growing stock (stemwood)#21 Stemwood volume of living trees and shrubs (standing and lying) with a diameter at breast height (dbh) ≥12 cm with bark.
ownership (2 categories)#94 Forest ownership, classified according to the two categories: 'public' and 'private'. Reference: Forest Service Survey (MID 365: Eigentum)
diameter at breast height (10 classes)#1317 Diameter at breast height (dbh) of the trees and shrubs ≥12 cm dbh – in ten classes. Reference: Field Survey (MID 60: Brusthöhendurchmesser, MID 62: Umfang)
economic region#366 Division of Switzerland into 14 regions (2 in the Jura, 3 on the Plateau, 3 in the Pre-Alps, 5 in the Alps and 1 in the Southern Alps). The economic regions are a subdivision of the production regions according to economic-geographical criteria.
accessible forest without shrub forest#434 Forest of which less than two-thirds is covered with shrubs that can be accessed on foot.
1.4 km grid, subgrids 1-5#1746 Sub-grids 1, 2, 3, 4 and 5 of the field surveys on the sampling grid with a mesh size of 1.4 km (base grid).
The tables mainly show results that were calculated using statistical methods from the data of the sample inventory of the National Forest Inventory (NFI). Such results always consist of two figures: (1) the estimated value and (2) the sampling error, the so-called standard error.
Example 1: Estimated value and standard error
NFI5
volume of deadwood (stemwood)
ownership (2 categories)
regional demarcation: production region
unit: m³/ha
evaluation area: accessible forest without shrub forest
grid: 1.4 km grid, subgrids 1-5
state 2018/26
production region
Jura
Plateau
Pre-Alps
Alps
Southern Alps
Switzerland
ownership (2 categories)
m³/ha
±%
m³/ha
±%
m³/ha
±%
m³/ha
±%
m³/ha
±%
m³/ha
±%
public
30
10
17
13
37
9
36
6
26
10
30
4
private
27
17
20
12
50
10
32
8
39
13
34
5
total
29estimated value
9standard error
19
9
44
7
35
5
29
8
32
3
The tables usually show the relative (percentage) standard error (“±%”), but occasionally – in the case of estimated percentages – the absolute standard error (“±”).
The standard error can be used to define confidence intervals around the estimated value, which contain the true value of the population with a certain statistical certainty.
The statistical certainty is:
68% if the confidence interval is calculated using the standard error
(68% confidence interval = estimated value ± standard error), and
95% if the confidence interval is calculated using twice the standard error
(95% confidence interval = estimated value ± 2 × standard error*)
Example 2: Calculating confidence intervals
LFI5
volume of deadwood (stemwood)
ownership (2 categories)
regional demarcation: production region
unit: m³/ha
evaluation area: accessible forest without shrub forest
grid: 1.4 km grid, subgrids 1-5
state 2018/26
production region
Jura
ownership (2 classes)
m³/ha
±%
public
30
10
private
27
17
total
29
9
Question
What are the 68% and 95% confidence intervals of the above estimates?
Procedure
Calculate the absolute standard error (= relative standard error × estimated value / 100)
Calculate the confidence intervals
68% confidence interval = estimated value ± absolute standard error
95% confidence interval = estimated value ± 2 × absolute standard error
Answer
Step 1
Step 2
ownership (2 categories)
volume of deadwood Jura NFI5
estimated value
standard error
confidence interval
relative
absolute
68%
95%
m³/ha
±%
±m³/ha
m³/ha
m³/ha
public
30
10
3
27-33
24-36
private
27
17
5
22-32
17-37
total
29
9
3
26-32calculated with the standard error, i.e. 29 ± 3
23-25calculated with twice the standard error, i.e. 29 ± 2 × 3
The volume of deadwood in the Jura is between 26 and 32 m³/ha with a statistical certainty of 68% and between 23 and 35 m³/ha with a statistical certainty of 95%.
The 95% confidence interval is larger than the 68% confidence interval. This results in higher statistical certainty with the 95% confidence interval.
Example 3: Visualisation of the 68% and 95% confidence intervals
Data: see example 2
When interpreting the results, one must define the level of statistical certainty that one would like to apply to the statement.
The 68% confidence interval is generally used in the National Forest Inventory (NFI).
This can be checked by comparing the confidence intervals of two estimated values:
If the 68% confidence intervals of two estimates do not overlap, it can be assumed with some certainty that the two populations differ.
If the 95% confidence intervals of two estimates do not overlap, it can be assumed with high certainty that the two populations differ.
Example 4: Interpretation of two results from the same inventory
NFI5
growing stock (stemwood)
ownership (2 categories)
regional demarcation: production region
unit: m³/ha
evaluation area: accessible forest without shrub forest
grid: 1.4 km grid, subgrids 1-5
state 2018/26
production region
Jura
Plateau
Pre-Alps
Alps
Southern Alps
Switzerland
ownership (2 categories)
m³/ha
±%
m³/ha
±%
m³/ha
±%
m³/ha
±%
m³/ha
±%
m³/ha
±%
public
331
3
311
3
405
4
300
3
256
5
314
2
private
387
5
432
4
454
4
348
4
285
6
398
2
total
345
2
363
2
431
2
314
2
262
4
343
1
case 2
case 1
case 1
Question
Is the growing stock per hectare greater in the Alps than in the Southern Alps?
Procedure
Calculate the absolute standard errors
Calculate the confidence intervals depending on the desired level of statistical certainty:
68% confidence intervals (some certainty; absolute standard error)
95% confidence intervals (high certainty; twice the absolute standard error)
Assess whether the confidence intervals corresponding to the desired level of statistical certainty do not overlap
Answer
ownership (2 categories)
growing stock NFI5
Alps
Southern Alps
estimated value
standard error
confidence interval
estimated value
standard error
confidence interval
relative
absolute
68%
95%
relative
absolute
68%
95%
m³/ha
±%
±m³/ha
m³/ha
m³/ha
m³/ha
±%
±m³/ha
m³/ha
m³/ha
total
314
2
6
308-320
302-326
262
4
10
252-272
242-282
Neither the 68%-confidence intervals nor the 95%-confidence intervals overlap (pairs of values in ).
In this case, the level of statistical certainty selected has no influence on the result.
Overall, this means that there is high statistical certainty that the growing stock per hectare is greater in the Alps than in the Southern Alps.
Case 2
Question
Is the growing stock per hectare greater in the Plateau than in the Jura?
Procedure
See case 1.
Answer
ownership (2 categories)
growing stock NFI5
Jura
Plateau
estimated value
standard error
confidence interval
estimated value
standard error
confidence interval
relative
absolute
68%
95%
relative
absolute
68%
95%
m³/ha
±%
±m³/ha
m³/ha
m³/ha
m³/ha
±%
±m³/ha
m³/ha
m³/ha
total
345
2
7
338-352
331-359
363
2
7
356-370
349-377
The 68%-confidence intervals do not overlap (pairs of values in ).
In contrast, the 95%-confidence intervals overlap (pairs of values in ).
In this case, the level of statistical certainty selected has an influence on the interpretation of the results. At the 68% confidence interval level, the conclusion is that the growing stock per hectare is higher in the Plateau than in the Jura. At the 95% confidence interval level, however, this conclusion cannot be drawn.
Considering both confidence interval levels, it can be said that there is some, but not high, statistical certainty that the growing stock per hectare is greater in the Plateau than in the Jura.
The confidence intervals can also be used to determine whether a value estimated with a sample from the National Forest Inventory (NFI) deviates from a target value (e.g. from Swiss forest policy) or whether a change between two inventories is statistically certain.
Example 5: Interpretation of two results from different inventories
ownership (2 categories)
growing stock Plateau*
NFI4
NFI5
m³/ha
±%
m³/ha
±%
public
340
3
309
3
private
447
4
432
4
total
386
2
363
2
* accessible forest without shrub forest NFI4/NFI5
Question
Has the growing stock per hectare in the Plateau decreased from NFI4 to NFI5?
Procedure
Calculate the absolute standard errors
Calculate the confidence intervals depending on the desired level of statistical certainty:
68% confidence intervals (some certainty; absolute standard error)
95% confidence intervals (high certainty; twice the absolute standard error)
Assess whether the confidence intervals corresponding to the desired level of statistical certainty do not overlap.
Answer
ownership (2 categories)
growing stock Plateau*
NFI4
NFI5
estimated value
standard error
confidence interval
estimated value
standard error
confidence interval
relative
absolute
68%
95%
relative
absolute
68%
95%
m³/ha
±%
±
m³/ha
m³/ha
m³/ha
±%
±
m³/ha
m³/ha
public
340
3
11
329-351
318-362
309
3
11
298-320
287-331
private
447
4
16
431-463
415-479
432
4
17
415-449
398-466
total
386
2
8
378-394
370-402
363
2
9
354-372
345-381
* accessible forest without shrub forest NFI4/NFI5
The 68%-confidence intervals do not overlap in the public forest (pairs of values in ), but they do in the private forest and the total forest (pairs of values in ). At the certainty level of the 68% confidence intervals, it can be concluded that the growing stock per hectare in the public forest of the Plateau has decreased. For the private forest, as well as for the total forest, the decrease is not statistically certain at this level.
The 95%-confidence intervals overlap in all three categories. At the certainty level of the 95% confidence intervals, it is therefore not certain that the growing stock has decreased, even for the public forest.
See also examples 6 and 7, in which changes between two inventories are interpreted using the more sensitive metric of net change.
For many target variables in the NFI, it is possible to determine whether a change between two inventories is statistically certain, not only by comparing the states in the two inventories (see example 5), but also by analysing the net change** between the two inventories.
To do this, one must first define the level of statistical certainty that one would like to apply to the statement (as done above):
A net change has occurred with some certainty if the relative standard error is less than 100% or if the confidence interval calculated with the absolute standard error (68% confidence interval) does not include the value 0.
A net change has occurred with high certainty if twice the relative standard error is less than 100% or if the confidence interval calculated with twice the absolute standard error (95% confidence interval) does not include the value 0.
Example 6: Interpretation of net changes with the relative standard error
ownership (2 categories)
change in growing stock from NFI4 to NFI5, Plateau*
estimated value
standard error
m³/ha
±%
public
-34
30
private
-9
147
total
-23
34
* accessible forest without shrub forest NFI4/NFI5
Question
Has the growing stock per hectare in the Plateau decreased from NFI4 to NFI5?
Procedure
Define the level of statistical certainty (68% or 95% confidence interval)
Determine whether:
the relative standard error is less than 100% (certainty level of the 68% confidence interval)
twice the relative standard error is less than 100% (certainty level of the 95% confidence interval)
Answer
ownership (2 categories)
change in growing stock from NFI4 to NFI5, Plateau*
estimated value
standard error
single
double
m³/ha
±%
±%
public
-34
30
60
private
-9
147
294
total
-23
34
68
* accessible forest without shrub forest NFI4/NFI5
The single relative standard error is less than 100% for both the public forest and the total forest (highlighted values). For the private forest, however, it is greater than 100% (highlighted values). At the certainty level of the 68% confidence interval, it can be concluded that the growing stock in the Plateau has decreased in the public forest and in total. For the private forest, on the other hand, the decrease in stock is not statistically certain at this level.
The same conclusion is reached in this example with the certainty level of the 95% confidence interval, as twice the relative standard error is again less than 100% for both the public forest and the total forest.
Overall, this means that there is high statistical certainty that the growing stock per hectare has decreased in the public forest in the Plateau, as well as overall. For private forests, on the other hand, the decrease in stock is not statistically certain (as twice the relative standard error and the relative standard error are both less than 100%).
Example 7: Interpretation of net changes with the absolute standard error
ownership (2 categories)
change in growing stock from NFI4 to NFI5, Plateau*
estimated value
standard error
%
±
public
-10
3
private
-2
3
total
-6
2
* accessible forest without shrub forest NFI4/NFI5
Question
Has the growing stock per hectare in the Plateau decreased from NFI4 to NFI5?
Procedure
Define the level of statistical certainty (68% or 95% confidence interval)
Calculate the confidence interval based on the defined certainty level
68% confidence interval with the absolute standard error
95% confidence interval with twice the absolute standard error
Determine whether the corresponding confidence interval does not include the value 0
Answer
ownership (2 categories)
change in growing stock from NFI4 to NFI5, Plateau*
estimated value
standard error
confidence interval
single
double
68%
95%
%
±
±
%
%
public
-10
3
6
-13 to -7
-16 to -4
private
-2
3
6
-5 to +1
-8 to +4
total
-6
2
4
-8 to -4
-10 to -2
* accessible forest without shrub forest NFI4/NFI5
Neither the 68% nor the 95% confidence interval includes the value 0 for the public forest or for the total forest. At both certainty levels, this leads to the conclusion that the growing stock in the Plateau has decreased in the public forest and in total. For the private forest, on the other hand, the decrease in stock is not statistically certain (as the confidence intervals include the value 0).
Net changes can be interpreted using the absolute or relative standard error (see examples 6 and 7). It is advisable to use the absolute standard error if the estimated value in the table is shown as a percentage (%; as in example 7), and the relative standard error if the estimated value in the table is shown in absolute terms (m³, m³/ha, pc, m²; as in example 6). This means that the standard error can be taken directly from the table and does not need to be converted.
To assess whether a change is statistically certain, it is advisable to analyse the net change between the two inventories wherever possible. Net changes are more sensitive than status comparisons, which makes it easier to detect differences statistically. See examples 6 and 7 (net change) and 7 (comparison of two results from different inventories).
4. When is it not sufficient to consider only the standard error?
The National Forest Inventory (NFI) is a sample-based large-scale inventory whose sample areas are arranged on a grid with a mesh size of 1.4 km × 1.4 km. The NFI was designed in such a way that the growing stock for Switzerland as a whole can be predicted with a maximum standard error of 1%.
If results are requested for individual regions or for individual classes, the standard error quickly becomes much larger. This is because the number of sample areas and subjects (e.g. sample trees, young forest plants, pieces of deadwood) analysed for the queried combination of variable expressions* is considerably lower than for the total.
Example 8: Standard error and combination of variable expressions
region
growing stock
total
maple
sycamore
Norway maple
estimated value
standard error
estimated value
standard error
estimated value
standard error
estimated value
standard error
m³/ha
±%
m³/ha
±%
m³/ha
±%
m³/ha
±%
Switzerland
343
1
12
5
11
5
1
20
production region "Plateau"
363
2
15
10
14
11
0
50
Canton of Aargau
289
7
15
20
13
20
1
63
The standard error increases as the level of detail increases.
Large standard errors are to be expected if:
forest districts are selected as the regional demarcation or results for small cantons (e.g. Appenzell Innerrhoden, Nidwalden) are queried,
a classification variable with many classes is selected (e.g. tree species in 56 classes),
several classification variables are combined with each other (e.g. main tree species and development stage).
Large standard errors are an indication that the estimate may have been based on too small a number of sample areas or subjects and that the result of the estimate therefore may not be reliable.
For the target variable “number of stems of young forest plants with browsing damage” (browsing intensity), an uncertain estimate is not necessarily recognisable by a large standard error. This is because this target variable is a quotient estimator**, which is – due to the survey method – only based on a small number of assessed young forest plants for rarer tree species (e.g. pine, larch, Arolla pine, oak, chestnut). Accordingly, for this target variable one should always check how many young forest plants were assessed for the individual estimates. As a rule of thumb, at least 30 young forest plants per estimate should have been assessed for browsing in order to obtain a reliable estimate.
There are two types of changes in the National Forest Inventory (NFI):
The first type of change involves specific target variables for change components such as increment, fellings or mortality. These target variables are only available for two consecutive measurement cycles, e.g. NFI4 to NFI5. When change components are analysed, the classification variable expression of the second measurement cycle is generally assigned to the first measurement cycle. These analyses therefore do not take into account any change in the expression (e.g. from private to public ownership) from the earlier to the later measurement cycle.
In the second type of change, the difference in target variables, such as stem number, growing stock or forest area, is used to calculate the net change between two measurement cycles. These target variables are usually used to represent states, e.g. that in NFI5, but can also show the net change between any two measurement cycles, e.g. between NFI1 and NFI5. In these net change analyses, the change in expression is taken into account for some of the classification variables, including “tree condition” and “forest, non-forest”. In this way, it can be seen, for example, that the forest area has increased. For the remaining classification variables, the expressions are regarded as static. This means that the most recent state – whether it was assessed in a measurement cycle (e.g. “primary forest function NFI5”) or taken from an external data source (e.g. “protection forest [2022]”) – is assigned to all measurement cycles.
6. Change analyses: When are the results (not) additive?
The results are:
additive if they are reported as the total change between two measurement dates. For example, the fellings for the various production regions reported in cubic metres (m³) can be added together to obtain the total fellings for Switzerland.
not additive if they are reported as a change per year (e.g. m³/year). For example, the fellings for the various production regions reported in cubic metres per year (m³/year) cannot be added together to obtain the total fellings for Switzerland.
Example 9: : Additivity/non-additivity of changes
growing stock: total change between NFI4 and NFI5 (in 1000 m³)*
Jura
Plateau
Pre-Alps
Alps
Southern Alps
Switzerland
higher/lower altitude zone
1000 m³
±%
1000 m³
±%
1000 m³
±%
1000 m³
±%
1000 m³
±%
1000 m³
±%
lower altitude zone
-3759.0
28
-4909.1
36
-1025.2
133
-317.1
195
3464.1
31
-6546.3
42
higher altitude zone
574.3
117
-328.0
62
1093.0
123
7128.4
21
666.7
93
9134.3
24
total
-3184.7
40
-5237.1
34
67.9
2805
6811.3
23
4130.8
30
2588.1
136
* accessible forest without shrub forest NFI4/NFI5
additive
growing stock: annual change between NFI4 and NFI5 (in 1000 m³/year)*
Jura
Plateau
Pre-Alps
Alps
Southern Alps
Switzerland
higher/lower altitude zone
1000 m³/year
±%
1000 m³/year
±%
1000 m³/year
±%
1000 m³/year
±%
1000 m³/year
±%
1000 m³/year
±%
lower altitude zone
-421.1
28
-560.6
36
-115.7
133
-35.9
195
389.5
31
-740.7
42
higher altitude zone
64.7
117
-38.3
62
122.4
123
810.4
21
74.9
93
1032.7
24
total
-357.3
40
-598.4
34
7.6
2805
773.8
23
464.4
30
292.7
136
* accessible forest without shrub forest NFI4/NFI5
not additive
The non-additivity of changes expressed per year arises because the total change is divided by the average number of years between the two measurement dates in the domain* under consideration, and this average number of years varies slightly depending on the domain.
Example 10: Average number of years per domain
domain
mean number of years*
production region
higher/lower altitude zone
Mittelland
-
8.75
Plateau
higher altitude zone
8.56
lower altitude zone
8.76
Southern Alps
-
8.90
Southern Alps
higher altitude zone
8.90
lower altitude zone
8.89
* between the NFI4 and NFI5 measurements in the accessible forest without shrub forest
7. Why is a dot (“.”) sometimes given in the cells for standard error or estimated value?
In the calculation of a results table, data is not always available for all combinations of variable expressions*. In most cases, this indicates that the variable estimated with the relevant target variable does not occur or only occurs very rarely. The value 0 is then usually used. However, as this value is not based on any direct measurements, a dot (“.”) is given for the associated standard error. If reference is made to the assumed value of 0 in the calculation, e.g. in the case of percentages or certain change estimates, no value can be used. In this case, a dot (“.”) is given for the estimated value and the standard error.
For example, no Arolla pines have yet been found and measured in the Plateau in the National Forest Inventory (NFI) (growing stock of Arolla pine by production region). It can therefore be assumed that the values are missing because the Arolla pine actually does not occur in the Plateau, and therefore the growing stock in that region must be 0.
8. Why are no standard error values shown in some tables?
The data in these tables originates from a complete survey and not from a sample inventory. Accordingly, it is not necessary to specify a standard error because there is no uncertainty due to sampling.
The forest road network survey that the National Forest Inventory (NFI) periodically carries out with the local forestry services is an example of such a complete survey.
9. Negative values for growing stock, increment or fellings?
A negative value is possible if the result could only be calculated on the basis of a few trees. The estimate is therefore not reliable. This is also reflected in the standard error, which is usually extremely large for negative stock, increment or felling values.
Negative values can occur because, when the stemwood volume of the tally trees is determined, the volume estimated solely on the basis of the diameter at breast height (DBH) (tariff volume) is adjusted using the volume of the tally trees estimated on the basis of DBH, diameter at 7 m height and tree height. This procedure enables an unbiased and more accurate calculation of the stemwood volume. However, it can lead to negative values for all target variables that are based on the stemwood volume of the tally trees (e.g. growing stock, increment, fellings) if the number of tally trees in the selected combination of variable expressions* is small.