Basic Statistics and Data Analysis

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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

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Level of Measurements | Basic Statistics | MCQs Statistics

In statistics, data can be classified according to the level of measurements, dictating the calculations that can be done to summarize and present the data (graphically), it also helps to determine, what statistical tests should be performed. For example, suppose there are six colors of candies in a bag and you assign different numbers (codes) to them in such a way that brown candy has a value of 1, yellow 2, green 3, orange 4, blue 5, and red a value of 6. From this bag of candies, adding all the assigned color values and then dividing by the number of candies, yield an average value of 3.68. Does this mean that the average color is green or orange? Of course not. When computing statistic(s), it is important to recognize the data type, which may be qualitative (nominal and ordinal) and quantitative (interval and ratio).

The level of measurements has been developed in conjunction with the concepts of numbers and units of measurement. Statisticians classified measurements according to levels. There is four-level of measurements, namely, nominal, ordinal, interval, and ratio, described below.

Nominal Level of Measurement

At the nominal level of measurement, the observation of a qualitative variable can only be classified and counted. There is no particular order to the categories. Mode, frequency table (discrete frequency tables), pie chart, and bar graph are usually drawn for this level of measurement.

Ordinal Level of Measurement

In the ordinal level of measurement, data classification is presented by sets of labels or names that have relative values (ranking or ordering of values). For example, if you survey 1,000 people and ask them to rate a restaurant on a scale ranging from 0 to 5, where 5 shows a higher score (highest liking level) and zero shows the lowest (lowest liking level). Taking the average of these 1,000 people’s responses will have meaning. Usually, graphs and charts are drawn for ordinal data.

Interval Level of Measurement

Numbers also used to express the quantities, such as temperature, size of the dress, and plane ticket are all quantities. The interval level of measurement allows for the degree of difference between items but no the ratio between them. There is a meaningful difference between values, for example, 10 degrees Fahrenheit and 15 degrees is 5, and the difference between 50 and 55 degrees is also 5 degrees. It is also important that zero is just a point on the scale, it does not represent the absence of heat, just that it is a freezing point.

Ratio Level of Measurement

All of the quantitative data is recorded on the ratio level. It has all the characteristics of the interval level, but in addition, the zero points are meaningful and the ratio between two numbers is meaningful. Examples of ratio levels are wages, units of production, weight, changes in stock prices, the distance between home and office, height, etc.
Many of the inferential test statistics depend on the ratio and interval level of measurement. Many authors argue that interval and ratio measures should be named as scales.

Level of Measurements
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