ICAR AICE-JRF/SRF Biometry, Statistics & Computing for Forestry: practice questions

ICAR AICE-JRF/SRF (PhD) — Subject 59 Forestry · India · National Testing Agency for ICAR

Original practice questions written to the published syllabus · not past papers

10worked here, free

53written 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

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

Where the 53 questions fall

How our questions for ICAR AICE-JRF/SRF spread across the units of Biometry, Statistics & Computing for Forestry. Difficulty: 4 easy, 27 medium, 22 hard.

Non-linear regression for tree allometry	9
Introduction to R or Python for forest data	9
Tests of significance: z, t, F and chi-square	6
Correlation and simple and multiple linear regression	6
Probability and the binomial, Poisson and normal distributions	5
Sampling distributions, standard error and confidence intervals	5
Descriptive statistics, frequency distributions and diameter distributions	4
Data quality, field data recording and databases	4
Analysis of variance and basic experimental designs (CRD, RBD, Latin square)	3
Spreadsheets for field data	2

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 · Probability and the binomial, Poisson and normal distributions · medium

Tree heights are normal with mean 20 m and SD 2 m. About what percentage of trees exceed 23 m?

15.9%
6.7%
2.3%
43.3%

Answer and working

B. 6.7%

z = (23 − 20)/2 = 1.5; upper-tail area 0.0668. 15.9% is for z = 1; 2.3% for z = 2; 43.3% is the area between 0 and 1.5.

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

2 · Sampling distributions, standard error and confidence intervals · medium

If the allowable error in an inventory is halved, the required number of plots:

Doubles
Quadruples
Halves
Stays the same

Answer and working

B. Quadruples

n ∝ 1/E², so halving E multiplies n by four.

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

3 · Tests of significance: z, t, F and chi-square · medium

Of 100 seedlings, 70 are normal and 30 albino; a 3:1 ratio is expected. What is χ² and is the fit acceptable at 5% (critical value 3.84)?

1.33; the fit is rejected
1.33; fit acceptable
6.67; the fit is rejected
0.33; the fit is rejected

Answer and working

B. 1.33; fit acceptable

Expected 75 and 25: χ² = 25/75 + 25/25 = 1.33 < 3.84, so the 3:1 ratio is not rejected.

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

4 · Tests of significance: z, t, F and chi-square · medium

A Type II error is:

Rejecting a true null hypothesis
Using the wrong degrees of freedom
Failing to reject a false null hypothesis
Measuring trees at the wrong height

Answer and working

C. Failing to reject a false null hypothesis

Type I is rejecting a true H₀ (α); Type II is missing a real effect (β).

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

5 · Correlation and simple and multiple linear regression · medium

Why is a prediction interval for a new tree wider than a confidence interval for the mean height at the same diameter?

It uses a lower confidence level than the mean interval
It ignores uncertainty in the fitted coefficients
It adds the scatter of individual trees around the line
It is calculated only at the mean diameter

Answer and working

C. It adds the scatter of individual trees around the line

Prediction intervals add residual variance to coefficient uncertainty.

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 · easy

An allometric equation y = aD^b becomes linear when:

Only y is squared
Both y and D are log-transformed
D is replaced by D²H
Both are divided by their means

Answer and working

B. Both y and D are log-transformed

ln y = ln a + b ln D is a straight line.

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 biomass equation fitted to plantation eucalypts is applied to large trees in a natural forest. The main risk is:

None, since allometric exponents are universal
Overestimation of wood density only
Large bias outside its fitting range
A reduction in the correction factor

Answer and working

C. Large bias outside its fitting range

Equations are valid only for the sizes, species and conditions used to fit them.

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

8 · Analysis of variance and basic experimental designs (CRD, RBD, Latin square) · hard

With error MS 6, 5 replicates per treatment and t = 2.12 for the error df, what is the least significant difference at 5%?

2.32
2.54
1.55
3.28

Answer and working

D. 3.28

LSD = t√(2 × MSE/r) = 2.12 × √2.4 = 3.28. Omitting the 2 gives 2.32; omitting t gives 1.55.

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 · easy

Which R function fits an ordinary linear regression of height on diameter?

nls()
lm()
aov()
read.csv()

Answer and working

B. lm()

lm fits linear models; nls fits non-linear models; aov is ANOVA; read.csv reads data.

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

10 · 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?

nls()
lm()
t.test()
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

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