Measurement vs Count Data
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Measurement
Variables and data types
A measurement is the recorded value of a variable for one observational unit, reported on a scale and usually carrying units.
Keep three things apart: the variable is height, the observational unit is student 12, and the measurement is the number 168 centimeters that ties them together. Measurements carry units and a level of precision, so the same underlying quantity can be recorded on different scales. For example, a height of 168 centimeters becomes inches, which divides the mean and the standard deviation by 2.54 but leaves the shape of the distribution and any correlation unchanged. Recording to the nearest centimeter also builds in rounding, one reason repeated measurements of the same object are not identical.
Count data
Variables and data types
Count data are whole-number tallies of how many observational units fall in a category or how many times an event happened.
Counts are non-negative whole numbers and they depend on how big the group is, which is why comparing raw counts across groups of different sizes misleads. For example, 45 walkers in a 300-student school is a larger share than 60 walkers in a 600-student school, since beats . Converting each count to a proportion or a rate is the fix. Counts are also what chi-square procedures require, because the test compares observed counts to expected counts; entering percentages instead produces a meaningless statistic.