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Estimates and standard error of the estimates

The results published in the NFI tables are estimates for variables in the Swiss forest (population parameters) whose true values are not known and must therefore be extrapolated (estimated) from the NFI sample data.

The extrapolations carry uncertainties. However, the accuracy of the extrapolations can be reliably estimated from the NFI sample, which is designed to be a random sample. To this end, all NFI tables include a second figure in addition to the estimate itself, namely the standard error of the estimate.

In most tables the percent standard error is reported (±%), but the absolute standard error (±) is also reported occasionally, especially for estimated percentages. The relationship between absolute and percent standard error is as follows:

percent standard error = absolute standard error / estimate × 100

absolute standard error = percent standard error × estimate / 100

Information on the forest road network is based on a full survey of all forest roads. In this case, there is no need to specify a standard error because there is no uncertainty caused by sampling.

Confidence interval of the estimate

With the estimate and the standard error of the estimate, the limits of the so-called confidence interval of the estimate can be calculated as:

lower limit = estimate – tQ × absolute standard error

upper limit = estimate + tQ × absolute standard error

If the simple standard error is used for the calculation (tQ = 1), then the 68% confidence interval is formed. In this case, the true value of the population parameter has a 68% probability of lying within this confidence interval of the estimate. If the double standard error is used (tQ = 2), then there is a 95% probability that the true value lies within this 95% confidence interval.

Significance of the estimate

The confidence interval can be used to statistically test whether the estimated population parameter is larger or smaller than a specific reference or target value, or whether two estimated population parameters truly differ (in the real population). For practical applications, proceed as follows: if a reference value lies outside the confidence interval, the estimated population value can be interpreted as being significantly different from it; if it lies within the confidence interval, the difference between the estimated population parameter and the reference value can be interpreted as random or not significant. When two population parameters are compared, they can be interpreted as differing significantly if their confidence intervals do not overlap.

Dealing with missing values

When calculating a results table, data are not always available for all combinations of characteristics^* of the classification variables and regional demarcation applied. In most cases, this indicates that the attribute estimated with the respective target variable does not occur or occurs only very rarely. Usually, the value 0 is used (imputed). However, as this value is not based on direct measurements, the associated standard error is represented with a full stop [.]. If the imputed value of 0 is referred to in the calculation, e.g. in the case of percentages or certain change estimates, no value can be entered. In this case, the estimated value and standard error are both represented with a full stop [.].

For example, no Arolla pines have been found and measured in the Swiss Plateau to date (growing stock of Arolla pines by production region). The values can be assumed to be missing because Arolla pine does not occur in the Swiss Plateau and therefore the growing stock there must be 0.

^* e.g. ‘Arolla pine’ characteristic of the classification variable ‘tree species’ and ‘Swiss plateau’ characteristic of the ‘regional demarcation’

Changes

There are two types of changes in the NFI:

The first type involves specific target variables relating to components of change, such as increment, fellings, mortality and losses. These target variables are only available for two consecutive inventory cycles, e.g. NFI3–NFI4. In the evaluation of components of change, the classification variable characteristic of the second inventory cycle is assigned to the first inventory cycle. These evaluations therefore do not take into account potential changes in a classification variable characteristic from the earlier to the later inventory (e.g. from private to public ownership).

With the second type of change, the difference in target variables, such as number of stems, growing stock or forest area, is used to assess the change between two inventory cycles. Target variables are generally used to represent states, such as that in NFI4, but can also indicate the net change between any two inventory cycles, e.g. NFI1–NFI4. In evaluations of change using these target variables, the change in a classification variable characteristic is considered in the analysis. Consequently, one can detect, for example, that the forest area without shrub forest increased between the two inventory cycles. This only has an effect on classification variables whose characteristic (class) can actually change, e.g. the affiliation with a forest area or the tree condition.

NFI1
growing stock (stemwood)
tree species (56 classes)
regional demarcation: protection forest region
unit: 1000 m³
evaluation area: accessible forest without shrub forest
grid: 1.4-km grid
state 1983/85
	protection forest region
	Jura + Plateau		Northwestern Alps		Northeastern Alps		Southwestern Alps		Southeastern Alps		Southern Alps		Switzerland
tree species (56 classes)	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%
n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
Abies alba	27107	4	14818	6	7301	9	1005	21	1164	19	1293	20	52687	3
Larix decidua, Larix kaempferi	1386	15	383	30	549	31	6482	8	4660	10	3373	10	16833	5
Picea abies	58840	3	44208	4	28455	6	11884	7	25830	5	7248	9	176466	2
Pinus cembra	0	.	26	86	19	71	670	17	1251	16	4	135	1969	12
Pinus mugo subsp. uncinata	0	.	219	35	113	46	168	40	494	21	29	100	1022	15
Pinus mugo subsp. mugo	0	.	0	.	4	54	9	77	26	47	0	.	38	37
Pinus nigra	231	38	10	71	37	100	0	.	1	100	5	100	283	34
Pinus strobus	352	40	10	100	0	.	0	.	18	100	0	100	379	38
Pinus sylvestris	6681	8	360	48	494	26	1809	16	2205	15	319	40	11869	6
Pseudotsuga menziesii	507	31	25	98	0	.	0	.	0	.	0	.	532	30
Taxus baccata	88	29	4	64	6	62	0	.	0	.	0	.	98	26
other conifers	2	100	0	.	0	.	0	.	0	.	0	.	2	100
Acer campestre	143	20	9	49	13	73	16	71	4	100	7	66	192	17
Acer opalus	52	39	0	.	0	.	13	49	0	.	0	.	65	33
Acer platanoides	260	21	62	50	63	33	18	77	10	85	6	100	419	16
Acer pseudoplatanus	3858	6	1355	10	1486	11	54	36	79	35	123	30	6954	5
Aesculus hippocastanum	4	100	20	100	0	.	0	.	0	.	0	.	24	85
Alnus glutinosa	449	22	23	47	11	84	8	100	2	73	181	38	673	18
Alnus incana	61	39	152	24	225	31	124	30	170	27	259	29	991	13
Alnus viridis	0	.	5	88	0	.	0	.	0	.	0	100	6	81
Betula pendula	169	25	28	59	55	48	123	25	13	72	908	12	1295	10
Betula pubescens	5	98	31	60	0	.	14	74	0	.	149	34	200	28
Carpinus betulus	761	14	1	100	5	100	1	100	0	.	7	92	773	14
Castanea sativa	41	89	0	.	2	100	52	46	24	74	3763	10	3883	10
Fagus sylvatica	39281	3	9398	8	7874	8	420	24	946	27	3158	9	61077	3
Fraxinus excelsior	6237	6	1093	13	1537	14	134	29	118	43	232	21	9352	5
Fraxinus ornus	7	100	7	100	0	.	0	.	0	.	29	61	42	47
Ilex aquifolium	0	.	1	100	0	.	0	.	0	.	3	78	4	65
Juglans regia	23	50	3	78	3	100	0	.	0	.	4	100	33	39
Laburnum anagyroides	3	80	3	100	0	.	8	88	0	.	2	75	16	52
Malus sylvestris	2	73	1	100	0	.	0	.	0	.	0	.	3	62
Ostrya carpinifolia	0	.	0	.	0	.	0	.	0	.	143	30	143	30
Populus alba, Populus x canescens	58	100	65	78	0	.	1	100	0	.	0	.	124	62
Populus nigra s.l.	119	46	0	.	2	100	0	.	0	.	0	.	121	45
Populus (others)	108	51	0	.	0	.	46	100	0	.	23	97	177	42
Populus tremula	81	39	17	82	15	68	71	65	40	75	107	41	331	24
Prunus avium	509	18	89	33	61	30	28	39	4	100	57	28	747	14
Prunus padus	33	54	0	.	0	.	0	.	0	.	0	.	33	54
Pyrus communis, Pyrus pyraster	4	100	0	.	0	.	0	.	0	.	0	.	4	100
Quercus cerris	0	.	0	.	0	.	11	88	0	.	69	46	80	42
Quercus petraea	3131	10	87	45	62	48	55	35	107	60	372	31	3814	9
Quercus pubescens	12	100	0	.	0	.	3	57	0	.	36	40	52	37
Quercus robur	2635	11	129	36	104	44	4	177	11	100	146	46	3029	10
Quercus rubra	98	49	0	.	0	.	0	.	0	.	0	.	98	49
Robinia pseudoacacia	248	57	0	.	0	.	5	102	0	.	198	48	451	38
Salix (others)	173	30	27	41	14	69	58	62	28	55	51	26	350	20
Sorbus aria	209	16	55	24	42	38	13	33	18	52	37	27	375	11
Sorbus aucuparia	52	36	84	21	31	37	18	36	11	44	11	41	207	14
Sorbus torminalis	25	49	0	.	0	.	0	.	0	.	0	.	25	49
Tilia cordata	292	22	236	39	103	31	119	63	7	90	184	30	940	16
Tilia platyphyllos	244	29	40	62	63	63	50	52	0	.	103	31	499	19
Ulmus glabra	598	17	198	24	386	19	4	100	33	50	14	69	1233	11
Ulmus minor	20	62	0	.	1	100	0	.	0	.	10	71	31	46
other broadleaves	0	.	0	.	0	.	0	.	0	.	7	92	7	92
other shrubs	8	37	1	100	3	100	1	100	1	100	11	36	25	24
indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
total	155207	1	73281	3	49140	4	23499	5	37275	4	22677	4	361078	1

Table citation

Abegg, M.; Ahles, P.; Allgaier Leuch, B.; Cioldi, F.; Didion, M.; Düggelin, C.; Fischer, C.; Herold, A.; Meile, R.; Rohner, B.; Rösler, E.; Speich, S.; Temperli, C.; Traub, B.,
2023: Swiss national forest inventory - Result table No. 1217548. Birmensdorf, Swiss Federal Research Institute WSL

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