1. Computing in Archaeology
Session 9. Sampling Assemblages
© Richard Haddlesey

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

3. 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.
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

4. Archaeological sample
Sampled population
Target population

5. Formal definitions
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
Variable: a characteristic which is to be measured for the units, such as weight of spearheads
Fletcher & Lock 2005, 66

6. Formal definitions
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
Fletcher & Lock 2005, 67

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

8. population – 100 units
. . . etc
100 obsidian spearheads

9. population – 100 units 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100

10. A simple random number sample

11. Random sampling
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
You must avoid bias in your selection as this can result in scrutiny from others

12. a simple random number sample1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100

13. A systematic sample

14. Systematic sampling
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

15. a systematic sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100

16. A stratified sample

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

18. a stratified sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100

19. a stratified sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100

20. A cluster sample

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

22. a cluster sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100

23. a cluster sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100

25. Downside to systematic
Totally miss this context

28. 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)

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

30. Common sample statistics:
known value
estimate for
x – the sample mean
s – the sample standard
deviation
p – the sample
proportion
μ – the population mean

31. Common sample statistics:
known value
estimate for
x – the sample mean
s – the sample standard
deviation
p – the sample
proportion
μ – the population mean
σ – the population
standard deviation

32. Common sample statistics:
known value
estimate for
x – the sample mean
s – the sample standard
deviation
p – the sample
proportion
μ – the population mean
σ – the population
standard deviation
π – the population
proportion

33. 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
See
Fletcher & Lock (2nd ED) 2005, Digging Numbers Oxbow 70-9