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Computing in Archaeology Session 9. Sampling Assemblages © Richard Haddlesey www.medievalarchitecture.net

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Aims To become familiar with sampling practices in an archaeological context To become familiar with sampling practices in an archaeological context

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Introduction to Sampling An area of excavation is a sample of the complete site which in itself is a sample of all sites of that type. The same goes for artefact assemblages. An area of excavation is a sample of the complete site which in itself is a sample of all sites of that type. The same goes for artefact assemblages. The essence of all sampling is to gain the maximum amount of information by measuring or testing just a part of the available material The essence of all sampling is to gain the maximum amount of information by measuring or testing just a part of the available material Fletcher & Lock 2005, 66

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Archaeological sample Sampled population Target population

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Formal definitions Population: the whole group or set of objects about which inference is to be made Population: the whole group or set of objects about which inference is to be made Sampling fame: a list of the items, units or objects that could be sampled Sampling fame: a list of the items, units or objects that could be sampled Variable: a characteristic which is to be measured for the units, such as weight of spearheads Variable: a characteristic which is to be measured for the units, such as weight of spearheads Fletcher & Lock 2005, 66

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Formal definitions Sample: the subset or part of the population that is selected Sample: the subset or part of the population that is selected Sample size: the number in the sample. A sample size of 5 is considered small, while, formally, a sample size of 50 is large. The sample size maybe stated as a percentage of the sampling frame, e.g. a 10% sample Sample size: the number in the sample. A sample size of 5 is considered small, while, formally, a sample size of 50 is large. The sample size maybe stated as a percentage of the sampling frame, e.g. a 10% sample Fletcher & Lock 2005, 67

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Sampling strategies a simple random sample (probability sample USA) a systematic sample a stratified sample a cluster sample

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population – 100 units... etc 100 obsidian spearheads

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12345678910 11121314151617181920 21222324252627282930 31323334353637383940 41424344454647484950 51525354555657585960 61626364656667686970 71727374757677787980 81828384858687888990 919293949596979899100 population – 100 units

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A simple random number sample

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Random sampling If we have a sample of 100 spearheads, we simply pick 10 random numbers (i.e. 10%) If we have a sample of 100 spearheads, we simply pick 10 random numbers (i.e. 10%) Computers can help generate random sequences, but are not necessary Computers can help generate random sequences, but are not necessary You must avoid bias in your selection as this can result in scrutiny from others You must avoid bias in your selection as this can result in scrutiny from others

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12345678910 11121314151617181920 21222324252627282930 31323334353637383940 41424344454647484950 51525354555657585960 61626364656667686970 71727374757677787980 81828384858687888990 919293949596979899100 a simple random number sample

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A systematic sample

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Systematic sampling To take a systematic approach, we could choose every number ending in 4. Once again this would give us our 10% To take a systematic approach, we could choose every number ending in 4. Once again this would give us our 10% This method has the advantage of being easy to design unless the units have inherent patterning in their order This method has the advantage of being easy to design unless the units have inherent patterning in their order

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12345678910 11121314151617181920 21222324252627282930 31323334353637383940 41424344454647484950 51525354555657585960 61626364656667686970 71727374757677787980 81828384858687888990 919293949596979899100 a systematic sample

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A stratified sample

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Stratified sampling Here we take a random sample 5 from the top and five from the bottom Here we take a random sample 5 from the top and five from the bottom Or 5 from the left, 5 right etc Or 5 from the left, 5 right etc

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12345678910 11121314151617181920 21222324252627282930 31323334353637383940 41424344454647484950 51525354555657585960 61626364656667686970 71727374757677787980 81828384858687888990 919293949596979899100 a stratified sample

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12345678910 11121314151617181920 21222324252627282930 31323334353637383940 41424344454647484950 51525354555657585960 61626364656667686970 71727374757677787980 81828384858687888990 919293949596979899100 a stratified sample

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A cluster sample

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Cluster sampling Rather than select individual items, select clusters or groups of items that are close together Rather than select individual items, select clusters or groups of items that are close together This may result in bias values This may result in bias values

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12345678910 11121314151617181920 21222324252627282930 31323334353637383940 41424344454647484950 51525354555657585960 61626364656667686970 71727374757677787980 81828384858687888990 919293949596979899100 a cluster sample

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12345678910 11121314151617181920 21222324252627282930 31323334353637383940 41424344454647484950 51525354555657585960 61626364656667686970 71727374757677787980 81828384858687888990 919293949596979899100 a cluster sample

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Downside to systematic Totally miss this context

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Common sample statistics: x – the sample mean s – the sample standard deviation p – the sample proportion (i.e. the proportion of the sample having a particular characteristic)

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Stats The true population values for these statistics are usually unknown, and formally denoted by Greek letters The true population values for these statistics are usually unknown, and formally denoted by Greek letters

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x – the sample mean s – the sample standard deviation p – the sample proportion Common sample statistics: μ – the population mean known valueestimate for

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x – the sample mean s – the sample standard deviation p – the sample proportion Common sample statistics: μ – the population mean σ – the population standard deviation known valueestimate for

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x – the sample mean s – the sample standard deviation p – the sample proportion Common sample statistics: μ – the population mean σ – the population standard deviation π – the population proportion known valueestimate for

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The central-limit theorem (the law of averages) In order to comment on how good an estimate the sample statistics are, the nature of their distribution needs to be known In order to comment on how good an estimate the sample statistics are, the nature of their distribution needs to be known See See Fletcher & Lock (2 nd ED) 2005, Digging Numbers Oxbow 70-9Fletcher & Lock (2 nd ED) 2005, Digging Numbers Oxbow 70-9

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