Statistics is broadly either descriptive (aka, exploratory data analysis, EDA) or inferential (e.g., making predictions or forecasts). There is generally only one defined population and descriptive measures of the population are called parameters (and denoted with Greek symbols; e.g., mu, µ, for the population mean). A quantity that describes a sample is a statistic. Hence the difference between population parameters and sample statistics.
Measurement scales--ordered from weakest to strongest--include the following:
In regard to percentiles, the CFA approach is equivalent to Excel's =PERCENTILE.EXC() such that, if we want the (P) percentile, we lookup the position given by (n+1)*P; for example, if there are 15 observations and we want the 75th %ile, then we retrieve the (15+1)*0.75 = 12th ranked observation; if 90th %ile, we retrieve the observation in the position given by (15+1)*0.90 = 14.4, which is between the 14th and 15th position.
Measurement scales--ordered from weakest to strongest--include the following:
- Nominal measures are categories without rank; e.g. hedge fund styles.
- Ordinal measures are ranked categories; e.g., credit ratings.
- Intervals measures have equal differences but, because the origin is not a true absence, do not lend themselves to ratios; e.g., Celsius/Fahrenheit temperature scales such that 20 degrees Celsius is not twice 10 degrees.
- Ratios improve on intervals because the origin is a true absence; e.g., measures of money are ratio measures.
In regard to percentiles, the CFA approach is equivalent to Excel's =PERCENTILE.EXC() such that, if we want the (P) percentile, we lookup the position given by (n+1)*P; for example, if there are 15 observations and we want the 75th %ile, then we retrieve the (15+1)*0.75 = 12th ranked observation; if 90th %ile, we retrieve the observation in the position given by (15+1)*0.90 = 14.4, which is between the 14th and 15th position.
