Percentile Calculation Options in STATISTICA

The Percentile option, available on the Analyses/Graphs: Limits tab of the Options dialog box, is used to select from among six methods for computing percentile values, including medians (50th percentile) and quartiles (25th and 75th percentiles). The method that you select here will apply to every place in the STATISTICA program where medians, quartiles, or percentiles are computed. Below is an explanation of the six methods to help you to decide which method to select. An example is available for each method.

For the following methods, let n be the number of cases, and p be the percentile value divided by 100 (e.g., 50/100 = .5 for the median). Then, the available choices for computing percentiles are:

Weighted average at Xnp method (Weighted average centered at Xnp). Express np (n times p) as np=j+g where j is the integer part of np, and g is the fractional part of np; then compute:

PercentileValue = (1-g)xj + gxj+1

Note that X0 in the above computation is replaced by X1 (e.g., if j = 0, then the above formula would be (1-g)x1 + gx(0+1)).

Example

Weighted average at X(n+1)p method (Weighted average centered at X(n+1)p). Express (n+1)p as (n+1)p=j+g where j is the integer part of (n+1)p, and g is the fractional part of (n+1)p; then compute:

PercentileValue = (1-g)xj + gxj+1

Note that Xn+1 in the above computation is replaced by Xn (e.g., if j = n, then the above formula would be (1-g)xn + gxn).

Example

Empirical distribution function method. Express np (n times p) as np=j+g where j is the integer part of np, and g is the fractional part of np; then choose the percentile value as:

PercentileValue = xj

if g=0

PercentileValue = xj+1

if g>0

Example

Empirical distribution function with averaging method. Express np (n times p) as np=j+g where j is the integer part of np, and g is the fractional part of np; then compute the percentile value as:

PercentileValue = (xj + xj+1)/2

if g=0

PercentileValue = xj+1

if g>0

Example

Empirical distribution function with interpolation (MS Excel) method. Express (n-1)p ((n-1) times p) as (n-1)p=j+g where j is the integer part of (n-1)p, and g is the fractional part of (n-1)p; then compute the percentile value as:

PercentileValue = xj+1

if g=0

PercentileValue = xj+1 + g(xj+2 - xj+1)

if g>0

Example

Closest observation method (Observation closest to np). Compute j as the integer part of np+1/2, then compute:

PercentileValue = xj

Example