Lecture 2 - Sampling Flashcards
what is sampling? (definition)
predetermined procedure for selection, withdrawal, preservation, transportation and preparation of portions to be removed from a lot as samples
why do sampling?
- using a fraction of population is faster and cheaper
- analyzing a whole population is practically difficult
- gives info about whole population
increasing sample size increases…
- accuracy
- also time, cost, sampling methods, logistics of sample handling, analysis and data processing
appropriate sampling avoids…
- consumer risk
2. producer’s risk
what is consumer risk?
what is producer’s risk?
risk of accepting defective product
risk of rejecting an acceptable product
what are sampling and non-sampling errors?
sampling: arises when sample is not representative of population
non sampling: arises b/c of other reasons (ie environmental error from wrong strage)
what is variance?
total variance?
estimate of uncertainty
total variance: function of sum of variances associated w/ each step
- error occuring during sampling?
- during sample prep?
- during lab analysis?
- during data processing?
- during interpretation?
- sampling error
- erroneous sample prep
- manual or instrumental error
- erroneous data handling
- erroneous inference
factors that affect choice of sampling plans?
- purpose of inspection
- nature of population
- nature of product
- nature of test method
def of sample?
portion selected from large quantity of material. (general term)
- diff than lab sample
def of lab sample?
sample prepared for testing or analysis
def of population?
set of all objects in system being investigated
def of lot
quantity of bulk material of similar composition whose properties are under study
def of batch
quantity of food that is known or assumed to be produced under uniform conditions
batch number should always be noted when sampling foods
def of unit
Each of the discrete, identifiable units of food that are suitable for removal from the population as samples and that can be individually described, analyzed or combined (e.g. an apple, a bunch of bananas, a can of beans, a prepared dish).
def of homogeneity
degree to which a property or substance is randomly distributed throughout a material.
def of increment
An individual portion of material collected by a single operation of a sampling device.
- Increment can be tested individually or combined and tested as a unit.
def of increment
An individual portion of material collected by a single operation of a sampling device.
- Increment can be tested individually or combined and tested as a unit.
attribute vs variance sampling?
attribute:
- to decide on acceptability of a population based on whether the sample possess a certain characteristic or not
- 2 possible outcomes (conforming or nonconforming –> present or absent)
- sample size must be at least ten times smaller than population size
variance
- estimate quantitatively the amount of substance (ie proteint content or moisture content) or a characteristic (ie color) on a continuous scale
- esterimate obtained from sample is compared w/ an acceptable value
manual vs continuous sampling
manual:
- person doing sampling is trained
- picks samples randomly from sample lot
continuous:
- performed mechanically
- less prone to human bias than manual
3 criteria used to determine sample size?
- level of precision (or sampling error): defines desired level of precision when attributes are measured by using the sample
- level of confidence (or risk): 9% confidence level means 95 out of 100 samples have true population value within the range of precision specified
- degree of variability among population for attributes being measured: refers to distribution of attributes in population
sample size determination can be based on….
- precision analysis (confidence level)
2. power analysis (power of prediction)
Determine the sample size to test the total sugar in a lot of doughnuts with a level of confidence of 95 % and 5% accuracy (precision level). Preliminary test have estimated the average value to be 30 g of sugar per tray. The standard deviation was calculated to be 5g
n = ( (1.96 x 5)/(0.05 x 30) )^2
n=43
higher standard deviation means what?
a more heterogeneous sample
thus the sample size must increase
equation for calculating sample size when population size is known?
sample size (n) = N / (1+N[e]^2)
n= sample size
N=population size
e=level of precision
Q: we have 1000 milk boxes each box contains 6 milk bottles, calculate sample size for 5% accuracy?
(n) = N / (1+N(e)^2))
n= 6000 / ( 1+6000[0.05]^2 )
sampling plans is classified into…
- probability sampling plans
2. non probability sampling plans
probability sampling plans are classified into… (5)
- simple random sampling
- stratified
- cluster
- composite
- systematic
non-probability sampling plans are classified into… (5)
- judgement sampling
- convenience
- restricted
- quoata
what is random sampling?
- each element of population has an equal chance of being included in the samples
- number of units in the population needs to be known
- uses a random selection process
advantages of random sampling?
- easy to conduct
- high probability of achieving a representative sample
- meets assumptions of many statistical procedure
disadvantages of random sampling?
identification of all units of the population can be difficult
what is stratified sampling?
example?
- involves dividing the population into homogeneous subgroups (strata)
- selecting a simple random sample or another sampling from each stratum
example: eggs are divided into strata: small, medium, large and extra large
advantages of stratified sampling?
- homogenous data within each stratum than in the population
- cost is lower
- small variances for sample size (higher statistical efficiency)
disadvantages of stratified sampling?
- classification error
- prior knowledge of composition and distribution of population
what is cluster sampling?
- population is divided into clusters similar to each other
- only some randomly selected clusters are sampled
advantages of cluster sampling
disadvantages
adv: less costly than simple or stratified
dis: higher sampling error
what is composite sampling
- used to obtain samples from bagged products (ie flour, seeds)
- small portions are taken from different locations, bags or containers and combines in a simple sample
what is systematic sampling?
- first unit is selected at random start from first k population units.
- units are taken every nth unit (sample interval).
- randomly select number j between 1 and k
- the required systematic random sample then comprises units numbered as by: j, j+k, j+2k….j + (n-1)k
N population: units numbered serially from 1 to N
sample size n = drawn from N
k = sampling interval
k = N/n
advantages of systematic sampling?
easy to perform
less subject to error
provides greater info per unit cost
what is probability sampling
selection of a sample from a population based on chance
probability of inclusion and sampling errors are known
what is the equation for calculating sample size according to precision analysis?
n = [ ((z) * (SD)) / (y * x) ]^2
n= sample size z=z value according to level of confidence SD=standard deviation Y = accuracy x = population mean
