VARIABLE SAMPLING
VARIABLE SAMPLING OR QUANTITATIVE ESTIMATION IS A STATISTICAL
TECHNIQUE USED TO ESTIMATE THE DOLLAR AMOUNT OF AN ACCOUNT
BALANCE. WHEN VARIABLE SAMPLING IS USED THE RESULT IS USUALLY
STATED IN TERMS OF A RANGE OF NUMBERS (E.G., $2,100,000 TO $2,700,000)
WHICH THE AUDITOR IS X% (E.G., 95%) CONFIDENT INCLUDES THE TRUE
VALUE. UNLIKE ATTRIBUTE SAMPLING WHERE THE CONCERN IS WITH
THE UPPER PRECISION LIMIT, VARIABLE ESTIMATION USES BOTH AN
UPPER AND LOWER PRECISION LIMIT, I.E., AN ACCOUNT BALANCE CAN BE
EITHER UNDERSTATED OR OVERSTATED. THERE ARE THREE BASIC
VARIABLE SAMPLING PLANS AVAILABLE TO THE AUDITOR. THESE THREE
METHODS ARE DEFINED BELOW. HOWEVER, WE WILL NOT USE THEM IN
THIS COURSE. THE METHOD MOST OFTEN USED BY AUDITORS IN
ESTIMATING DOLLAR AMOUNTS IS REFERRED TO AS PROBABILITY
PROPORTIONAL TO SIZE (PPS) OR MONETARY UNIT (MUS) SAMPLING. PPS
SAMPLING IS COVERED THIS COURSE.
THE STATISTICAL ACCOUNTING ESTIMATION MODELS ARE:
1.
UNSTRATIFIED MEAN PER UNIT (UNSTRATIFIED MPU)
AFTER A SAMPLE IS SELECTED AND A VALUE IS DETERMINED FOR
EACH SAMPLE ITEM, THE SAMPLE MEAN OF SAMPLE VALUES IS
MULTIPLIED BY THE NUMBER OF ITEMS IN THE POPULATION TO
PRODUCE AN ESTIMATE OF THE TOTAL DOLLAR VALUE OF THE
SAMPLED POPULATION. THE REQUIRED STATISTICAL TECHNIQUES
REQUIRES LARGE SAMPLE SIZES BECAUSE OF THE WIDE POSSIBLE
RANGE OF VALUES. IN OTHER WORDS, THE USE OF THIS METHOD IS
COSTLY BECAUSE OF THE REQUIRED LARGE SAMPLE SIZE. IN
ORDER TO REDUCE THE SAMPLE SIZE, THE AUDITOR MAY USE THE
STRATIFIED MEAN PER UNIT MODEL.
2.
STRATIFIED MEAN PER UNIT (STRATIFIED MPU)
AS NOTED ABOVE, WHEN A POPULATION IS HIGHLY VARIABLE (HAS
A LARGE STANDARD DEVIATION), UNSTRATIFIED MPU MAY
PRODUCE VERY LARGE SAMPLE SIZES. IN MANY SUCH CASES,
STRATIFICATION Of THE POPULATION PRODUCES AN ESTIMATE
THAT HAS A DESIRED LEVEL OF PRECISION WITH A REDUCED
SAMPLE SIZE. STRATIFIED MPU MAY BE APPLIED TO POPULATIONS
WHERE NO MONETARY MISSTATEMENT S ARE EXPECTED, OR
WHERE A MODERATE RATE OR AMOUNT OF MONETARY
MISSTATEMENTS ARE EXPECTED.