Statistics is baffling enough without being footloose with terminology. So let’s clear up what we mean by a statistical sample.
The term “Statistical Sample” has a very specific meaning in the Cogent system. It refers to a sample that is randomly selected from the entire population of loans eligible for a particular sample type (aka “audit shell”). The suggested sample size is calculated every period by the system and is designed to yield a 95% confidence and 2% precision over 12 months. This is the standard originally established by FNMA, FHLMC, and HUD for lenders who qualify to substitute ‘statistical sampling’ for the traditional 10% random sample.
The generic term ‘statistical sample’ is not very meaningful, in and of itself. It simply refers to a sample in which some statistical principle has been employed, without defining which principle. For example, it could refer merely to a randomly drawn sample, without specifying what population is being drawn from or how much precision will be achieved across what period.
Image by johnbullas
Rick Astley reference
To illustrate: most Cogent ProductionQC clients have at minimum a “Production” sample type, for which all loans originated in a particular period (typically a month) are eligible. When a Statistical Sample (in the Cogent definition) is randomly drawn from this population, all loans have the same probability of being selected. No distinction is made between loan type, loan source or any other loan characteristic. It is intended to establish a baseline of overall loan quality across the organization.
In order to achieve a 95% confidence and 2% precision for a particular category of loan, it is necessary to go beyond the “Statistical Sample”. For example, in the Cogent system, to achieve this standard for all FHA loans originated, define a Targeted Query (Loan Type = FHA) and run the query. The resulting screen displays all qualifying loans, including qualifying loans that were randomly drawn previously in the “Statistical Sample” or any other samples in this period. These count towards the total required. Use the embedded Cogent Statistical Calculator to calculate the required (“suggested”) sample size for the period. From the suggested sample size, subtract the number of qualifying loans that have previously been sampled and enter the result in the Sample Size box. The Cogent system will then randomly select the entered number of loans from the qualifying loans.
The Cogent “Stratified Sample” is in effect a pre-defined Targeted Sample. Most typically, the Cogent system stratifies originations by Source or Channel and automatically tracks and calculates the sample size required for each stratum (Source or Channel), net of qualifying loans randomly drawn in the “Statistical Sample.” Over 12 months, the Stratified Sample achieves 95% confidence and 2% precision for each stratum. In Targeted Samples, this automated operation is performed by the user, using Cogent’s embedded tools.
Thus, in order to leverage the Cogent system’s sampling optimization, clients should begin sampling from the broadest category (all loans eligible) to the most narrow category (e.g., individual underwriters). In this way, all loans selected in previous broad categories are counted towards ever narrower categories, minimizing the number of loans to be sampled and audited.