Food Analysis: Sampling Lecture PDF

Food Analysis: Sampling Saji George Associate Professor, Department of Food Science and Agricultural Chemistry, Macdonald-Stewart Building, Room-1039 (MS1-039) Tel: 514-398-7920, Fax: 514-398-7990 Email: [email protected] Web: ht...

Food Analysis: Sampling Saji George Associate Professor, Department of Food Science and Agricultural Chemistry, Macdonald-Stewart Building, Room-1039 (MS1-039) Tel: 514-398-7920, Fax: 514-398-7990 Email: [email protected] Web: http://safe-nano.lab.mcgill.ca/ SAJI GEORGE @ S.A.F.E NANO, MCGILL UNIVERSITY Scope of this lecture To provide a basis for, understanding, developing, and evaluating sampling plans, calculating sample size and sample handling procedures. 2 Workflow of food analysis Planning stage 1 What, why and how Sampling plan 2 Best representation of the population Sample processing/preparation 3 Ensure homogeneity of sample Analysis and detection 4 Appropriate technic Data and result Data processing (statistics) and result 5 interpretation and reporting What is sampling? Sampling: “A predetermined procedure for the selection, withdrawal, preservation, transportation, and preparation of the portions to be removed from a lot as samples” (According to International Union of Pure and Applied Chemistry (IUPAC)) Why do we do Sampling? - A fraction of the population is obtained quickly, and with less expense. - Analyzing a whole population is practically difficult - Getting information about large populations 4 Common terminologies 5  Terminologies Population: the set of all objects in the system being investigated. Sample: A portion selected from a large quantity of material. - General term used for a unit taken from the total amount of food. Laboratory sample: A sample prepared for testing or analysis. Lot: A quantity of bulk material of similar composition whose properties are under study. According to Safe Food for Canadian Act, Lot code should enable us to identify units that were manufactured, prepared, produced, stored, graded, packaged or labelled, under the same conditions. A lot code can be numeric, alphabetic or alphanumeric. Batch: A quantity of food that is known, or assumed, to be produced under uniform conditions. - Batch number should always be noted when sampling foods. 6  Terminologies Unit: Each of the discrete, identifiable portion of food that are suitable for removal from a population as samples that can be individually described, analyzed or combined (e.g. an apple, a bunch of bananas, a can of beans, a prepared dish). Homogeneity: The degree to which a property or substance is randomly distributed throughout a population. Increment: An individual portion of material collected by a single operation of a sampling device. 7  Attribute sampling Variance sampling To decide on the acceptability of a Sampling is performed to estimate population based on whether the quantitatively the amount of a sample possesses a certain substance (e.g., protein content, characteristic or not. moisture content, etc.) or a characteristic (e.g., color) on a Two possible outcomes-either continuous scale conforming or nonconforming The estimate obtained from the (present or absent) sample is compared with an acceptable value (normally specified Sample size should be at least ten by the label, regulatory times smaller than the population size Generally, the sample size is less in comparison to attribute sampling Exampling testing for the presence There is a normal distribution of of Clostridium botulinum measured attribute. 8  Manual vs. Continuous Sampling Manual sampling- Person doing the sampling should be trained, should pick samples randomly, location from a sample lot, or liquid container as specified by the approved standard methods Continuous sampling is performed mechanically. Continuous sampling is less prone to human bias than manual sampling. An automatic liquid sampling device. The control box (left) regulates the sampling frequency (Courtesy of LiquidSampling Systems Inc., Cedar Rapids, IA) 9 Sample size and accuracy of estimation Accuracy of estimation Population Analysis for ▪ Spoilage Sample size ▪ Juice, sugar ▪ Vitamin content Increase in sample size-→ increase accuracy of Sample etc estimation…but also increases time and cost of analysis 10  Importance of accurate sampling Sampling has to be appropriate to avoid, 1. Consumer risk- The risk of accepting defective product 2. Producer’s risk- The risk of rejecting an acceptable product. Sampling and non-sampling error - Sampling error arises when a sample is not representative of the population. - Non-sampling error arises because of some other reasons (e.g. Transferring the data from the questionnaire). 11  Factors contributing to inaccuracies Population Sample collection Sampling error Variance is an estimate of Sample preparation the uncertainty. Erroneous sample preparation The total variance is a Laboratory analysis function of the sum of the Manual or instrumental error variances associated with each step Data processing Erroneous data handling Interpretation. Erroneous inference 12 Calculating sample size 13  Determining sample size Normal distribution is assumed for characteristics that change continuously in a scale (e.g. moisture/protein content). Therefore, sample size distribution is mostly for variance sampling rather than attribute sampling Normal/probability distribution curve Probability Defines the level of confidence 14 Determining sample size Besides the population size and purpose of sampling, the sample size will be determined mostly based on three criteria, 1. Level of precision (or sampling error). Defines the desired level of precision when attributes are measured by using the sample. E.g. if the average sugar content in a sample is calculated to be 100 mg with 5% accuracy, then you can conclude that the sugar content is between 95 to 105 mg. 2. Level of confidence (or risk) 95% confidence level means that 95 out of 100 samples will have the true population value within the range of precision specified 3. Degree of variability among the population for the attributes being measured Refers to the distribution of attributes in the population (homogenous or heterogeneous)…large sample size for population with higher variability and vice versa….defined by standard deviation 15  Calculating sample size Sample size determination can be based on precision analysis (confidence level). According to precision analysis, z-values for confidence intervals 2 CL z Zα/2 SD 0.70 1.04 n= __ 0.75 1.15 γ×X 0.80 1.28 0.85 1.44 n= sample size 0.90 1.645 Zα/2 z-value corresponding to the 0.92 1.75 desired level of confidence 0.95 1.96 SD Known, or estimated std deviation 0.96 2.05 0.98 2.33 γ (gamma) Accuracy (desired precision level) 0.99 2.58 __ X Population mean 16  Example: calculating sample size 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 5 g. 2 2 Zα/2 SD 1.96 X 5 n= n= n = 43 __ 0.05 × 30 γ×X Higher std deviation (i.e more heterogeneous the sample is…the sample size increases. 17 Simple formula for calculating sample size when population size is known 𝑁 Sample size (n)= 1+𝑁 ⅇ 2 Where n is the sample size, N is the population size, and e is the level of precision. Example: we have 1000 milk boxes each box contains 6 milk bottles, calculate sample size for 5% accuracy? 6000 2 = 375 𝑁 1 + 6000 0.05 Sample size (n)= = 1+𝑁 ⅇ 2 18 Sampling plans 19  Classification of Sampling Plans Sampling Plans Probability Sampling Plans Non-Probability Sampling Plans 1-Simple Random Sampling 1-Judgment Sampling 2-Stratified Sampling 2-Convenience Sampling 3-Cluster Sampling 3-Restricted Sampling 4-Quota Sampling 4-Composite Sampling 5-Systematic Sampling 20 Probability Sampling Plans: Generally, every unit of a population has a known and equal chance of being selected - Provide a statistically sound basis for obtaining representative samples - Eliminate human bias - Scientific, operationally convenient and simple in theory - Best methods to achieve a representative sample. 21  Probability Sampling Plans: 1-Simple Random Sampling: ▪ Each element of the population has an equal chance of being included in the samples. ▪ the number of units in the population needs to be known. ▪ uses a random selection process (e.g. Tables of random numbers). Advantages: ▪ Easy to conduct; ▪ High probability of achieving a representative sample; ▪ Meets assumptions of many statistical procedures. Limitation: ▪ Identification of all units of the population can be difficult 22  Probability Sampling Plans: 2-Stratified Sampling: - Involves dividing the population into mutually exclusive subgroups (Strata) and then using simple random sampling to choose units from each stratum. - Example: - In a shell egg packing station the boxes of eggs are placed on pallets according to their grade size, the population is naturally divided into strata ( e.g. small, medium, large and extra large). 23  Probability Sampling Plans: Continuing… Advantages: ▪ The data is more homogenous within each stratum than in the population. ▪ The cost seems to be lower because of administrative convenience. ▪ Small variances for the sample size (Higher statistical efficiency). Disadvantages/limitations: Classification error Prior knowledge of composition and distribution of population Tedious and time consuming, especially when creating larger samples. 24 Probability Sampling Plans: 3-Cluster Sampling: The population is divided into clusters that are designed to be similar as possible to one another. In the cluster sampling only some randomly selected clusters are sampled, while in the stratified sampling samples are taken from every single subgroup. Advantage: Less costly than simple or stratified sampling. Disadvantage: Higher Sampling error (Representation is likely to become an issue). 25 Probability Sampling Plans: 4- Systematic Sampling: The first unit is selected at random start from the first k population units and then units are taken every nth unit (sample interval). - Consider N population units numbered serially from 1 to N. - Sample size ‘n’ needs to be drawn from N. - We calculate an integer k ( sampling interval) by equation 1 N - k= (1) n - Then randomly select a number j between 1 and k inclusively. - The required systematic random sample then comprises the units numbered as by equation 2 - j, j+k, j+2k, j+3k, …………………….., j+ (n-1)k (2) 26 Probability Sampling Plans: Example: We have 6000 cans (N=6000) Sample size n= 375 Therefore, k= 6000/375 =16 Then we need to choose a random number (j) between 1 and k (16). - 5+ 16, 5+ 2*16, 5+ 3*16, 5+ 4*16,,………….. - 21, 37 , 53 , 69, 27  Advantages: - Creates samples that are highly representative of the population, without the need for a random number generator - Easier to perform - Less prone to error - Provides more information per unit cost Disadvantage: Not as random as simple random sampling 28 5- Composite Sampling: Composite sampling consists of a collection of numerous individual discrete samples at regular intervals (over a period of time, or occurrence in a stack) Used to obtain samples from bagged products such as flour, seeds, and larger items in bulk Small portions are taken from different locations, bags, or containers, and combined in a simple sample. A composite sample may be a physical mix of individual sample units or a batch of unblended individual sample units that are tested as a group. 29 1 2 3 4 30 Probability sampling (the selection of a sample from a population based on chance…probability of inclusion and sampling errors are known) Simple random sampling (known number of units in a population, randomly selecting sample) Systematic sampling (sampling regularly at a determined interval) Stratified sampling (total population divided into subgroups and samples are drawn from each subgroup) Cluster sampling (population is divided into clusters and samples are drawn from certain clusters) Composite sampling (samples drawn from different units in a population are pooled for analysis..eg. Flour sampling from different sacks, sample collected from same location at different time interval) 31  Classification of Sampling Plans Sampling Plans Probability Sampling Plans Non-Probability Sampling Plans 1-Simple Random Sampling 1-Judgment Sampling 2-Stratified Sampling 2-Convenience Sampling 3-Cluster Sampling 3-Restricted Sampling 4-Quota Sampling 4-Composite Sampling 5-Systematic Sampling 32 Non-Probability Sampling Plans: A sampling technique where the odds of any unit being selected for a sample cannot be calculated since the selection is based on nonrandom procedures. - Randomization is always desired, but is not always feasible. - Nonprobability sampling may be more economical and convenient than probability sampling. - e.g. in adulteration, the objective of sampling plan is to check or highlight the adulteration rather than collection a representative sample. 33 Non-Probability Sampling Plans 1-Judgment Sampling: Dependent on the subjective judgement of the person who is drawing the samples 2- Convenience Sampling: - selecting only the accessible part of the population. - It is also called chunk sampling or grab sampling. 3- Restricted Sampling: - used when the entire population is not accessible (e.g. boxcar). 4- Quota Sampling: -The population is divided into groups, and samples are chosen based on experience and judgment. 34 Non-probability sampling Deliberate sampling by sampler The probability of including any specific portion of the population is not equal Done when probability sampling is not feasible It is not possible to estimate the sampling variability and possible bias Convenience sampling-when ease of sampling is the key Bulk Commodities: factor. Example: Tankers containing Milk/ Cereals/ Sugar Railcars containing oil seeds Restricted sampling- when the Sea barges containing Sugar/ Molasses entire population is not accessible - Random sampling is preferable to the collection of readily Quota sampling:- sampling accessible units. from groups representing - It is advised to take samples during the loading or unloading of various categories, a consignment. - Special probes or triers are required for sampling foods. 35 Factors Affecting the Choice of Sampling Plans (1) Purpose of inspection Is it to accept or reject the lot? Is it to measure the average quality of the lot? Is it to determine the variability of the product? (2) Nature of population Is the lot large but uniform? Does the lot consist of smaller, easily identifiable sub plots? What is the distribution of the units within the population? (3) Nature of product Is it homogeneous or heterogeneous? What is the unit size? How consistently have past populations met specifications? What is the cost of the material being sampled? (4) Nature of test method Is the test critical or minor? Will someone become sick or die if the population fails to pass the test? Is the test destructive or non-destructive? How much does the test cost to complete? 36 Recap Generally used terminologies Relevance of sampling Classification of sampling plans Factors affecting the choice of sampling Sample size calculation Extra reading material: Glenn D. Israel. Determining Sample Size. 37