Biostats

Measurement scales

Measures of Central Tendency

Measures of Variability

Determine if a variable is nominal, ordinal, or continuous data

Categorical Data

Nominal data has no scale or direction

• Two or more “groups”

  • Dichotomous = 2 groups 

• Ex:

  • Diagnosis

  • Biological sex category 

  • Hair color

Original data has direction but no fixed scale 

• Numeric scales have no measurable “value,” only show direction

• Ex:

  • Likert scale (1-5)

  • NYHA functional Class

  • Pain scale (numeric or faces)

Continuous Data
Interval data has scale and direction 

• No “true” zero

  • “Infinite” scale in both +/- directions

• Ex:

  • Time

  • Temperature

  •  Change in heart rate

Ration data has scale and direction 

• “True zeros” exists

  • “Infinite” in only one direction 

• Ex:

  • Age in years

  • Weight in kg

  • Heart rate (bpm)

example

Standard Deviation

IQR or Range?

• IQR informs variability around center of data (50%)

• Range informs how far outliers are lying out from the center

Example

If there are 100 people in a study:

• Within 1 standard deviation of the mean: about 68 people

• Within the interquartile range (IQR): 50 people

• Within the range: 100 people

Easy way to remember:

Measure	% of data	Out of 100 people
±1 standard deviation	~68%	68 people
IQR	50%	50 people
Range	100%	100 people

The 68% comes from the empirical rule (68–95–99.7 rule).

Mode < Median < Mean

• Mode = 3 days

• Median = 3.5 days

• Mean = 6.5 days

When mean > median > mode, the data are right-skewed (positively skewed).

Why?

A few patients likely have very long hospital stays, which pulls the mean upward.

👉 Answer: Skewed (right/positively skewed)

• A variable measured on the ordinal scale is best summarized by the Median, paired with the IQR (Interquartile Range).

Why this pair?

• Central Tendency (Median): Ordinal data has a meaningful rank order, but the intervals between ranks are not uniform or mathematically defined (e.g., Likert scales, cancer staging, pain scales 1–10). Because arithmetic operations like addition and division are invalid without equal intervals, calculating a Mean is inappropriate. The Median only requires knowing the middle ranked value.

• Variability (IQR): Measures of dispersion like Standard Deviation (SD) require distances from a mean, making them unsuitable for ranked data. The IQR (the distance between the 25th and 75th percentiles) relies purely on ranked cutoffs, making it the standard companion to the median.