children of ages 10 and 12, we would compute the interval difference, i.e. 2 years. We would not say the 12-year old is 20% older than the 10-year old. But comparing prices or incomes, for example, we would tend to compute percentage differences, making them ratio-scale variables. A good example is the inflation rate, comparing the prices of a basket of products over time, not as a difference but as a percentage. As a general rule, most data on monetary values and those coming from physical measurements (e.g., lira, gold price, centimeters, kilograms) are ratio-scale variables.

As also understood from the information given, the correct answer is I, II, III and IV.

Data come in various forms and are measured in different ways. For example, a doctor measures your blood pressure with an instrument, a survey researcher asks you a question and you give a verbal response, you go on holiday to a particular country, you are at a certain age and have a certain income, you have a grade for a completed university course, or this past week you have gone to the supermarket a certain number of times, and bought a certain basket of products, etc. Blood pressure, question response, country, age, income, course grade, number of supermarket visits and purchased products, these are all statistical variables. The observations made on these variables constitute the data. The subjects or individuals or companies on which these observations are made are called cases. Thus, cases might be a group of tourists entering Turkey, for each of whom we have data on which country they come from, how many days they plan to stay in Turkey, what their tourism objectives are (e.g., cultural events, beach holiday, etc.). Or cases might be hospital patients, on whom we have measured the standard medical indicators such as blood pressure, cholesterol levels, blood sugar, and so on.

As also understood from the information given a group of tourist entering Turkey is case, so the correct answer is A group of tourists entering Turkey. “which country they come from”, “how many days they plan to stay” and “what their tourism objectives are” are statistical variables.

The easiest form of data is called categorical, or qualitative, for example data on variables “country” (e.g., the data observation might be Germany) or “question response” (e.g., believe that climate change is manmade) or “exam grade” (e.g., B). Categorical variables and data can be either nominal or ordinal. The question about climate change, with possible responses “natural”, “manmade” or “don’t know/can’t answer” is a nominal categorical variable, as is the variable “country” - there is no ordering in the categories of these variables. By contrast, exam grade is an ordinal categorical variable, since its categories are ordered: A is better than a B, B is better than a C, and so on.

Other examples of nominal categorical variables are gender, region of residence, field of study, type of transport, type of housing, etc.

Other examples of ordinal categorical variables are income group (if incomes have been categorized), an attitude question in a survey where possible responses are strongly agree/agree/disagree/strongly disagree (these categories have an order), social class (with classes usually in an inherent order), terrorist threat levels (in the UK these are low/moderate/substantial/severe/critical), etc.

As also understood from the information given, “Region of Residence”, “Field of Study”, “Type of Transport” and  “Type of Housing” are nominal categorical variables. Exam grade is ordinal categorical variable.