Scales of measurement

Scales of measurement

Scales of measurement definition

• describes the nature of the information contained in a given set of data

Scales of measurement (four types)

• nominal

• ordinal

• interval

• ratio

nominal scale data

• the data is non numerical

• the data can only be qualitative

• each item in the data set belongs to a class or category

What are some examples of nominally-scaled data?

• Gender (e.g. male, female)

• Political orientation (e.g republican/democratic)

• Race (e.g White/African American)

ordinal scale data

• builds on nominal scale data

• they can be quantitative or qualitative

• there can be numbers in the data set or words in the data set

• The “ord” stands for order

• the items are ordered in a meaningful direction

• Distance between items is not necessarily equal (there is no equal interval between different points in the data)

What are some example of ordinally-scaled data?

• Race results (e.g. 1st place, 2nd place, 3rd place) = in the spread sheet we can make this quantitative by writing down 1,2,3, or make it qualitative in action by writing down first place, second place and third place.

• surveys to collect data: Strongly agree/ Agree/ Disagree/ Strongly Disagree = thus we are looking at qualitative data with a meaningful order making it ordinal scaled data

• Ranking students performance in a classroom =

  • rank 1 gets 99%

  • rank 2 gets 91%

  • rank 3 gets 90%

    (the students score is ordered, but not necessarily equal: between rank 1 & rank 2 there is 8% difference, but between rank 2 & rank 3 there is 1% difference).

interval scale data

• they are numerical

• can only be quantitative data (has to be numbers)

• distance between points is equal and meaningful

• but relationship between points is not meaningful

• can have values below 0 (zero)

What are some examples of data on an interval scale?

• Time of day (e.g. 1 PM, 2 PM 3 PM)

• Temperature (e.g. degrees in Fahrenheit)

  • numerical (e.g. 1 degree, 2 degrees, 3 degrees, the distance between points is equal = the distance between 1 & 2 degrees is the same as the distance between 2 & 3 degrees and that is meaningful it is one degree difference in heat and it means something consistently, BUT the relationship between the points is not meaningful - we can not say that 10 degrees Fahrenheit is twice as hot as 5 degrees Fahrenheit / or we can not say that 08.00 o clock is twice as much as 16.00 o clock.

Ratio scale data

• numerical

• can only be quantitative (only numbers)

• All the qualities of the interval scale plus a true zero

• the absence of whatever is being measured is possible

• the relationship (ratio) between points is meaningful

What are some examples of data on a ratio scale

• inches = if you are zero inches tall its a complete absence of you, we can also say that 8 inches is twice as much as 4 inches thus the relationship between points is meaningful

• Percent correct on an exam = the once who scored 100% did twice as much as the students who scored 50%. if you can 0% on an exam it refers to complete absence of points on the exam.

• The amount of money on your wallet = if you have zero dollars in your wallet there is a complete absence of money in the wallet, and the person who has 10 dollars in the wallet has twice as much as the person who has 5 dollars in their wallet.

Nominal the use of central tendency

• Mode

Ordinal the use of central tendency

• Median

• Mode

Interval the use of central tendency

• Mean

• Median

• Mode

Ratio the use of central tendency

• Mean

• Median

• Mode