What are we NOT covering?

• Rigorous statistical analysis
• How to use R/other tools

Different types of data

• Categorical/nominal data
• Ordinal data
• Ratio data
• Real number data
• Natural language

Categorical/nominal data

• Constrained to "categories" -- can be characters or numbers
• Race, gender, religion, yes/no, success/fail
• Yes/no, True/false are a subset known as binary data
• Cannot compare along a relative scale
• Cannot use mean/median, must use mode
• Very useful in creating crosstabs

Ordinal data

• Ordered along a scale, but the distances between categories are not known
• For instance, Likert scale questions -- 5 is higher than 4, but is my 5 the same amount higher than your 5?
• Other examples: Income brackets, highest level of education
• Can use to create a ranking, but cannot use other statistics -- What does "3.5 out of 5" mean?
• Look at relative numbers of responses, like nominal data

Interval data

• Order as well as the differences between responses (e.g. the "intervals") are known
• Fahrenheit/Celsius temps, time/date, income vs. spending
• No "true zero" -- negative values can exist, zero has meaning (it's not just "does not exist")
• Can say one value is "higher" than the other, but not necessarily "twice" as high

Ratio data

• Just like interval data, but now absolute zero has meaning and means "does not exist"
• Kelvin temp, height/weight, number of children, years of education, income
• Zero means "does not exist" -- so you can more easily say "X is 2x higher than Y"

Natural Language

• Written by the respondent themselves in a free-text field
• Usually needs to be coded in some way before it can be analyzed
• Can possibly use text analysis tools on this type of data too

Some tricky ones for discussion

What do you think?

PollEv.com/ryanclement191

• Age
• Grades
• Political party
• Number of poor mental health days in the past week

Mode

• The value that occurs most often
• Almost completely unaffected by outliers
• Can be unimodal: [1, 1, 2, 2, 4, 4, 4, 5, 6, 6] or more
  • [1, 1, 1, 2, 2, 3, 4, 4, 4] (bimodal)
• Often used for categorical data

Mean

• We're talking about the arithmetic mean (there are others)
• Often referred to as "the average"
• Calculated by adding up the values and dividing by the number of values: (1+1+2+4+5+5)/6 = 3
• Can be very sensitive to outliers:
  • (1+1+2+4+5+20)/6 = 5.5

Median

• The "middle" value in data -- the number that separates the top half from the bottom half
• Calculated by lining up the values and finding the middle value: [1, 1, 2, 4, 4, 5, 5]
• If you have an even number, take the mean of the middle two values:
  • [1, 1, 2, 4, 5, 5] -> (2+4)/2 = 3
• Less sensitive to outliers than the mean:
  • [1, 1, 2, 4, 5, 5]
  • [1, 1, 2, 4, 5, 20]

Standard Deviation

• Measure of how "spread out" the data is
• Need to use the mean to calculate (we won't get into that)
• Lower SD means numbers are mostly clustered around the mean, higher SD means they are more spread out (e.g. there is more variance)

Look at summaries of your data

• What are type of data are all of your variables?
• How many "complete" cases do you have? (i.e. how much missing data do you have?) Is there meaning/pattern behind this?
• Look at the central trends in your data (mode, mean) - do they make sense?

Distributions - histograms

Distributions - bar charts

Distributions - pie charts

2 categorical variables - crosstabs

Likert scale data -- stacked bar charts