İSTATİSTİK I

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. Other measures of time are interval-scale variables (the word “interval” gives you a clue to that!), for example hours of sleep (on Sundays I sleep an hour longer - I would not say I sleep 14% longer) and time to run 100 meters (e.g., at the 2009 World Championships in Berlin, Usain Bolt shaved more than a tenth of a second off his record, clocking 9.58 seconds - we wouldn’t say he reduced the time from 9.69 seconds by 1.1%).

As also understood from the information given “Age”, “Hours of Sleep” and “Time to Run 100 meters” are interval scale variables, so the correct answer is I, II and V. “The Inflation Rate” and “Gold Price” 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.

As also understood from the information given, the correct answer is IV and V. “Verbal responses in questionnaires” and “Social media posts” need recoding in order to create quantitative variables. “Frequently occurring words”, “The lengths of sentences” and “The number of words used just once” are the ones which are recoded in order to create quantitative variables.

A study that involves Statistics will clearly involve a process of data collection. But there are differences in study objectives which are important to recognize. The main distinguishing factor is whether the study aims to find some evidence of a result or whether it aims to find causes of a result. Medical research is a good context to understand these differences - Statistics in medical research is often called Biostatistics.

It is true that many benefits have been detected of taking a low-dosage of aspirin every day. For example, it has been observed that people who take aspirin regularly (less than 300 mg per day) generally have less health problems such as heart attacks, strokes and cancers. The keyword is “observed”: in a community health study involving thousands of people there will be many that take aspirin regularly for problems such as back pain or headaches. For those people it could be observed that they have less chronic diseases compared to people who don’t take aspirin. This is evidence of a difference, but it does not prove that aspirin is the actual cause of the improved health. People who do not take aspirin daily might be poorer and neglect taking medication, and they suffer from more chronic diseases than people with a higher income, so the real difference is socio-economic. From such an observational study it is not possible to conclude a causal effect, it just gives some tentative evidence of a possible relationship between the treatment and the outcome.

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. Suppose we take a large group of men in the age group 60- 70 years of age that have no history of chronic disease. We divide them into two groups so that the groups are “balanced” in terms of known factors such as age, social class, and so on (we don’t want one group to have older men than the other). By the way, this “dividing into two groups” is not a trivial matter, but that is a subject for later in this course. Assuming the two groups are comparable, then one group is given the daily low dose of aspirin and the other not, and the groups are followed up for a five-year period and then compared for the incidence of health problems that develop during this time. If the group taking aspirin has less health problems, this would indicate a beneficial effect caused by the aspirin.

This type of experiment on people has all sorts of problems, but it is really leading to a conclusion about whether aspirin is the real cause of differences between the two groups. There is the ethical problem of not giving the daily aspirin, which has suspected benefits, to a large group of people. There is also the problem that one group knows it is taking the medication and might change their lifestyle to favour a good outcome by living more healthily. This effect can be eliminated by not telling either group what they are getting and giving the non-aspirin group a so-called placebo, which is medication in the form of an aspirin, so both groups think they are getting the medication.

As also understood from the information given, “A study which aims to find some evidence of a result” is an example of observational studies, so the correct answer is only I. “A study which aims to find causes of a result”, “A study in which the groups are “balanced” in terms of known factors” and “A study conducted where conditions are controlled” are the examples of experimental studies.

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. The need has been recognized for someone who not only has statistical skills, but also advanced programming skills and knowledge about handling huge data sets, the so-called “Big Data” of today. Thus a new profession has been born, that of the Data Scientist. Again, don’t be fooled: the main skill of a data scientist is knowledge of Statistics,

As also understood from the information given, the correct answer is I and V. “Statistics” and “Analytics” really mean the same thing. Statistics, Computer Science, Database Management and Data Visualization are the areas which Data Science includes. They do not mean the same thing.

What are the “big data” sets today and where do they come from? These are mostly found in the following areas:

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

Statisticians are trained to interpret and analyse data. This profession mainly deals with the analysis of data; not to check and decide for other profesion lines.

There is no absolute zero in the temperature measurements. So body temperature is a continuous interval-scale variable.

Grades like "AA" or "BB" taken from a course is an ordinal categorical variable.

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.

The subjects or individuals or companies on which these observations are made are called cases. Hospital patients on whom we have measured the standard medical indicators such as blood pressure, cholesterol levels, blood sugar, and so on might be cases.