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National Postgraduate Entrance Exam Biometry, Statistics & Computing for Forestry: practice questions

National Postgraduate Entrance Exam (考研) — 0907 Forestry · China · Ministry of Education / CHSI and admitting universities

Original practice questions written to the published syllabus · not past papers
10worked here, free
23written to this exam in this subject
10syllabus units

What this subject covers

The statistics and computing used in forest inventory, experiments and modelling, from descriptive statistics and sampling to regression, designed experiments and scripting. Econometrics and business statistics are taught in the Agribusiness track, and sampling theory and spatial statistics in full in the Agricultural Statistics track; they are not repeated.

In the exams: ICAR AIEEA-PG Group 09 Unit I (elements of statistics); background to all mensuration and inventory questions

Where the 23 questions fall

How our questions for National Postgraduate Entrance Exam spread across the units of Biometry, Statistics & Computing for Forestry. Difficulty: 0 easy, 7 medium, 16 hard.

Non-linear regression for tree allometry6
Correlation and simple and multiple linear regression3
Introduction to R or Python for forest data3
Descriptive statistics, frequency distributions and diameter distributions2
Probability and the binomial, Poisson and normal distributions2
Sampling distributions, standard error and confidence intervals2
Tests of significance: z, t, F and chi-square2
Analysis of variance and basic experimental designs (CRD, RBD, Latin square)1
Spreadsheets for field data1
Data quality, field data recording and databases1

10 practice questions, worked

Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.

1 · Descriptive statistics, frequency distributions and diameter distributions · hard

A diameter distribution of tree biomass is strongly positively skewed. Which statement is true?

  1. The median exceeds the mean
  2. The mean exceeds the median
  3. Mean and median are always equal
  4. The mode exceeds the mean
Answer and working

B. The mean exceeds the median

A long right tail pulls the mean above the median; the mode is usually lowest.

Further reading: See the manual sources: Freese 1967; Zar; Snedecor and Cochran; Gomez and Gomez; Husch et al.; Baskerville 1972

2 · Probability and the binomial, Poisson and normal distributions · hard

A disease test detects 95% of infected trees and gives false positives in 5% of healthy trees. If 1% of trees are infected, what is the probability that a tree testing positive is infected?

  1. 0.95
  2. 0.50
  3. 0.05
  4. 0.16
Answer and working

D. 0.16

Bayes: (0.95 × 0.01)/(0.95 × 0.01 + 0.05 × 0.99) = 0.0095/0.059 = 0.16. Most positives are false when the disease is rare.

Further reading: See the manual sources: Freese 1967; Zar; Snedecor and Cochran; Gomez and Gomez; Husch et al.; Baskerville 1972

3 · Sampling distributions, standard error and confidence intervals · hard

Which interpretation of a 95% confidence interval is correct?

  1. 95% of such intervals contain the true mean
  2. 95% of individual trees fall inside this interval
  3. The sample mean has a 95% chance of being the true mean
  4. The interval contains 95% of all the plot values
Answer and working

A. 95% of such intervals contain the true mean

Confidence refers to the procedure over repeated sampling; individual values are described by prediction or tolerance intervals.

Further reading: See the manual sources: Freese 1967; Zar; Snedecor and Cochran; Gomez and Gomez; Husch et al.; Baskerville 1972

4 · Non-linear regression for tree allometry · medium

A biomass equation is ln B = −2.0 + 2.4 ln D (B in kg, D in cm). What is the uncorrected predicted biomass of a 30 cm tree?

  1. 70 kg
  2. 35.1 kg
  3. 475 kg
  4. 6.16 kg
Answer and working

C. 475 kg

ln B = −2.0 + 2.4 × 3.401 = 6.163; B = e^6.163 = 475 kg. Using log₁₀ for D but not the coefficients gives 35.1 kg; 6.16 is still on the log scale.

Further reading: See the manual sources: Freese 1967; Zar; Snedecor and Cochran; Gomez and Gomez; Husch et al.; Baskerville 1972

5 · Non-linear regression for tree allometry · medium

A log–log biomass regression has a standard error of estimate of 0.3 (natural logs). What correction factor should multiply back-transformed predictions?

  1. 1.300
  2. 1.046
  3. 1.350
  4. 0.955
Answer and working

B. 1.046

CF = exp(SEE²/2) = exp(0.045) = 1.046. exp(0.3) forgets to square and halve.

Further reading: See the manual sources: Freese 1967; Zar; Snedecor and Cochran; Gomez and Gomez; Husch et al.; Baskerville 1972

6 · Non-linear regression for tree allometry · medium

The Chapman–Richards function y = A(1 − e^(−kt))^c is mainly used to model:

  1. Growth of height, diameter or volume over time
  2. Diameter distributions of uneven-aged stands
  3. Probability of seedling survival
  4. Spatial autocorrelation of plot data
Answer and working

A. Growth of height, diameter or volume over time

It is a flexible sigmoid with asymptote A, widely used for growth and site index curves.

Further reading: See the manual sources: Freese 1967; Zar; Snedecor and Cochran; Gomez and Gomez; Husch et al.; Baskerville 1972

7 · Non-linear regression for tree allometry · hard

A non-linear least-squares fit fails to converge. What is the most likely remedy?

  1. Remove all trees larger than the mean
  2. Switch to a chi-square test
  3. Supply better starting values
  4. Use the median instead of the mean
Answer and working

C. Supply better starting values

Iterative algorithms need sensible starting values, for example from a log-linear fit or published coefficients.

Further reading: See the manual sources: Freese 1967; Zar; Snedecor and Cochran; Gomez and Gomez; Husch et al.; Baskerville 1972

8 · Non-linear regression for tree allometry · medium

For above-ground biomass against diameter, the allometric exponent b is commonly about:

  1. 2 to 3
  2. 0.2 to 0.5
  3. 5 to 7
  4. Exactly 1
Answer and working

A. 2 to 3

Mass scales roughly with D²H, and height rises less than proportionally with D.

Further reading: See the manual sources: Freese 1967; Zar; Snedecor and Cochran; Gomez and Gomez; Husch et al.; Baskerville 1972

9 · Introduction to R or Python for forest data · medium

Which R function would you use to fit the power model y = aD^b directly by non-linear least squares?

  1. nls()
  2. lm()
  3. t.test()
  4. chisq.test()
Answer and working

A. nls()

nls fits non-linear models iteratively from starting values.

Further reading: See the manual sources: Freese 1967; Zar; Snedecor and Cochran; Gomez and Gomez; Husch et al.; Baskerville 1972

10 · Data quality, field data recording and databases · hard

Which query language is used to join and summarise tables in relational databases?

  1. SQL
  2. HTML
  3. CSV
  4. PDF
Answer and working

A. SQL

Structured Query Language selects, joins and aggregates records.

Further reading: See the manual sources: Freese 1967; Zar; Snedecor and Cochran; Gomez and Gomez; Husch et al.; Baskerville 1972

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Biometry, Statistics & Computing for ForestryThe full study manual, free National Postgraduate Entrance ExamFormat, sections and how it has changed

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