Data

Levels of Measurement

Levels of Measurement (Scale of Measure)

The levels of measurement (scale of measures) have been classified into four categories. It is important to understand these measurement levels since they play an important part in determining the arithmetic and different possible statistical tests carried on the data. The scale of measure is a classification that describes the nature of the information within the number assigned to a variable. In simple words, the level of measurement determines how data should be summarized and presented. It also indicates the type of statistical analysis that can be performed. The four-level of measurements are described below:

1) Nominal Level of Measurement (Nominal Scale)

At the nominal level of measurement, the numbers are used to classify the data (unordered group) into mutually exclusive categories. In other words, for the nominal level of measurement, observations of a qualitative variable are measured and recorded as labels or names.

2) Ordinal Level of Measurement (Ordinal Scale)

In the ordinal level of measurement, the numbers are used to classify the data (ordered group) into mutually exclusive categories. However, it does not allow for a relative degree of difference between them. In other words, for the ordinal level of measurement, observations of a qualitative variable are either ranked or rated on a relative scale and recorded as labels or names.

3) Interval Level of Measurement (Interval Scale)

For data recorded at the interval level of measurement, the interval or the distance between values is meaningful. The interval scale is based on a scale with a known unit of measurement.

4) Ratio Level of Measurement (Ratio Scale)

Data recorded at the ratio level of measurement are based on a scale with a known unit of measurement and a meaningful interpretation of zero on the scale. Almost all quantitative variables are recorded on the ratio level of measurement.

Levels of Measurement

Examples of levels of measurement

Examples of Nominal Level of Measurement

  • Religion (Muslim, Hindu, Christian, Buddhist)
  • Race (Hispanic, African, Asian)
  • Language (Urdu, English, French, Punjabi, Arabic)
  • Gender (Male, Female)
  • Marital Status (Married, Single, Divorced)
  • Number plates on Cars/ Models of Cars (Toyota, Mehran)
  • Parts of Speech (Noun, Verb, Article, Pronoun)

Examples of Ordinal Level of Measurement

  • Rankings (1st, 2nd, 3rd)
  • Marks Grades (A, B, C, D)
  • Evaluations such as High, Medium, and Low
  • Educational level (Elementary School, High School, College, University)
  • Movie Ratings (1 star, 2 stars, 3 stars, 4 stars, 5 stars)
  • Pain Ratings (more, less, no)
  • Cancer Stages (Stage 1, Stage 2, Stage 3)
  • Hypertension Categories (Mild, Moderate, Severe)

Examples of Interval Levels of Measurement

  • Temperature with Celsius scale/ Fahrenheit scale
  • Level of happiness rated from 1 to 10
  • Education (in years)
  • Standardized tests of psychological, sociological, and educational discipline use interval scales.
  • SAT scores

Examples of Ratio Level of Measurement

  • Height
  • Weight
  • Age
  • Length
  • Volume
  • Number of home computers
  • Salary

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Quantitative and Qualitative Variables: Data

The post is about Quantitative and Qualitative Variables. First, we need to understand the concept of data and variables. Let us start with some basics.

The word “data” is used in many contexts and is also used in ordinary conversations frequently. Data is Latin for “those that are given” (the singular form is “datum”). Data may therefore be thought of as the results of observation. In this post, we will see about quantitative and qualitative variables too.

Data are collected in many aspects of everyday life.

  • Statements given to a police officer, physician, or psychologist during an interview are data.
  • So are the correct and incorrect answers given by a student on a final examination.
  • Almost any athletic event produces data.
  • The time required by a runner to complete a marathon,
  • The number of spelling errors committed by a computer operator in typing a letter.

  Data are also obtained in the course of scientific inquiry:

  • the positions of artifacts and fossils in an archaeological site,
  • The number of interactions between two members of an animal colony during a period of observation,
  • The spectral composition of light emitted by a star.

Data comprise variables. Variables are something that changes from time to time, place to place, and/or person to person. Variables may be classified into quantitative and qualitative according to the form of the characters they may have.

Quantitative and Qualitative Variables

Let us understand the major concept of Quantitative and Qualitative variables by defining these types of variables and their related examples. The examples are self-explanatory and all of the examples are from real-life problems.

A variable is called a quantitative variable when a characteristic can be expressed numerically such as age, weight, income, or several children, that is, the variables that can be quantified or measured from some measurement device/ scales (such as weighing machine, thermometer, and liquid measurement standardized container).

On the other hand, if the characteristic is non-numerical such as education, sex, eye color, quality, intelligence, poverty, satisfaction, etc. the variable is referred to as a qualitative variable. A qualitative characteristic is also called an attribute. An individual or an object with such a characteristic can be counted or enumerated after having been assigned to one of the several mutually exclusive classes or categories (or groups).

Mathematically, a quantitative variable may be classified as discrete or continuous. A discrete variable can take only a discrete set of integers or whole numbers, which are the values taken by jumps or breaks. A discrete variable represents count data such as the number of persons in a family, the number of rooms in a house, the number of deaths in an accident, the income of an individual, etc.

A variable is called a continuous variable if it can take on any value- fractional or integral––within a given interval, that is, its domain is an interval with all possible values without gaps. A continuous variable represents measurement data such as the age of a person, the height of a plant, the weight of a commodity, the temperature at a place, etc.

A variable whether countable or measurable is generally denoted by some symbol such as $X$ or $Y$ and $X_i$ or $X_j$ represents the $i$th or $j$th value of the variable. The subscript $i$ or $j$ is replaced by a number such as $1,2,3, \cdots, n$ when referred to a particular value.

Quantitative and Qualitative Variables

Note that statistical data can be found everywhere, few examples are:

  • Any financial/ economics data
  • Transactional data (from stores, or banks)
  • The survey, or census (of unemployment, houses, population, roads, etc)
  • Medical history
  • Price of product
  • Production, and yields of a crop
  • My history, your history is also statistical data

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Statistical Data: Introduction and Real Life Examples

By statistical Data we mean, the piece of information collected for descriptive or inferential statistical analysis of the data. Data is everywhere. Therefore, everything that has past and/ or features is called statistical data.

One can find the statistical data

  • Any financial/ economics data
  • Transactional data (from stores, or banks)
  • The survey, or census (of unemployment, houses, population, roads, etc)
  • Medical history
  • Price of product
  • Production, and yields of a crop
  • My history, your history is also statistical data

Data

Data is the plural of datum — it is a piece of information. The value of the variable (understudy) associated with one element of a population or sample is called a datum (or data in a singular sense or data point). For example, Mr. Asif entered college at the age of 18 years, his hair is black, has a height of 5 feet 7 inches, and he weighs about 140 pounds. The set of values collected for the variable from each of the elements belonging to the sample is called data (or data in a plural sense). For example, a set of 25 weights was collected from the 25 students.

Types of Data

The data can be classified into two general categories: quantitative data and qualitative data. The quantitative data can further be classified as numerical data that can be either discrete or continuous. The qualitative data can be further subdivided into nominal, ordinal, and binary data.

Qualitative data represent information that can be classified by some quality, characteristics, or criterion—for example, the color of a car, religion, blood type, and marital status.

When the characteristic being studied is non-numeric it is called a qualitative variable or an attribute. A qualitative variable is also known as a categorical variable. A categorical variable is not comparable to taking numerical measurements. Observations falling in each category (group, class) can only be counted for examples, gender (either male or female), general knowledge (poor, moderate, or good), religious affiliation, type of automobile owned, city of birth, eye color (red, green, blue, etc), etc. Qualitative variables are often summarized in charts graphs etc. Other examples are what percent of the total number of cars sold last month were Suzuki, what percent of the population has blue eyes?

Quantitative data result from a process that quantifies, such as how much or how many. These quantities are measured on a numerical scale. For example, weight, height, length, and volume.

When the variables studied can be reported numerically, the variable is called a quantitative variable. e.g. the age of the company president, the life of an automobile battery, the number of children in a family, etc. Quantitative variables are either discrete or continuous.

Statistical Data

Note that some data can be classified as either qualitative or quantitative, depending on how it is used. If a numerical is used as a label for identification, then it is qualitative; otherwise, it is quantitative. For example, if a serial number on a car is used to identify the number of cars manufactured up to that point then it is a quantitative measure. However, if this number is used only for identification purposes then it is qualitative data.

Binary Data

The binary data has only two possible values/states; such as, defected or non-defective, yes or no, and true or false, etc. If both of the values are equally important then it is binary symmetric data (for example, gender). However, if both of the values are not equally important then it can be called binary asymmetric data (for example, result: pass or fail, cancer detected: yes or no).

For quantitative data, a count will always give discrete data, for example, the number of leaves on a tree. On the other hand, a measure of a quantity will usually be continuous, for example, weigh 160 pounds, to the nearest pound. This weight could be any value in the interval say 159.5 to 160.5.

The following are some examples of Qualitative Data. Note that the outcomes of all examples of Qualitative Variables are non-numeric.

  • The type of payment (cheque, cash, or credit) used by customers in a store
  • The color of your new cell phone
  • Your eyes color
  • The make of the types on your car
  • The obtained exam grade

The following are some examples of Quantitative Data. Note that the outcomes of all examples of Quantitative Variables are numeric.

  • The age of the customer in a stock
  • The length of telephone calls recorded at a switchboard
  • The cost of your new refrigerator
  • The weight of your watch
  • The air pressure in a tire
  • the weight of a shipment of tomatoes
  • The duration of a flight from place A to B
  • The grade point average

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