Quantitative Qualitative Variables: Statistical Data (2021)

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

The word “data” is frequently used in many contexts and ordinary conversations. 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 learn about quantitative qualitative variables with examples.

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 a computer operator commits 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 Qualitative Variables

Let us understand the major concept of Quantitative 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.

Qualitative Variables

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).

Quantitative Variables

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 Qualitative Variables

Examples of Statistical Data

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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Qualitative vs Quantitative Research (2021)

In this post, we will discuss Qualitative vs Quantitative Research. Qualitative and quantitative research are two fundamental approaches to research, each with its own strengths and applications. Qualitative vs quantitative research involves collecting data based on some qualities and quantities, respectively. Let us discuss both the Qualitative and Quantitative Research in detail below.

Qualitative vs Quantitative Research

Qualitative Research

Qualitative research involves collecting data from in-depth interviews, observations, field notes, and open-ended questions in questionnaires, etc. The researcher himself is the primary data collection instrument and the data could be collected in the form of words, images, patterns, etc. For Qualitative Research, Data Analysis involves searching for patterns, themes, and holistic features. Results of such research are likely to be context-specific and reporting takes the form of a narrative with contextual description and direct quotations from researchers.

Quantitative Research

Quantitative research involves collecting quantitative data based on precise measurement using some structured, reliable, and validated collection instruments (questionnaires) or through archival data sources. The nature of quantitative data is in the form of variables and its data analysis involves establishing statistical relationships. If properly done, the results of such research are generalizable to the entire population. Quantitative research could be classified into two groups depending on the data collection methodologies:

Research Design: qualitative vs Quantitative Research

Experimental Research

The main purpose of experimental research is to establish a cause-and-effect relationship. The defining characteristics of experimental research are the active manipulation of independent variables and the random assignment of participants to the conditions to be manipulated, everything else should be kept as similar and as constant as possible. To depict the way experiments are conducted, a term used is called the design of the experiment. There are two main types of experimental design.  

Within-Subject Design
In a within-subject design, the same group of subjects serves in more than one treatment

Between Subjects Design
In between-group design, two or more groups of subjects, each of which is tested by a different testing factor simultaneously.

Non-Experimental Research

Non-Experimental Research is commonly used in sociology, political science, and management disciplines. This kind of research is often done with the help of a survey. There is no random assignment of participants to a particular group nor do we manipulate the independent variables. As a result, one cannot establish a cause-and-effect relationship through non-experimental research. There are two approaches to analyzing such data: 

Tests for approaches to analyzing such data such as IQ level of participants from different ethnic backgrounds.

Tests for significant association between two factors such as firm sales and advertising expenditure.

Examples:

  • Quantitative: A study that surveys 1000 people to determine the average income in a city and its correlation with education level.
  • Qualitative: Research that interviews cancer patients about their experiences with treatment and explores the emotional impact of the disease.

Choosing Qualitative or Quantitative Research

The best approach depends on the research question. However, a general guideline is:

  • Use quantitative research to explore “what” and “how much” questions, measure relationships, and test theories.
  • Use qualitative research to understand “why” and “how” questions, gain insights into experiences, and explore social contexts.

Remember, Qualitative and Quantitative researches are not mutually exclusive. Sometimes, researchers use a mixed methods approach that combines both quantitative and qualitative methods for a more comprehensive understanding.

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Absolute Error of Measurement

The absolute error of measurement is the difference between the measured value of an object and its true value.

When we measure an object, the measured value may be either a little more or a little lower than its true value, that is, an absolute error has occurred.
For example, if a scale (a measurement device) states the weight 10KG but you know the true weight is about 9KG, then the scale has an absolute error of 1KG ($ 10KG-9KG=1KG$).

This error may be caused by the scale used itself ‌ not measuring the exact amount of measurement you are trying to measure. For example, your measuring device may be accurate to the nearest KG. That is, if the weight is 9.6 kg, your scale may “round up” and give 10 kg. Thus, the absolute error is about $ 10KG-9.6KG=0.4KG$.

Absolute Error of Measurement

Mathematically, it can be described by the formula given below,
$ (\Delta X)=X_i-X$, where $ X_i$ is the measurement quantity by the device used and $X$ is the true value.

The measurement device may either little more or a little lower than the true value, the formula can be described in absolute form, that is
$$(\Delta X)=|X_i-X| $$

Absolute Error of a Measurement

‌Note that

  • If someones know the true value and the measured value, then the absolute error of measurement is just the subtraction of these numbers. However, sometimes, one may not know about the true value, one should use the maximum possible error as the absolute error.
  • Any possible measurement that one makes is ‌ an approximation, 100% accuracy of any measurement is impossible. It is also possible that if a measurement of the same object is made twice, then the two measurements may not be identical. Such ‌ differences between measurements (of the same object) are called variations in the measurement.
  • The absolute error of measurement does not provide any details about the graveness or importance of the error. For example, when measuring the distances between cities Kilometers apart, an error of a few centimeters is negligible. However, an error of centimeters when measuring a small piece of a machine is a ‌ significant error.
  • The largest possible absolute error of a measurement is always half of the value of the smallest unit used.
Types of Errors: Absolute Errors

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