The relationship between variables and levels of measurement

Full Answer Section

1. What meaningful conclusions can be drawn: The level of measurement determines how much information you can infer from your data.

There are four main levels of measurement, from least to most informative:

1. Nominal Scale: Categories only, no order or rank.
2. Ordinal Scale: Categories with a meaningful order or rank, but unequal intervals between them.
3. Interval Scale: Ordered data with meaningful intervals between points, but no true zero point.
4. Ratio Scale: Ordered data with meaningful intervals and a true zero point.

The relationship is that every variable will fall into one of these levels of measurement, and identifying its level is the first step in properly analyzing and interpreting the data collected for that variable.

Distinguishing Between Categorical and Continuous Variables

Variables are broadly classified into two main types:

1. Categorical Variables (Qualitative Variables):

   • Represent types of data which may be divided into groups.
   • Their values are distinct categories, not numerical measurements.
   • They answer questions like "what type?" or "which group?"
   • Examples: Gender (male, female, non-binary), Blood Type (A, B, AB, O), Marital Status (single, married, divorced), Favorite Color (red, blue, green).
   • Relationship to Levels of Measurement: Categorical variables can be measured on the nominal or ordinal scales.

2. Continuous Variables (Quantitative Variables):

   • Represent numerical data that can take any value within a given range.
   • They are measured along a continuum and can be infinitely divided into smaller increments.
   • They answer questions like "how much?" or "how many?"
   • Examples: Height (1.75m, 1.755m), Weight (65.3 kg), Temperature (25.7°C), Time (2.5 seconds), Income (KSh 150,000.50).
   • Relationship to Levels of Measurement: Continuous variables can be measured on the interval or ratio scales.

Key Distinction: The core difference lies in whether the values represent distinct groups/labels (categorical) or measurable quantities on a scale (continuous).

Categorizing Variables According to the Appropriate Level of Measurement

Let's categorize some examples:

1. Variable: Type of Car (e.g., Sedan, SUV, Truck, Hatchback)

   • Categorization: Categorical
   • Level of Measurement: Nominal - There's no inherent order or ranking among car types. An SUV isn't "more" or "less" than a Sedan.

2. Variable: Education Level (e.g., High School, Bachelor's Degree, Master's Degree, PhD)

   • Categorization: Categorical
   • Level of Measurement: Ordinal - There's a clear order or hierarchy in educational attainment (PhD is higher than a Bachelor's). However, the "distance" between High School and Bachelor's isn't necessarily the same as between Master's and PhD.

3. Variable: Temperature in Celsius (°C)

   • Categorization: Continuous
   • Level of Measurement: Interval - The intervals between values are meaningful and equal (e.g., the difference between 10°C and 20°C is the same as between 20°C and 30°C). However, there is no true zero point where "0°C" means "no temperature" (e.g., 20°C is not twice as hot as 10°C).

4. Variable: Height in Centimeters (cm)

   • Categorization: Continuous
   • Level of Measurement: Ratio - The intervals are equal and meaningful (e.g., the difference between 150cm and 160cm is the same as 170cm and 180cm). Crucially, there is a true zero point (0cm means no height). Therefore, a person who is 180cm tall is twice as tall as someone who is 90cm tall.

Differentiating Between Reliability and Validity of a Measure

Both reliability and validity are crucial aspects of evaluating the quality of a measurement tool or research study. They address different questions about the measurement.

• Reliability:

  • Definition: Refers to the consistency and stability of a measure. A reliable measure produces the same or similar results under consistent conditions. It's about whether the tool consistently measures something.
  • Question it answers: "If I measure this again, will I get the same result?" or "Is this measure free from random error?"
  • Analogy: Think of a weighing scale. If you step on it five times in a row and it gives you wildly different weights each time, it's not reliable. If it gives you the same weight every time (even if that weight is consistently 5kg too high), it's reliable.
  • Types: Test-retest reliability, inter-rater reliability, internal consistency (e.g., Cronbach's Alpha).

• Validity:

  • Definition: Refers to the accuracy of a measure. A valid measure actually measures what it intends to measure. It's about whether the tool measures the right thing.
  • Question it answers: "Am I truly measuring what I claim to be measuring?" or "Does this measure accurately reflect the concept I'm interested in?"
  • Analogy: Following the weighing scale analogy, if the reliable scale consistently tells you that you weigh 5kg more than you actually do, it's reliable but not valid (it's consistently wrong). A valid scale would give you your true weight.
  • Types: Content validity, criterion validity (concurrent, predictive), construct validity (convergent, discriminant).

Key Relationship: A measure must be reliable to be valid, but a reliable measure is not necessarily valid. You can consistently get the wrong answer (reliable but invalid), but you cannot consistently get the right answer if your tool is inconsistent (cannot be valid if not reliable).

Evaluating the Reliability and Validity of a Measure

Let's consider a hypothetical measure: a new "Workplace Stress Scale" (WSS) designed for nurses in Kenyan hospitals.

Evaluating Reliability of WSS:

1. Test-Retest Reliability:

   • Method: Administer the WSS to a group of 50 nurses today. Re-administer the exact same WSS to the same 50 nurses two weeks later (assuming no significant changes in their work stress levels in that short period).
   • Evaluation: Calculate the correlation coefficient between the scores from the first and second administrations. A high positive correlation (e.g., r > 0.70) would indicate good test-retest reliability, suggesting the WSS yields consistent results over time.

2. Internal Consistency (e.g., using Cronbach's Alpha):

   • Method: Administer the WSS (which likely has multiple questions/items) to a large group of nurses. Use statistical software to calculate Cronbach's Alpha.
   • Evaluation: A Cronbach's Alpha value above 0.70 (and ideally above 0.80 for well-established scales) would suggest good internal consistency. This means that all the items on the WSS are measuring the same underlying construct (workplace stress) consistently. If one item shows a very low correlation with the overall score, it might need to be revised or removed.

Evaluating Validity of WSS:

1. Content Validity:

   • Method: Gather a panel of experts (e.g., occupational health psychologists, experienced nurse managers, stress researchers). Ask them to review each item on the WSS and rate its relevance and representativeness in measuring "workplace stress" for nurses.
   • Evaluation: If experts agree that the WSS adequately covers all important aspects of workplace stress relevant to nurses (e.g., workload, patient demands, inter-colleague conflict, shift patterns) and excludes irrelevant ones, it has good content validity.

2. Criterion Validity (Concurrent Validity):

   • Method: Administer the new WSS to a group of nurses. Simultaneously, administer a well-established and validated existing "Nurse Burnout Inventory" (a measure that is known to correlate with stress) to the same nurses.
   • Evaluation: Calculate the correlation between scores on the new WSS and the established Burnout Inventory. A significant positive correlation would indicate good concurrent validity, meaning the WSS produces results similar to other validated measures of related constructs.

Sample Answer

Relationship Between Variables and Levels of Measurement

A variable is any characteristic, number, or quantity that can be measured or counted. It's a data item that can take on different values. For example, age, income, gender, or educational attainment are all variables.

Levels of measurement (also known as scales of measurement) refer to the different ways in which variables can be defined and categorized. They describe the nature of the information within the values assigned to variables. Understanding the level of measurement for a variable is crucial because it dictates:

1. What statistical analyses are appropriate: Certain statistical tests only work with specific levels of measurement.