Estadistica

 


          Marcello Pagano     

[JOTTER 1 A, WEEK ONE] 
      

Types of data • Nominal Data 1 ̶ male 2 ̶ female Blood group: • A ̶ • B ̶ • AB ̶ • O ̶ 1 2 3 4

0 ̶ alive 1 ̶ dead

Nominally numbers • Name only • No order • Magnitude unimportant

In biostatistics and epidemiology we use numbers to tell our story. Numbers not only play a central role in our investigations, butthey also allow us to use computers to do all the hard work, such as calculations, storage and graphics. Plus, the computers do all this without making any errors – we make the errors! Often we do not need the full power of numbers for every application, although we still need limited properties, guided by our wish to accurately communicate with the computer. To make this point clear we classifyour use of numbers into different class. For example, one kind of data is what we call a nominal data; when we label males as 0, females as 1, then that’s nominal data. Another example of nominal data is if we use 0 to denote who's alive and 1 for denoting people who are dead. In both these examples, they are nominally numbers, just 0 or 1. The only property we're making use of the number systemhere is that 0 is different from 1. We're not saying 1 is bigger than 0. We're not saying that 1 is one unit away from 0. Simply that 0 and 1 are different. This is the simplest example we have of nominal data. This is sometimes called binary data or dichotomous data, depending upon whether you prefer the Greek or the Latin root for two. But it doesn't just have to have two values. For example, ifwe're looking at blood groups, here we would need four values: one each for blood groups A, B, AB and O. Now, if you go to the Framingham Heart Study data set, you can take a look and see how many nominal data there are in that data set. So in summary, these are nominally numbers, only in name are they numbers. There's no order. The magnitude is unimportant. So that's nominal data.

Types of data• Nominal Data • Ordinal Data 1. Mild 2. Moderate 3. Severe

Now, as we go up the ladder of complexity and properties of data, the next one up is ordinal data, where the order is important; for example, we might classify some disease as mild, moderate, or severe, where we might label mild as a 1, moderate as a 2, and severe a 3. We use the order of the data because 2 is a little bit more severethan 1, and 3 is a little bit more severe than 2. So the order is important. And this is called ordinal data.

Recommended treatment strategy for schistosomiasis in preventive chemotherapy

Types of data • Nominal Data • Ordinal Data 1. Mild 2. Moderate 3. Severe

ECOG performance status: 0 Fully active 1 Ambulatory. Light work. 2 No work. Ambulatory > 50% 3 Ambulatory < 50% 4 DisabledOrdinal data • Order important • Magnitude unimportant

Another example is provided by the Eastern Cooperative Oncology Group, which is a clinical trials group in cancer. In clinical trials they classify patients’ performance status using a fivelevel classification system. It ranges from 0, where the patient is fully active, to 4, where the patient is disabled. And it progressively gets worse asone goes down the scale. So here the order is important. Thus ordinal data has more structured than nominal data. So in summary, for ordinal data, the order is important, but the magnitude is unimportant. We're not saying here that the distance from 1 to 2 is the same as the distance from 3 to 4. The magnitude is not important.

Rank data
e.g. Ten leading causes of death in the USA —preliminary data for 2010 (National Center for Health Statistics)
Rank 1 2 3 4 5 6 7 8 9 10 Cause Heart disease Cancer Chronic lower respiratory disease Stroke Accidents (unintentional injuries) Alzheimer’s disease Diabetes Influenza and Pneumonia Nephritis group Suicide Number 599,413 567,628 137,353 128,842 118,021 79,003 68,705 53,692 48,935 36,909

There is a special case of ordinal data that we...