Data Scales

Data scales, also known as levels of measurement or scales of measure, refer to the different ways that variables can be quantified and classified. Understanding the scale of data is crucial in statistical analysis, as it determines the types of statistical tests that can be performed and the conclusions that can be drawn from the data.

Types of Data Scales

The four main types of data scales are:

1. Nominal Scale:

    Characteristics: Represents categorical data which can be divided into distinct groups but without any order or rank.

    Examples: Gender (male, female), blood type (A, B, AB, O), marital status (single, married, divorced).

    Statistical Operations: Counting, mode calculation, contingency correlation.

    Operations: Counting, mode.

    Description: Data on a nominal scale are categorized into distinct groups without any order or hierarchy. For example, gender, nationality, or eye color. You can count the frequency of data points in each category and determine the mode (most frequent category), but operations like addition or average don't make sense for nominal data.

    Data Analysis: Can be used in qualitative data analysis, like frequency distribution.

2. Ordinal Scale:

    Characteristics: Similar to nominal scale but with an added element of order or rank amongst the categories. However, the differences between the ranks are not equal or quantifiable.

    Examples: Education level (high school, bachelor's, master's, PhD), satisfaction rating (unsatisfied, neutral, satisfied).

    Statistical Operations: Median and mode calculations, nonparametric statistical tests.

    Operations: Counting, mode, median, rank order.

    Description: Ordinal data is similar to nominal data but with a meaningful order or ranking among the categories. However, the intervals between the ranks are not necessarily equal. For example, customer satisfaction ratings like "satisfied", "neutral", and "dissatisfied". You can determine the mode, median, or create a rank order, but you cannot meaningfully add or subtract these data points.

    Data Analysis: Useful for nonquantitative analysis where order matters.

3. Interval Scale:

    Characteristics: Numeric scales in which both order and exact differences between values are meaningful. There is no true zero point, so ratios are not meaningful.

    Examples: Temperature (in Celsius or Fahrenheit), calendar years, IQ scores.

    Statistical Operations: Mean and standard deviation calculations, parametric statistical tests.

    Operations: Addition, subtraction, mean, standard deviation.

    Description: Interval data have meaningful intervals between measurements, but there is no true zero point. Temperature is a classic example. You can add and subtract values (e.g., the difference in temperature between two days), calculate the mean and standard deviation, but operations like multiplication or division are not appropriate since the ratio of two interval scale values is not meaningful.

    Data Analysis: Appropriate for analyses that require understanding the distance between measurements.

4. Ratio Scale:

    Characteristics: Contains all the properties of an interval scale, with the addition of a clear definition of zero. Differences and ratios are both meaningful.

    Examples: Height, weight, duration, salary, age.

    Statistical Operations: All statistical operations (mean, mode, median, standard deviation, correlation, regression).

   Operations: All arithmetic operations (addition, subtraction, multiplication, division), mean, mode, median, standard deviation.

   Description: Ratio scales are similar to interval scales but with a meaningful zero point, which allows for the full range of arithmetic operations. Examples include weight, height, or age. You can calculate differences, ratios, averages, and other statistical measures.

    Data Analysis: Suitable for most kinds of quantitative analysis.

Each scale type has its own implications in terms of the appropriateness of statistical methods. For instance, mean and standard deviation are meaningful for interval and ratio scales but not for nominal or ordinal scales. Understanding these scales helps in choosing the right statistical tools and techniques for data analysis.

 Data Scales in Python

Github link :

Nominal Variable may be converted to one-hot encoding

import pandas as pd

df = pd.DataFrame({'Color': ['Red', 'Green', 'Blue']})
print("Dataset : \n",df)
print(type(df['Color'][0]))
#df['Color'] = df['Color'].astype('category')
#print(type(df['Color'][0]))
print("After 1 hot encoding")
pd.get_dummies(df, columns=['Color'])

Ordinal Variable converted to numbers
import pandas as pd

df = pd.DataFrame({'Color': [1,2,3]})
print("Dataset : \n",df)
print(type(df['Color'][0]))
print("After 1 hot encoding")
pd.get_dummies(df, columns=['Color'])

Operations on numerical values
education_order = ['High School', 'Bachelor', 'Master', 'PhD']
df = pd.DataFrame({'Education': ['Bachelor', 'PhD', 'Master']})

# Convert to Categorical type with specific order
df['Education'] = pd.Categorical(df['Education'], categories=education_order, ordered=True)

# Convert to integer codes
df['Education'].cat.codes  

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