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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—NFI5
change: 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
change 2009/17–2018/26
	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	.	.	.	.	.	.	.	.	.	.	.	.	.	.
Abies alba	553	155	1564	41	600	67	334	32	56	149	268	47	3376	34
Larix decidua, Larix kaempferi	45	258	85	63	-18	197	388	58	316	82	580	38	1395	31
Picea abies	-6821	20	-1732	74	-1162	86	817	56	1370	61	641	156	-6888	36
Pinus cembra	.	.	19	100	.	.	51	100	157	60	3	100	230	48
Pinus mugo subsp. uncinata	.	.	73	54	23	87	4	339	20	283	9	100	129	57
Pinus mugo subsp. mugo	.	.	0	100	1	71	-2	67	-4	79	.	.	-5	75
Pinus nigra	-53	109	.	.	.	.	.	.	.	.	.	.	-53	109
Pinus strobus	67	101	11	100	.	.	.	.	.	.	.	.	77	89
Pinus sylvestris	-545	41	20	452	36	89	-109	88	61	210	-34	109	-571	51
Pseudotsuga menziesii	230	101	10	100	.	.	.	.	.	.	31	100	270	87
Taxus baccata	89	45	8	65	27	80	1	100	.	.	1	100	125	37
other conifers	2	100	6	100	.	.	.	.	.	.	.	.	8	77
Acer campestre	49	35	12	76	10	107	2	89	-1	89	0	100	72	31
Acer opalus	-8	295	-13	113	.	.	2	70	.	.	.	.	-19	144
Acer platanoides	53	144	-12	202	4	928	29	97	13	140	-5	100	82	116
Acer pseudoplatanus	1202	18	114	123	464	41	81	42	75	65	59	80	1994	17
Aesculus hippocastanum	3	100	.	.	.	.	.	.	.	.	.	.	3	100
Alnus glutinosa	67	134	.	.	2	100	.	.	.	.	78	64	147	70
Alnus incana	-40	79	6	572	-48	87	-3	836	20	256	-15	214	-80	114
Alnus viridis	.	.	.	.	.	.	.	.	.	.	.	.	.	.
Betula pendula	108	55	3	96	3	339	-20	101	4	723	46	304	143	108
Betula pubescens	.	.	-1	100	0	100	11	100	2	100	5	100	17	71
Carpinus betulus	-27	260	.	.	-5	115	4	100	.	.	-1	390	-29	248
Castanea sativa	-8	82	-1	100	.	.	7	81	5	91	62	375	65	358
Fagus sylvatica	-1437	55	395	108	629	62	-36	230	0	212879	977	22	527	191
Fraxinus excelsior	-1648	29	-42	452	-286	70	79	52	3	1823	173	61	-1720	33
Fraxinus ornus	.	.	.	.	.	.	.	.	.	.	4	274	4	274
Ilex aquifolium	5	59	1	71	2	67	2	100	.	.	19	41	28	30
Juglans regia	11	73	-11	137	.	.	-3	100	7	160	4	100	8	250
Laburnum anagyroides	-1	92	0	0	.	.	0	100	.	.	1	100	0	354
Malus sylvestris	-5	100	-1	100	.	.	.	.	.	.	.	.	-7	81
Ostrya carpinifolia	.	.	.	.	.	.	.	.	.	.	20	236	20	236
Populus alba, Populus x canescens	55	100	31	100	.	.	-2	100	.	.	.	.	85	75
Populus nigra s.l.	82	71	.	.	-101	100	.	.	.	.	.	.	-20	598
Populus (others)	-203	71	.	.	.	.	.	.	-5	100	.	.	-208	69
Populus tremula	36	43	11	103	-5	100	-20	167	-69	65	48	253	1	11033
Prunus avium	10	613	-8	145	-7	364	28	56	8	81	63	44	93	81
Prunus padus	19	68	.	.	.	.	.	.	1	100	.	.	20	64
Pyrus communis, Pyrus pyraster	0	100	.	.	.	.	40	100	.	.	.	.	40	100
Quercus cerris	.	.	.	.	.	.	.	.	.	.	20	164	20	164
Quercus petraea	-291	91	29	104	17	115	2	259	19	78	60	80	-164	166
Quercus pubescens	6	167	.	.	.	.	41	47	.	.	15	151	62	51
Quercus robur	166	128	23	69	15	173	12	100	.	.	-51	71	165	132
Quercus rubra	47	72	.	.	.	.	.	.	.	.	.	.	47	72
Robinia pseudoacacia	1	785	.	.	.	.	-7	127	.	.	200	51	195	52
Salix (others)	39	191	-57	143	4	113	4	923	30	83	-35	103	-14	866
Sorbus aria	-38	110	-8	97	-5	219	15	34	-11	120	27	40	-19	250
Sorbus aucuparia	-15	84	5	306	-2	165	3	446	7	51	3	94	1	4215
Sorbus torminalis	-19	83	.	.	.	.	.	.	.	.	.	.	-19	83
Tilia cordata	102	42	-52	107	41	77	-10	103	-13	72	-28	308	40	289
Tilia platyphyllos	-40	122	12	110	38	50	35	92	9	100	-8	244	46	144
Ulmus glabra	84	58	40	127	-4	966	.	.	-10	87	12	138	121	69
Ulmus minor	24	100	-2	100	.	.	.	.	.	.	.	.	22	110
other broadleaves	57	97	-23	100	.	.	.	.	.	.	2	100	36	167
other shrubs	2	361	-1	675	-7	98	2	130	0	1027	29	67	25	87
indeterminable	0	0	0	0	0	0	0	0	0	0	0	0	0	0
total	-7986	26	514	321	266	499	1778	33	2070	45	3282	38	-76	4478

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. 1375942. Birmensdorf, Swiss Federal Research Institute WSL

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