Geog 380: Geospatial Communication - Sampling Methods - PDF

Geog 380: Geospatial Communication Source: https://earth.nullschool.net Topic 13: Sampling GEOG 380 - Topic 13 © Geoffrey Hay (2023) 1 Learning outcomes By the end of this topic a successful student should be able to: § Identify the similarities between non-spatial and spatial sampling § Recog...

Geog 380: Geospatial Communication Source: https://earth.nullschool.net Topic 13: Sampling GEOG 380 - Topic 13 © Geoffrey Hay (2023) 1 Learning outcomes By the end of this topic a successful student should be able to: § Identify the similarities between non-spatial and spatial sampling § Recognize the different elements considered when selecting the number of samples § Apply different methods for sampling and recognize their relative merits and drawbacks GEOG 380 - Topic 13 2 Samples and Populations § Population: the total set of individuals or potential observations in a defined group § E.g., all the residents of Calgary § In order to measure them all, we would need to conduct a census, and this often not feasible https://www.omniconvert.com/what-is/sample-size/ § Sample: a subset of individuals or observations in the population § Hopefully, the sample represents the population! GEOG 380 - Topic 13 3 The Role of Sampling § Sampling helps us answer several difficult questions 1. How large should the sample be? 2. How/where should the samples be chosen? 3. How much reliability will we have in results based on this sample? https://www.omniconvert.com/what-is/sample-size/ GEOG 380 - Topic 13 § All of these revolve around the fact that we normally can’t conduct a census of an entire population! 4 Sampling Units § Sampling units: the individual items in a sample, and the basic entity upon which observations are made § May be discrete entities (e.g., people, households, cities, etc.), points, or areas (e.g., quadrats, strips, plots, pixels, etc.) § Must be explicitly defined! § Sampling units must be selected to match the scale of the information desired § e.g., household income à households § Personal income à individual people https://ccnmtl.columbia.edu/projects/qmss/samples_and_sampli ng/types_of_sampling.html GEOG 380 - Topic 13 5 Steps for sampling McGrew and Monroe (2000) GEOG 380 - Topic 13 6 2015, 2009, 1966 (Majorville medicine wheel) New Project: Use Machine Learning to Discover Medicine Wheels in Alberta § Alberta is very big, where can I find Medicine Wheels: Where Study site? § Siksika Native Reserve (700km^2) § Where are the objects of interest located on the site? § Alberta Archaeological Site Inventory Records (100+ locations) § What scale imagery do I need? § Can I see the objects of interest in the Scene/Image? § How many samples do I need to train the Machine Learning system? § Machine learning heuristics (80% training, 20% test) GEOG 380 - Topic 13 7 2009 2015 GEOG 380 - Topic 13 8 Steps for sampling McGrew and Monroe (2000) GEOG 380 - Topic 13 9 Q1: How large a sample? § One important question to be addressed in a proper sample design is how large should the sample be to be representative? https://www.fredhutch.org/en/news/centernews/2020/02/sample-size.html § Less certainty with small samples § More certainty with larger samples § Larger samples = more cost § What factors do you think should go into this decision? GEOG 380 - Topic 13 10 Sample size determination § Different methods depending on the objectives: https://7esl.com/rule-of-thumb/ § There are two commonly used strategies for sample-size determination: (i) rules of thumb, and (ii) formulas § Formulas: the precision of the estimate of a population parameter is a function of the variance of the population, the sample size, and the allowable error GEOG 380 - Topic 13 11 Random Sampling and Nonsampling Errors Sampling Designs and Sampling Procedures – Bertina Mitchell § Random Sampling Error § The difference between the sample result and the result of a census conducted using identical procedures. § A statistical fluctuation that occurs because of chance variations in the elements selected for a sample § Systematic Sampling Error § Systematic (non sampling) error results from non-sampling factors, primarily the nature of a study’s design and the correctness of execution. https://www.investopedia.com/terms/s/samplingerror.asp § § It is not due to chance fluctuations Less than Perfectly Representative Samples § Random sampling errors and systematic errors associated with the sampling process may combine to yield a sample that is less than perfectly representative of the population. GEOG 380 - Topic 13 12 Sample size determination (method 1) § For determining the sample size necessary to estimate the population mean ⎛ Zs ⎞ n =⎜ ⎟ ⎝E⎠ 2 McGrew and Monroe (2000) Where: n = number of samples Z = desired level of confidence s = standard deviation of a pilot sample E = tolerable error GEOG 380 - Topic 13 Calculating for Sample size https://www.youtube.com/watch?v=qVDVAZigXg0 13 Sample size determination (method 2) 2 t * CV n= 2 E 2 Husch et al. (2003) Where: n = Sample size t = Student’s t-value for the specified probability t-test: a statistic that checks if two means are reliably different from each other. t-value = (variance between groups)/(variance within groups) big t-value = different groups; small t-value = similar groups CV = Coefficient of variation (ratio of the std to the mean; shows variability in relation to mean of population) E = Tolerable error, expressed as % of the mean GEOG 380 - Topic 13 Statscast – what is a t-test? https://www.youtube.com/watch?v=0Pd3dc1GcHc 9.56 mins 14 Sample Size Determination - Procedure 1. Make a reasonable guess at the value of n § How much time do you have? Resources? 2. Look up critical Student’s t-value § Two-tailed probability of obtaining a larger value 3. Select value for E (allowable error) § 10-20% is a reasonable place to start 4. Select value for CV (coefficient of variation) § Large Sample Sizes Increase Statistical Power and Increase The Flexibility Of The Effect Size GEOG 380 - Topic 13 Need prior estimate of variation in population – preliminary (pilot) sample? 5. Calculate n 6. Proceed iteratively until n is reasonable § Things to change: n and E 15 Q2: Where/how to choose samples? § OK, so we know that we need n samples. Where or how do we choose them? § There are many techniques designed to help achieve a sample that is ‘representative’ of the population § The major issue to avoid is bias § Under-representing or over-representing elements of the population because of inappropriate sample design GEOG 380 - Topic 13 16 Sampling methods/designs § Non-probability (selective) methods § Judgmental § Quota § Snowball § Probability methods § § § § GEOG 380 - Topic 13 Systematic Simple Random Stratified random Clustered random 17 Selective Sampling § Observer manually selects sampling unit locations in areas that appear to be representative § Expert knowledge § Advantages § Many would argue that it has no place in well-designed sampling strategies, BUT § Can bail you out in some practical situations https://www.statology.org/snowball-sampling/ Snowball or chain-referral sampling. This sampling method is often used when researchers wish to study a population where the subjects are particularly hard to identify or reach i.e., individuals with rare diseases, homeless individuals, ex-convicts. This is a non-probability sampling method, thus not every population member has the same opportunity to be selected for the study. GEOG 380 - Topic 13 § Disadvantages § Relies on human choice, which is prejudiced by individual opinion, and may result in results that are not representative of the population 18 Simple Random Sampling § The fundamental sampling method. § Each sampling unit in the population has an equal chance of being selected § The selection of any individual should not affect the chance of selecting another individual McGrew and Monroe (2000) GEOG 380 - Topic 13 19 Advantages § Given sufficient samples, this produces an unbiased estimate of population mean and information needed to assess the sampling error § Computers assist greatly through random number generators or random point generators Wheelofnames.com GEOG 380 - Topic 13 20 Disadvantages § The two criteria (equal and independent) is harder to achieve than you might realize § Requires developing a system that is consistent with the sampling unit § How would you conduct a random sample of all the trees in a forest? § Individuals must be sampled with replacement (thus the samples are independent of each other) in order to be a true random sample. This means that an individual can get selected more than once, even if its unlikely. GEOG 380 - Topic 13 21 … continued ... § Cost and difficulty in accessing widely-dispersed locations, if field work is involved § Locating them § Traveling between them https://www.pond5.com/stock-footage/item/79413480-cowboy-sits-horse-cliffmonument-valley-utah GEOG 380 - Topic 13 § May miss small groups in the population, or produce estimates that are biased towards larger groups 22 Systematic Sampling § Samples are selected in a systematic or regular fashion, though the starting point is random § e.g., Every fourth address in the phone book, or every 10 meters along a transect McGrew and Monroe (2000) GEOG 380 - Topic 13 23 … continued… § Advantages § Can provide reliable population estimates by spreading sample over the entire population § Simple to execute in practice, because sample units are located at regular intervals and travel is straight-forward § Disadvantages § Not completely unbiased, because selections are not truly equal and independent § Can fare poorly if systematic patterns occur within population GEOG 380 - Topic 13 24 Stratified Random Sampling § Population is stratified, or divided into groups with reduced variability, and sampled randomly within each strata § Proportional allocation: sampling intensity proportional to sizes of strata § Optimum allocation: sampling intensity proportional to standard deviation of the distribution variable McGrew and Monroe (2000) GEOG 380 - Topic 13 25 … continued … § Advantages § May produce more accurate results because small groups are not missed, and large ones are not over-represented § Can generate separate estimates for each strata § Disadvantages § A basis for stratification is required § Sampling estimates are subject to errors in the stratification criteria GEOG 380 - Topic 13 26 Cluster sampling § The population is broken up into clusters § Exhaustive § Clusters selected at random § Two options § Randomly select samples from the cluster § Use all members of cluster (population) McGrew and Monroe (2000) GEOG 380 - Topic 13 27