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FRST 238 > Lesson 3 - Sampling Design 1 > Flashcards

Lesson 3 - Sampling Design 1 Flashcards

1
Q 
Define the following:
variable of interest
sampling units
population
population size
sampling frame
A

variable of interest: the variable of interest on a specific measurement occasion
sampling units: objects on which you measure the variables of interest
population: the collection of all the elements of interest
population size: the number of elements in the population
sampling frame: a list of all the elements in a population

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2
Q

what is a sample

A

a group of elements (a subset of the population) selected in some manner from the population, size of the sample is n

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3
Q

random selection v. systematic selection

A

random: choosing the elements that will be in the sample using some procedure that depends on random chance
- allows us to use probability theory to make inferences about the population

systematic selection: choosing elements according to some pattern or system
- widely used in forestry

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4
Q

what are parameters? give examples

A

characteristics of a population

  • typically denoted in greek letters
  • exampled include: population standard deviation (sigma), population variance (sigma squared), population mean (mu), population total (tan)
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5
Q

What is a statistic? give examples

A

a characteristic of a sample that may be used to estimate a population parameter, its a point estimate of the corresponding parameter

  • mean of y (y-bar)
  • standard deviation of y (sy)
  • variance of y (sy squared)
  • total of y (yT)
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6
Q

What are interval estimates

A

an interval around the point estimate with a width determined so that the probability that the interval will contain the parameter of interest matches some desired level
- ex. 95% confidence interval for Uy is an interval estimate

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7
Q

Define bias, precision and accuracy in terms of statistics

A

bias: the difference between the expected value of a statistic used to estimate a parameter and that parameter
precision: the spread of a statistic, calculated from repeated samples, about its long-run means

accuracy: how close a statistics calculated from a particular sample might be to its associated parameter
- can be measured using mean squared error (MSE)

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8
Q

What is relative efficiency

A 
relative efficiency (RE): the efficiency of one sampling method compared to another sampling method
- ratio of variances of a given statistic obtained on the same population using an identical sample size
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9
Q

Why do we sample?

A
  1. considerably quicker and cheaper than a census
  2. information required may involve destructive measures
  3. sampling may be more accurate than census
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10
Q

what is simple random sampling

A

SRS: based on a selection procedure where every combination of n elements in the population has an equal chance of bein the sample

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11
Q

What are the steps involved in SRS

A
  1. obtain a sampling frame
  2. select the sampling plots
  3. measure the elements selected, record the measurements, and produce summaries
    • always sum all the different values for y, and sum all the different squared values for y
  4. calculate point estimates
    • sample mean
    • population total
    • variance of the observations (which estimates the population variance)
    • standard deviation of observations (which estimates the population sd)
      - square root of the variance!
    • standard deviation of the mean, variance of the sample mean
  5. calculate interval estimates
    • for estimates of the mean and total
    • Yt +/- t(n-1,1-a/2) x Syt
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12
Q

What is AE

A

Allowable sampling error: half the width of the widest confidence interval that you would be willing to accept

  • used to determine sample size
  • t-value times the standard deviation of the mean
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13
Q

When should SRS be used?

A
  • population is relatively homogeneous
  • a sampling frame is available
  • no other information is available
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14
Q

What are the difficulties of SRS?

A
  • time consuming
  • does not ensure complete coverage of the population
  • does not take advantage of other information that may be available
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15
Q

What is STRS

A

Stratified random sampling: when the population is not homogenous, they can be split up into different strata, each stratum is then treated as a separate sub population and sampled separately, the results are then combined using appropriate weights to obtain overall estimates for the population

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16
Q

What is the STRS procedure

A
  1. obtain a sampling frame and stratify the population
  2. select the sample plots
  3. measure the elements selected, record the measurements, and produce summaries
    - sum of the y’s and sum of the squared ys for each stratum
    - mean y, variance y, standard deviation of y, standard deviation of the mean for each stratum
  4. calculate point and interval estimates for the parameters of interest within each stratum
    - equations are the same as for SRS
  5. calculate point and interval estimates for the population as a whole
    - this is where equations start to differ
17
Q

explain effective degrees of freedom

A

before we construct confidence limits we need to determine the appropriate degrees of freedom for our estimate of the overall mean, EDF is a good approximation of the degrees of freedom and it falls between over approximating and under approximating

18
Q

What are four ways we can allocate the sampling units among the different strata?

A
  1. equal allocation: each stratum gets an equal number of sampling units
    - does not take into account the size of the stratum or variability of the strata
  2. proportional allocation: assigns sample size proportionally to the relative sizes of the strata
    - frequently used if total sample size is given
  3. Neyman allocation: takes the variation within the different strata into account, as well as the size of the strata
    - requires standard deviation for each stratum
  4. optimum allocation: takes the cost of sampling into account
    - will achieve a given error level (AE) for the lowest cost
19
Q

When should STRS be used?

A
  • the population is heterogeneous, but can be separated into distinctive, more homogeneous groups
  • the strata size are known in advance of sampling
  • a sampling frame is available
  • we are interested in estimating parameters for the various strata
20
Q

What is systematic sampling?

A

selecting sampling units according to some system

  • ex. select every tenth element in a population
  • provides unbiased estimates of the mean and total
21
Q

What are the advantages of systematic sampling over random sampling

A
  • the location of elements is cheaper (faster)
  • a detailed sampling frame is not required
  • ensures complete coverage of the population
  • the element included in any sample can be relocated easily
22
Q

What are two types of systematic sampling, explain them

A

strip cruises: long rectangle plots, strip cruise consists of selecting strips systematically from all the strips that could be established on the land area

line plots: plots (point centres) are located at equal intervals along lines that are also located at equal intervals

FRST 238 (5 decks)

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