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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.

NFI4
growing stock (stemwood)
tree species (56 classes)
regional demarcation: protection forest region
unit: 1000 m³
evaluation area: accessible forest without shrub forest NFI1-NFI5
grid: 1.4 km grid, subgrids 1-5
state 2009/17
	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	30796	6	15900	8	8729	11	1287	28	1341	24	1738	25	59792	4
Larix decidua, Larix kaempferi	1185	19	355	33	383	36	8161	12	5815	13	4818	13	20718	7
Picea abies	47578	4	40623	6	28690	8	13654	10	26451	7	10966	11	167961	2
Pinus cembra	0	.	-7	100	0	.	823	24	1342	19	5	100	2164	15
Pinus mugo subsp. uncinata	0	.	202	74	62	65	158	41	414	29	58	100	894	24
Pinus mugo subsp. mugo	0	.	1	100	6	100	15	58	39	39	0	.	61	30
Pinus nigra	210	63	0	.	0	.	0	.	0	.	0	.	210	63
Pinus strobus	142	45	27	100	0	.	0	.	0	.	0	.	168	41
Pinus sylvestris	4607	11	443	71	271	45	1837	21	2114	21	106	55	9379	9
Pseudotsuga menziesii	1445	33	71	100	0	.	0	.	0	.	50	100	1566	31
Taxus baccata	113	39	13	70	-8	292	0	.	0	.	0	.	117	43
other conifers	26	100	8	100	0	.	0	.	0	.	0	.	33	80
Acer campestre	90	29	21	71	0	6505	3	73	8	77	7	83	129	27
Acer opalus	111	39	104	40	0	.	9	75	0	.	0	.	225	27
Acer platanoides	381	31	118	46	210	37	54	87	38	89	20	100	821	20
Acer pseudoplatanus	5087	8	2517	12	2193	14	196	34	209	38	254	31	10457	6
Aesculus hippocastanum	8	100	0	.	0	.	0	.	0	.	0	.	8	100
Alnus glutinosa	855	27	0	.	0	0	0	.	0	.	224	51	1079	24
Alnus incana	117	41	133	36	202	37	148	44	384	42	117	39	1102	19
Alnus viridis	0	.	0	.	0	.	0	.	0	.	0	.	0	.
Betula pendula	86	45	47	81	70	53	198	30	131	47	1371	17	1903	13
Betula pubescens	0	.	9	100	2	100	36	100	3	100	0	.	50	75
Carpinus betulus	798	20	0	.	21	78	3	100	0	.	9	81	830	19
Castanea sativa	8	82	7	100	0	.	90	53	18	100	5269	12	5391	12
Fagus sylvatica	43108	4	11383	9	9272	10	922	30	1290	28	5418	12	71394	3
Fraxinus excelsior	9873	9	1940	20	2730	16	263	34	215	41	616	30	15636	7
Fraxinus ornus	0	.	0	.	0	.	0	.	0	.	40	77	40	77
Ilex aquifolium	5	71	7	82	3	71	0	.	0	.	42	57	56	44
Juglans regia	15	57	14	100	0	.	4	100	30	66	4	100	68	39
Laburnum anagyroides	9	76	0	0	0	.	2	100	0	.	2	100	12	57
Malus sylvestris	5	100	1	100	0	.	0	.	0	.	0	.	7	81
Ostrya carpinifolia	0	.	0	.	0	.	0	.	0	.	520	38	520	38
Populus alba, Populus x canescens	96	100	252	100	0	.	2	100	0	.	0	.	350	77
Populus nigra s.l.	131	56	0	.	101	100	0	.	0	.	0	.	232	54
Populus (others)	387	64	0	.	0	.	0	.	5	100	0	.	393	63
Populus tremula	61	56	27	73	16	100	89	42	72	65	223	53	489	28
Prunus avium	484	20	52	48	89	40	24	43	15	62	186	31	850	14
Prunus padus	33	79	0	.	0	.	0	.	0	.	0	.	33	79
Pyrus communis, Pyrus pyraster	2	100	0	.	0	.	-40	100	0	.	0	.	-38	104
Quercus cerris	0	.	0	.	0	.	0	.	0	.	78	61	78	61
Quercus petraea	3030	15	84	48	81	58	34	51	130	71	552	28	3912	13
Quercus pubescens	53	66	0	.	0	.	121	57	0	.	91	47	265	33
Quercus robur	2489	19	84	54	60	58	21	100	0	.	173	49	2827	17
Quercus rubra	254	61	0	.	0	.	0	.	0	.	0	.	254	61
Robinia pseudoacacia	37	71	0	.	0	.	21	72	0	.	226	57	283	47
Salix (others)	139	53	130	70	20	84	78	46	66	54	108	47	542	26
Sorbus aria	267	21	65	33	65	51	33	36	26	60	70	29	526	14
Sorbus aucuparia	79	28	131	30	30	45	43	35	16	41	11	64	311	16
Sorbus torminalis	57	51	0	.	0	.	0	.	0	.	0	.	57	51
Tilia cordata	265	27	308	45	211	48	17	92	40	77	603	31	1443	18
Tilia platyphyllos	340	39	10	85	147	40	166	52	10	100	17	100	690	24
Ulmus glabra	296	24	231	29	158	34	0	.	14	64	27	63	725	15
Ulmus minor	3	100	2	100	0	.	0	.	0	.	0	.	5	71
other broadleaves	0	0	23	100	0	.	0	.	0	.	23	100	46	71
other shrubs	21	33	8	53	8	83	5	50	13	55	48	30	104	19
indeterminable	0	0	0	0	0	0	0	0	0	0	0	0	0	0
total	155178	2	75344	4	53824	6	28478	7	40250	6	34090	4	387165	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. 1217632. Birmensdorf, Swiss Federal Research Institute WSL

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