FS 254 Test 2

Census

• Data gathered from entire population (complete enumeration)

• Very expensive, a lot of time, not always practical, even biased

• Census only on small or highly available populations

Scale complexity

Bias, accuracy & precision

• Bias is the difference between the mean of the measured values & the true value

• Accuracy is how close the measured values are to the true value

• Precision is how close the the measured values are to their own mean

• Biased estimate can be precise but not accurate

Statistical inference & sampling

• the theory, methods, and practice of forming judgments about population parameters and statistical relationships, typically based on random sampling

• Sampling has confidence limits, which describes how precise the estimate is to the entire population

  • goal of sampling is to acquire required amount of info about a population at minimum cost

Sampling design & sampling frame

• method of selecting sample units

• list of all possible units to be included in sample

Standard deviation & variance

• s² = Σ(x-x̄)² / n-1

• Variance is standard deviation squared

• variance = s² AKA σ²

t-value formula

Absolute error t-value formula

• C_M = t * sqrt( V_M / n )

• C_M is absolute error, t is t-value given, V_M is sample variance given (s²), n is sample size given

• Solving question: Calculate C_M of each t-value (which is related to respective confidence level), then write as “sample mean + C_M m³” and check if each respective abs error has the actual mean in its bounds

Improving t-value

• Larger sample size

• Use more efficient sampling technique

Sampling error & sampling observation error

• inherent inability of sample to provide totally accurate information about population parameter of interest

  • sample size or design reduces this error

• errors in the measurements made

  • sample size and design not relevant

Simple random sampling

• selecting units entirely at random without being influenced by any other unit

• Calculating mean DBH from SRS: x̄ = Σx / n

  • simple mean

• n = (ts / E)², minimum sample size

• s_x̄ = sqrt( s² / n )

Systematic sampling

• selects sample units in a predictable way, such as on a regular grid pattern, but it requires a truly random start point to be effective

• if pattern coincides with natural periodicity then large errors can occur

Stratified random sampling

• population sub-divided into homogeneous strata to minimize variation within those strata relative to total population variance

• Calculating mean DBH from stratified sample: each strata’s mean given a weighting, then x̄ = Σp_ix̄_i

  • multiply each mean by its weight then sum

StratRS optimal plot allocation

• Optimal plot allocation involves allocating more plots to strata that are highly variable & fewer to uniform stratum:

  • n_i = (A_is_i / ΣA_is_i) * n, where A_i is plot area, s_i is plot sd, n is total sample size

  • calculates weight of each strata, where variable stratum recieve higher weight

Standard error of stratified mean

• s_x̄ = sqrt( ΣA_i² s_x̄i² / A² )

• area of plot squared times standard area of mean of plot, summed, then divided by total area squared, then square-rooted

Cluster sample mean

• 400-row segments of equal tree number, but different mortality rate. Census impractical so 20 random rows selected. Simple mean then calculated.

• True average number trees per row (cluster) not known it is estimated simply by dividing sampled trees by number of sample rows

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