Give examples of nominal, ordinal, interval. and ratio data. Then, convert your ratio data example into interval, ordinal, and nominal scales.
Measurement Scales
Practice
1. Indicate the first letter (N, O, I, R) of the highest possible scale for each of the following measures, where N is lowest and R is highest:
Measure Highest Scale
a. Feet of snow -- Interval
b. Brands of carbonated soft drinks -- Nominal
c. Class rank at graduation -- Ordinal or Interval per measurement debate
d. GPA -- Interval
e. Speed of a baseball pitch -- Ratio
7. Are the following variables discrete or continuous? Mark “D” or “C” to indicate your answer.
Measure Variable Type
a. Inches of rainfall -- C
b. GPA -- C
c. Speed of base ball pitch -- C
d. Time taken to solve a puzzle -- C
e. Level of depression -- D
f. Number of angels that can fit on the head of a pin (Oops . .how’d that get in her again? You may skip this one -- D
http://drdavespsychologypage.intuitwebsites.com/Two___Two_____four.pdf
1a. Ratio (see article)
b. Nominal
c. Only ordinal (see article)
d. Interval
e. Ratio
7. All correct.
1. Converting ratio data to different scales:
Ratio data example: Height of individuals in centimeters
a. Interval scale: Convert the height into temperature categories (e.g., low, medium, high) based on predetermined criteria.
b. Ordinal scale: Rank individuals based on their height, from shortest to tallest.
c. Nominal scale: Group individuals into categories based on height ranges (e.g., under 150cm, 150-160cm, 160-170cm, etc.).
7. Variable types:
a. Inches of rainfall - C (continuous)
b. GPA - C (continuous)
c. Speed of baseball pitch - C (continuous)
d. Time taken to solve a puzzle - C (continuous)
e. Level of depression - D (discrete)
f. Number of angels that can fit on the head of a pin - D (discrete)
Examples of nominal data:
- Brand names of cars (e.g. Toyota, Ford, Honda)
- Colors of shirts (e.g. red, blue, green)
- Gender (e.g. male, female)
Examples of ordinal data:
- Educational levels (e.g. elementary, high school, college)
- Satisfaction ratings (e.g. very satisfied, satisfied, neutral, dissatisfied, very dissatisfied)
- Ranking of sports teams (e.g. 1st place, 2nd place, 3rd place)
Examples of interval data:
- Temperature in Celsius or Fahrenheit (e.g. 25°C, 50°F)
- Dates (e.g. January 1, 2022; December 31, 2022)
- IQ scores (e.g. 100, 120, 140)
Examples of ratio data:
- Age (e.g. 20 years old, 35 years old)
- Height (e.g. 5 feet 10 inches, 170 cm)
- Weight (e.g. 150 lbs, 70 kg)
Conversion of ratio data example (height) into different scales:
Interval scale: Dividing the heights into intervals or ranges. For example, categorizing heights as "Short" (under 5 feet 5 inches), "Average" (between 5 feet 5 inches and 6 feet), and "Tall" (above 6 feet).
Ordinal scale: Ranking the heights from shortest to tallest. For example, assigning ranks of 1, 2, and 3 to heights "Short" (1), "Average" (2), and "Tall" (3).
Nominal scale: Converting the heights into categories. For example, categorizing heights as "Short," "Medium," and "Tall."
Measurement Scales:
1. Highest Scale
a. Feet of snow - Ratio
b. Brands of carbonated soft drinks - Nominal
c. Class rank at graduation - Ordinal
d. GPA - Interval
e. Speed of a baseball pitch - Ratio
7. Variable Type
a. Inches of rainfall - Continuous (C)
b. GPA - Continuous (C)
c. Speed of baseball pitch - Continuous (C)
d. Time taken to solve a puzzle - Continuous (C)
e. Level of depression - Discrete (D)
f. Number of angels that can fit on the head of a pin - Discrete (D)
Examples of nominal, ordinal, interval, and ratio data:
1. Nominal data: Categories or labels with no specific order.
- Example: Eye color (blue, brown, green).
2. Ordinal data: Categories with a specific order or ranking.
- Example: Likert scale ratings (strongly agree, agree, neutral, disagree, strongly disagree).
3. Interval data: Numeric values with equal intervals between them, but no true zero point.
- Example: Temperature in Celsius or Fahrenheit.
4. Ratio data: Numeric values with equal intervals between them and a true zero point.
- Example: Height in centimeters or weight in kilograms.
Converting the ratio data example (height in centimeters) into different scales:
- Interval scale: Divide the data into intervals or ranges.
Example: Height intervals (0-50 cm, 51-100 cm, 101-150 cm, etc.).
- Ordinal scale: Assign ordinal rankings based on the values.
Example: Short (<100 cm), Average (100-150 cm), Tall (>150 cm).
- Nominal scale: Categorize the data into distinct groups.
Example: Height categories (Short, Average, Tall).
Now moving on to the provided practice questions:
1. Indicate the highest possible scale for each measure:
a. Feet of snow: Interval scale (measurements have equal intervals).
b. Brands of carbonated soft drinks: Nominal scale (no specific order).
c. Class rank at graduation: Ordinal scale (specific order based on rank).
d. GPA: Interval scale (measurements have equal intervals).
e. Speed of a baseball pitch: Ratio scale (has a true zero point).
7. Determine if the variables are discrete or continuous:
a. Inches of rainfall: Continuous (can be any value within a range).
b. GPA: Continuous (can have decimal values).
c. Speed of a baseball pitch: Continuous (can be any value within a range).
d. Time taken to solve a puzzle: Continuous (can have decimal values).
e. Level of depression: Discrete (falls into distinct categories or levels).
f. Number of angels that can fit on the head of a pin: Discrete (specific, countable values).