Distinguish interval and ratio measurement scales

One room is at 10 °C and another is at 20 °C. Does the second Celsius reading prove that the room has twice the temperature?

Two different event times are recorded as hours from a chosen starting instant. If that reference moves 10 hours earlier, 10 is added to both readings. Predict what stays unchanged

Two events have coordinates 8 h and 20 h from a chosen reference. Move the reference earlier by 10 h, then 40 h. Read the new coordinates and compare their difference with their ratio. The events themselves do not move

Which statement matches all three settings?

Interval or ratio?

Both scales use equal units. The difference is what zero means

1. 1Interval scale Zero is a chosen reference. Differences are meaningful, but ratios of the readings depend on that choice. Celsius temperature and event-time coordinates are examples
2. 2Ratio scale Zero means none of the quantity. Differences and ratios are meaningful. Mass, length, duration and counts are examples
3. 3Do not replace discrete or continuous These answer another question: which values can occur? A count can be discrete and ratio; a measured quantity can be continuous and either interval or ratio

First event

\(\displaystyle 18\text{ h}\)

Second event

\(\displaystyle 30\text{ h}\)

Two event-time coordinates are measured from the same reference. How many hours separate the events?

Subtract the earlier coordinate from the later one

Which statement about a duration of 0 seconds is correct?

A box contains 6 kg of material and another contains 3 kg. After converting to grams, can the first still be described as twice the mass?

A continuous measurement is recorded to the nearest whole centimetre. Does this make it an interval scale?

A library counts the books borrowed by each member. Which pair is correct?

Air temperature is measured in degrees Celsius. Which pair is correct?

A cafe records satisfaction as 1 = very low through 5 = very high. Does writing the ordered categories as digits prove equal intervals?

Ask two separate questions

First decide what the variable records. Then classify its numerical scale if it is a quantity

1. 1Possible values Counts have separate values. Continuous measurements can vary throughout a range
2. 2Meaning of zero Ask whether zero means none of the quantity or merely a chosen reference. A data set does not need to contain a zero for its scale to have a meaningful zero
3. 3Explain in context For duration, 0 seconds means no elapsed time. For Celsius, 0 °C does not mean no temperature. That reason matters more than memorising the label