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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/yr
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/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%
n/a	.	.	.	.	.	.	.	.	.	.	.	.	.	.
Abies alba	63	155	176	41	67	67	38	32	6	149	30	47	382	34
Larix decidua, Larix kaempferi	5	258	10	63	-2	197	45	58	36	82	65	38	158	31
Picea abies	-773	20	-195	74	-130	86	94	56	156	61	72	156	-779	36
Pinus cembra	.	.	2	100	.	.	6	100	18	60	0	100	26	48
Pinus mugo subsp. uncinata	.	.	8	54	3	87	0	339	2	283	1	100	15	57
Pinus mugo subsp. mugo	.	.	0	100	0	71	0	67	0	79	.	.	-1	75
Pinus nigra	-6	109	.	.	.	.	.	.	.	.	.	.	-6	109
Pinus strobus	8	101	1	100	.	.	.	.	.	.	.	.	9	89
Pinus sylvestris	-62	41	2	452	4	89	-12	88	7	210	-4	109	-65	51
Pseudotsuga menziesii	26	101	1	100	.	.	.	.	.	.	3	100	31	87
Taxus baccata	10	45	1	65	3	80	0	100	.	.	0	100	14	37
other conifers	0	100	1	100	.	.	.	.	.	.	.	.	1	77
Acer campestre	6	35	1	76	1	107	0	89	0	89	0	100	8	31
Acer opalus	-1	295	-1	113	.	.	0	70	.	.	.	.	-2	144
Acer platanoides	6	144	-1	202	0	928	3	97	1	140	-1	100	9	116
Acer pseudoplatanus	136	18	13	123	52	41	9	42	8	65	7	80	226	17
Aesculus hippocastanum	0	100	.	.	.	.	.	.	.	.	.	.	0	100
Alnus glutinosa	8	134	.	.	0	100	.	.	.	.	9	64	17	70
Alnus incana	-5	79	1	572	-5	87	0	836	2	256	-2	214	-9	114
Alnus viridis	.	.	.	.	.	.	.	.	.	.	.	.	.	.
Betula pendula	12	55	0	96	0	339	-2	101	0	723	5	304	16	108
Betula pubescens	.	.	0	100	0	100	1	100	0	100	1	100	2	71
Carpinus betulus	-3	260	.	.	-1	115	0	100	.	.	0	390	-3	248
Castanea sativa	-1	82	0	100	.	.	1	81	1	91	7	375	7	358
Fagus sylvatica	-163	55	44	108	71	62	-4	230	0	212879	110	22	60	191
Fraxinus excelsior	-187	29	-5	452	-32	70	9	52	0	1823	20	61	-195	33
Fraxinus ornus	.	.	.	.	.	.	.	.	.	.	0	274	0	274
Ilex aquifolium	1	59	0	71	0	67	0	100	.	.	2	41	3	30
Juglans regia	1	73	-1	137	.	.	0	100	1	160	0	100	1	250
Laburnum anagyroides	0	92	0	0	.	.	0	100	.	.	0	100	0	354
Malus sylvestris	-1	100	0	100	.	.	.	.	.	.	.	.	-1	81
Ostrya carpinifolia	.	.	.	.	.	.	.	.	.	.	2	236	2	236
Populus alba, Populus x canescens	6	100	3	100	.	.	0	100	.	.	.	.	10	75
Populus nigra s.l.	9	71	.	.	-11	100	.	.	.	.	.	.	-2	598
Populus (others)	-23	71	.	.	.	.	.	.	-1	100	.	.	-24	69
Populus tremula	4	43	1	103	-1	100	-2	167	-8	65	5	253	0	11033
Prunus avium	1	613	-1	145	-1	364	3	56	1	81	7	44	11	81
Prunus padus	2	68	.	.	.	.	.	.	0	100	.	.	2	64
Pyrus communis, Pyrus pyraster	0	100	.	.	.	.	5	100	.	.	.	.	4	100
Quercus cerris	.	.	.	.	.	.	.	.	.	.	2	164	2	164
Quercus petraea	-33	91	3	104	2	115	0	259	2	78	7	80	-19	166
Quercus pubescens	1	167	.	.	.	.	5	47	.	.	2	151	7	51
Quercus robur	19	128	3	69	2	173	1	100	.	.	-6	71	19	132
Quercus rubra	5	72	.	.	.	.	.	.	.	.	.	.	5	72
Robinia pseudoacacia	0	785	.	.	.	.	-1	127	.	.	23	51	22	52
Salix (others)	4	191	-6	143	0	113	0	923	3	83	-4	103	-2	866
Sorbus aria	-4	110	-1	97	-1	219	2	34	-1	120	3	40	-2	250
Sorbus aucuparia	-2	84	1	306	0	165	0	446	1	51	0	94	0	4215
Sorbus torminalis	-2	83	.	.	.	.	.	.	.	.	.	.	-2	83
Tilia cordata	12	42	-6	107	5	77	-1	103	-1	72	-3	308	5	289
Tilia platyphyllos	-5	122	1	110	4	50	4	92	1	100	-1	244	5	144
Ulmus glabra	9	58	5	127	0	966	.	.	-1	87	1	138	14	69
Ulmus minor	3	100	0	100	.	.	.	.	.	.	.	.	2	110
other broadleaves	7	97	-3	100	.	.	.	.	.	.	0	100	4	167
other shrubs	0	361	0	675	-1	98	0	130	0	1027	3	67	3	87
indeterminable	0	0	0	0	0	0	0	0	0	0	0	0	0	0
total	-905	26	58	321	30	499	204	33	235	45	370	38	-9	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. 1375909. Birmensdorf, Swiss Federal Research Institute WSL

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