Basic Statistics and Data Analysis

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Category: Data

Basic Statistics / Data

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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 levels of measurement since these levels of measurement play an important part in determining the arithmetic and different possible statistical tests that are 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 measurement 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.

Examples of level of measurements

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)
  • Evaluation such as High, Medium, 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 Level 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

For further details visit: Level of measurements

Basic Statistics / Data

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Quantitative and Qualitative Variables: Data

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 or 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.

A variable is called a quantitative variable when a characteristic can be expressed numerically such as age, weight, income, or a number of 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 is one that can take only a discrete set of integers or whole numbers, which are the values are 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.

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