Lecture 2 - sampling designs Flashcards
Definition and Attributes of sampling design
-The method of placement and the number of samples - going to placed randomly? ex. water samples collected randomly on a lake?
Attributes.. should be representative of the population under study (i.e., where should the samples be placed to achieve this?) - representative doesn’t mean biased, it means samples are taken and if take the mean of ten samples - that it represents the lake, or the part of the lake that you’re trying to describe
-The aim is to provide the best statistical estimates with the smallest possible confidence limits at the lowest cost. - like mean, or sum estiamte of confidence limits.
Sampling unit (SU)
object of interest that is independent (e.g., an organism or a forest plot). - or water sample..
Types of sampling designs
- Simple Random Sampling
- Stratified Random Sampling
- Systematic Sampling
- Multistage Sampling
Universal recommendation: random sampling or if not possible a variation like stratified random sampling.
Simple random sampling (What it is)
- From a statistical population consisting of N sampling units; n sample units are selected from the possible samples in a random fashion (i.e., each unit has an equal chance of being chosen).
- Random sampling meets the requirements of Parametric Statistics.
-Ability to select any sample unit from area of interest.. Sample unit is independent from area of interest
Simple random sampling (how it’s done)
- Numbers are randomly drawn
- Dimensional sampling - quadrats are selected
- Dimensionless sampling - grid is used and coordinates are sampled as point samples at crosshairs - very popular where not willing to look all inside
Simple Random Sampling (problems)
- problems may occur if a
- small number of samples are taken
- may not be representative… Possibility that all samples are taken in areas of homogeneity (rock outcrop etc)
- If this occurs.. May be deemed unacceptable and will have to choose a different design
Stratified random sampling (When to use it)
Recommended when…
- An area appears hetergeneous and/or differs with respect to population densities is a good candidate
- Number of samples is limited
- Recommendation is to sample each stratum randomly
Statified random sampling vs simple random sampling
*Stratified sampling does not require each stratum to be sampled radomly - they can be sampled systematically
*Simple random sampling would require more samples to adequately sample the same area because the randomness can have clusters - making it not representative of the area. (ex. all on bedrock..)
Stratified random sampling (procedure)
- The area is divided up into homogeneous geographic areas or subpopulations (= strata). ex.. lake, field etc.
ex. - has three strata, N1, N2, N3… Strata can be different sizes.. Based on proportionality. *Divided up representing real phenomena
Stratified random sampling calculations
N = N1 + N2 + N3
-
N = size of the area or population expressed as sample units
e.g., the sample unit is 10 x 20 m (= 200 m2), the size of the area is expressed in units of 200 m2 (not as total m2).
…thus 27,000 m2 area = 135 sample units (in total) - Total number of strata (= subpopulations) = 3 (in our example)
- Nh is the size of stratum h (# of possible sample units in stratum h)
e.g., for the following three strata:
2,000 m2: N1 = 2000 / 200 = 10
10,000 m2: N2 = 10,000 / 200 = 50
15,000 m2: N3 = 15,000 / 200 = 75 total = 135 SU
- determine stratum weights (Wh):
- Wh are proportions and add up to 1.0
-
Wh = Nh / N (stratum size / N):2,000 m2: W1 = 10/135 = 0.074
10,000 m2: W2 = 50 /135 = 0.370
15,000 m2: W3 = 75 / 135 = 0.556 total = 1.0 - Number of samples per stratum:
- proportional allocation
- decide on the total number of samples to be taken (e.g., 50)
-
multiply Wh for each stratum by the decided # of samples:
2,000 m2: N1 = 0.074 x 50 = 3.7 (4) 10,000 m2: N2 = 0.370 x 50 = 18.5 (19) 15,000 m2: N3 = 0.556 x 50 = 27.8 (27)
3 examples of stratified sampling..
Example 1. Study area divided into grid of 9 large squares (3 for each stratum)… Each large square divided into 4 smaller squares. Randomly select one smaller square. - Each strata is thus sampled with one random sample.. So, 3 samples/strata and 9 samples in total
Example 2. Series of (4) transect lines, parallel to a beach gradient.. Samples systematically placed at regular intervals (6 dots along the interval in total). One sample point randomly selected from each transect. Each sample point, is divided into four squares.. One smaller square is randomly selected and sampled from each transect = total of four samples… Attempt to randomize twice to reduce bias.
Example 3. Like example 2… Except one random sample is selected from each sample point (samplel point selected from interval split four smaller squares) for a total of 24 samples, instead of 4 in previous. - Many more samples
Systematic Sampling
- Samples are placed in a systematic fashion ex… Quadrats or live traps placed every 20m along a transect. - Equal distances
- Study area divided into equal squares & then every second square selected & center is sampled.
- Pro - covered entire area with the number of samples available to you.. Good to do if limited time or won’t be going back
- No stratification… But since spread across whole area can claim that feel representative of field
Stratified systematic sampling
Looks a lot like stratified random sampling but no attempt at randomization
Systematic Sampling (advantages)
- ease and simplicity of application - equally spaced out units.. Easy to find points
- Desire to sample evenly across the entire study area… Idea of being representative
- Few samples available… With a small number of samples
Systematic sampling (Disadvantage)
- The existence of possible periodic trends in the study area, that is exactly the same as the systematic sampling design - Unlikely… ex.. undulated field with ponds.. If the case, would need to change the design.
- General concensus is that data from systematic sampling can be treated as random samping data, without bias.
*If have choice, choose random sampling
