Levels of Measurement

Levels of Measurement

Definition

  • Levels of measurement refer to the classification of variables based on the amount of precision and the mathematical properties they possess. These levels influence the statistical tools applicable for analysis.
  • Understanding these levels is essential for selecting appropriate statistical analyses and accurately interpreting data.

Nominal Level

  • Description: The nominal level describes variables that indicate only a difference between categories, without any inherent order or ranking.
  • Function: These variables categorize data into distinct groups where the categories are mutually exclusive and collectively exhaustive.
  • Example: "Which school did you attend?" classifies respondents into different schools without implying hierarchy or order.

Key Characteristics of Nominal Variables:

  • Limited Precision: They do not provide information about the magnitude or order of differences.
  • Mathematical Properties: Operations supported include counting or determining if two items are the same or different.
  • Statistical Analysis Use: Limited to frequency counts, mode, and chi-square tests; cannot be used for calculations involving means or standard deviations.

Dichotomous Variables

  • Definition: A dichotomous variable is a specific type of nominal variable that measures the presence or absence of an attribute, resulting in only two possible categories.
  • Example: "Did you attend UT?" is recorded as 'yes' or 'no'.

Features of Dichotomous Variables:

  • Special Case of Nominal Variables: They are the simplest form, consisting of only two categories.
  • Flexibility: All nominal variables can be transformed into multiple dichotomous variables, useful in statistical models such as logistic regression.
  • Examples: Yes/no questions, alive/dead, employed/unemployed.

Advantages:

  • Simplifies complex nominal data.
  • Facilitates binary logistic analyses and other models requiring two categories.

Ordinal Level

  • Description: Ordinal variables add a layer of information by ranking categories in a specific order, reflecting a hierarchy or preference, but without assuming equal intervals between categories.
  • Example: "Please indicate the highest level of education you reached" (categories: elementary, high school, college, postgraduate).

Characteristics of Ordinal Variables:

  • Order Matters: Indicate which categories are higher or lower but do not specify how much higher.
  • More Precision than Nominal: Allow for some statistical analysis that considers rank.
  • Exhaustive and Exclusive Categories: Include all possible options and each response fits only one category.
  • Limitations: Cannot assume equal spacing between categories; statistical tests limited to non-parametric methods like Spearman's rank correlation.

Difference Between Nominal and Ordinal Measures:

  • Nominal Measures: Reflect differences in kind or type without order.
  • Ordinal Measures: Reflect differences in rank or order.
  • Clarity in Classification: Both types should be exclusive and exhaustive, ensuring mutual exclusivity in data classification.

Interval Level

  • Description: Interval variables include all the information of nominal and ordinal levels but further introduce meaningful intervals between values.
  • Example: "What did you score on the SAT?" where differences between scores (e.g., 1200 and 1300) are meaningful.

Features of Interval Variables:

  • Equal Intervals: The difference between any two points is consistent across the scale.
  • No Meaningful Zero: Zero does not indicate the absence of the attribute; it is an arbitrary point on the scale.
  • Statistical Utility: Can be analyzed with most statistical tools, including means, standard deviations, and correlation coefficients.

Examples:

  • Temperature in Celsius or Fahrenheit, standardized test scores.

Ratio Level

  • Description: The ratio level builds upon the interval level but includes a meaningful zero point, indicating the absence of the attribute being measured.
  • Example: "How many years of education have you completed?" where zero years means no education.

Characteristics of Ratio Variables:

  • Meaningful Zero: Indicates none of the attribute.
  • Highest Level of Measurement Precision: Supports all statistical operations, including ratios (e.g., twice as much).
  • Usefulness: Suitable for most statistical analyses, including calculating proportions, means, and ratios.

Examples:

  • Number of children, income, weight, height, years of education.

Summary of Levels of Measurement

  • Nominal: Categorizes data without order; limited to counts and mode.
  • Dichotomous: A special nominal with two categories; useful for binary data.
  • Ordinal: Ranks categories; can analyze order but not equal intervals.
  • Interval: Equal intervals between values; no true zero; suitable for parametric tests.
  • Ratio: Equal intervals with a meaningful zero; most flexible for statistical analysis.

Understanding these levels ensures appropriate data collection, analysis, and interpretation, leading to more accurate research findings and valid conclusions.

Measuring Democracy and Regime Types

Measurement and Operationalization

  • Measurement involves translating abstract concepts into measurable variables for empirical analysis.
  • Operationalization: The process of deciding how to record empirical observations of an attribute or behavior using specific criteria such as numerals, scores, or categorical labels.
  • This transformation is crucial for systematic analysis, allowing researchers to classify regimes, compare countries, and address empirical questions about political systems.

Historical Perspective on Democracy

  • The concept has evolved, historically seen as an obsolete or unstable political system during the 19th century, now viewed as a desirable form of governance.
  • The term demos, meaning "the common people," originates from ancient Greece, where philosophers like Aristotle and Plato discussed governance and its characteristics.

Aristotle’s Classification of Governments:

  • Based on rulers' number and type:
    • One: Monarchy vs. Tyranny.
    • Few: Aristocracy vs. Oligarchy.
    • Many: Politeia (Democracy).

Empirical Questions about Regimes

  • Researchers focus on substantive questions regarding different regime types:
    • Do democracies or dictatorships lead to higher economic growth?
    • What contributes to greater life expectancy?
    • What factors influence democracy survival or collapse?
    • Under what conditions does a dictatorship transition to a democracy?

Operationalizing Democracy

  • Establishing criteria to classify regimes accurately, reflecting core attributes of democracy, such as electoral competition and political rights.
  • Scholars investigate:
    • How can a democracy be identified in practice?
    • What institutional features indicate democratic governance?

Dahl’s Procedural or Minimalist View of Democracy

  • Robert Dahl's perspective emphasizes procedures over outcomes in understanding democracy.
  • A regime qualifies as a democracy if it features:
    • Free and fair elections.
    • Inclusive suffrage.
    • The right to run for office.
    • Multiple political parties.

Democracy-Dictatorship (DD) Measure

  • This measure classifies regimes based on electoral and institutional criteria:
    • The chief executive is elected.
    • The legislature is elected.
    • Multiple parties compete in elections.
    • There has been at least one alternation of power under consistent electoral rules.
    • Elections are contested, allowing opposition parties to have a real chance of winning.
    • Election outcomes are uncertain beforehand (ex ante uncertainty) and the winner actually takes office (ex post irreversibility).
    • Elections occur regularly (repeatability).
    • Voters must have more than two choices, excluding single-party lists.

Key Features of Contestation in DD

  • Contestation involves the presence of political opposition with a genuine chance of winning:
    • Ex ante Uncertainty: Election outcome is unknown before voting.
    • Ex post Irreversibility: The winner assumes office, confirming power transfer.
    • Regular Elections: Occur at predictable intervals.
    • Multiple Alternatives: Prevent single-party dominance.
    • Opposition Participation: Ensures meaningful electoral competition.

Alternation in Power

  • Alternation in power: Peaceful transfer of authority through elections is critical for democracy.
  • Distinguishes true democracies from regimes where incumbents maintain power through legitimacy or fraud, enhancing accountability and political renewal.

Polity IV Measure

  • Evaluates democracy and autocracy across 190 countries since 1800, providing:
    • Democracy Score (0-10)
    • Autocracy Score (0-10)
  • Polity Score Calculation:
    • Polity Score = Democracy Score – Autocracy Score.
    • Ranges from −10 to +10:
    • +6 to +10: Democratic regimes.
    • −5 to +5: Mixed regimes.
    • −6 to −10: Dictatorships.

Attributes Assessed:

  • Competitiveness of executive recruitment.
  • Openness of executive recruitment.
  • Executive constraints/decision rules.
  • Regulation of political participation.
  • Competitiveness of participation.
  • Each attribute is scored with different weights reflecting their importance in classification.

Freedom House Measure

  • Evaluates political and civil rights in nearly 200 countries and territories annually, producing composite scores that classify nations as:
    • Free
    • Partly Free
    • Not Free
  • Based on the Universal Declaration of Human Rights.

Political Rights Assessment Questions:

  • Is the head of state elected in free and fair elections?
  • Is there pervasive corruption?
  • Is the government accountable and transparent?
  • Do citizens have the right to organize and form opposition?
  • Are minorities granted autonomy?

Civil Rights Assessment Questions:

  • Is the media free and independent?
  • Are religious organizations free and autonomous?
  • Is the judiciary independent and impartial?
  • Are laws applied equally to all citizens?
  • Are trade unions free to operate?
  • Is there equality of opportunity and property rights?

This comprehensive overview synthesizes the key concepts and measurement approaches used to analyze regimes, emphasizing the importance of institutional features, contestation, and rights in defining and assessing democracy and authoritarianism globally.