# Describing Nominal and Ordinal Data

#### Descriptive versus Inferential Statistics

• Descriptive statistics talk about what the data is like: they describe it.
• Inferential statistics try to make inferences from the data: what does the data tell us about what is not in the data? (For example, what does a poll tell us about the actual outcome of an election?)

#### Some possible descriptions of a data set.

• Central tendency: mode, median, mean.
• Variability: range, variance, mean deviation, standard deviation.
• Shape: skew, kurtosis.
All Numbers Are Not Equal

#### Scales of Measurement

• Nominal
- a number signifies a category
ex: 1 = male, 2 = female
• Ordinal
- there is an order to the categories or events
ex: first, second, third
• Interval
- the magnitude between events is known but there is no true '0'
ex: °F and °C
• Ratio
- the magnitude between events is known and there is a true '0'
ex: height and weight
- can add, subtract, multiply and divide
Sometimes a number is just a name or a category
• Nominal data
• "chemistry major," "math major," "business major"
• Any numbers assigned are just a code: no arithmetic significance. Can't subtract math major from chemistry major.
• We can ask for the mode, the most common value.
• The is no measure of variability.
Sometimes a number tells us the order of events
• Ordinal data
• She ranked 1st in our class; he ranked 15th, etc.
Or, he is the richest person in America.
Or, my team finished in seventh place.
• We can ask for the mode, but also for the median, the middle value.
• Range is a measure of the spread of ordinal data.
Sometimes we can add and subtract numbers
• Interval data
• Temperature is the best example: °90 is ° hotter than °45, but it is not twice as hot!
• We can ask for the mean.
(Σ(all values)) / (number of values)
Some numbers can be multiplied and divided
• Ratio data
• We have a true zero: example, weight.
• We can multiply and divide: 90 pounds is twice as heavy as 45 pounds.
Seeing Clearly with Nominal Data
It's time to begin learning to see better
• Make a table of the number of items in each category.
• This is a frequency distribution.
• Example: Beings in the professor's house
Type of being Frequency
Humans 4
Other mammals 1
Reptiles 1
"Las Cucarachas" 15
Demons, poltergeists, etc. 3
Using graphs and charts
Seeing Clearly with Ordinal Data
First, Second, Third: I see a pattern
• Bar charts: order the bars!
• We can add range as a measure of variability.
If our sample contains the 4th, 9th, 10th, 16th, and 42nd ranked student in our class, the range is 38.