Types of data and measurement scales

Introduction to different types of data and the characteristics of different measurement scales.

The slides were developed for an introductory course on statistics for undergraduate students.

Transcript

1. Lecture 1B • Types of data • Measurement scales • Measurement error Peter Kamerman
2. Types of data
3. Types of data Nominal Discrete Data Categorical Numeric Ordinal Continuous
4. Types of data: Categorical Nominal • Mutually exclusive categories • No order to the categories Examples: o Gender (male, female) o Blood group (A, B, O) o Eye colour (blue, brown, green, etc) o Disease state (disease or no disease) • Data are said to be “binary” if there are only two possible categories
5. Types of data: Categorical Ordinal • Mutually exclusive categories • Logical ordering to the categories Examples: o Tumour grade (Tis, T1, T2, T3, T4) o Age categories (1-10 years, 11-20 years, 21-30 years, etc) o Socio-economic status (low income, middle income, high income) o Likert scales (extremely dislike, dislike, neutral, like, extremely like)
6. Types of data: Numerical Continuous • May take any value within a measurement range Examples: o Height o Weight o Temperature o Visual analogue scales • Precision and range is dependent on the measuring device
7. Types of data: Numerical Discrete • Whole numbers {0, 1, 2, 3,…} • Count data Examples: o Number of steps recorded on a pedometer o Number of times a bird returns to its nest each day o Number of days sick per year o Number of sites of pain on the body
8. “The heart of science is measurement” Erik Brynjolfsson (Academic)
9. Measurement scales
10. Measurement scales: Levels of measurement Nominal Ratio Ordinal Interval Named only Named + Ordered Named + Ordered + Equal distance between intervals Named + Ordered + Equal distance between intervals + True zero
11. Measurement scales Ordinal • Natural ordering of categories • But, the distance between intervals is not consistent • Therefore, cannot perform calculations using the values • Be careful of ordinal scales the appear to be interval or ratio measurements
12. Measurement scales Interval • Natural ordering of intervals • Equal distance between intervals • Therefore, can perform addition and subtraction on the values • Be careful not to treat interval scales as ratio scales
13. Measurement scales Ratio • Natural ordering of intervals • Equal distance between intervals • Has a true zero • Therefore, can perform addition, subtraction, multiplication, and division on the values
14. “An experiment is a question which science poses to nature, and a measurement is a recording of nature’s answer” Max Planck (Physicist)
15. Measurement error
16. Measurement error Types True value Measurement mean (𝑥) Systematic error (Bias = 𝑥 – true value) Random error (Measured by SDs)
17. Measurement error Types True value Measurement mean (𝑥) Systematic error • Bias = 𝑥 – true value Random error • Measured by SDs • Random error = precision Accuracy • Single measurement – true value
18. Measurement error Precision vs accuracy Density Values Accurate Precise Accurate Imprecise Inaccurate Imprecise Inaccurate Precise X X X XX X X X X X X X X X X X X X XX
19. Measurement error Correction of systematic error: Calibration Calibration of mercury-in-bulb thermometer
20. “One accurate measurement is worth a thousand expert opinions” Grace Hopper (Computer scientist)