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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.

NFI5
number of stems
tree species (56 classes)
regional demarcation: production region
unit: 1000 n
evaluation area: accessible forest without shrub forest NFI1-NFI5
grid: 1.4 km grid, subgrids 1-5
state 2018/26
	production region
	Jura		Plateau		Pre-Alps		Alps		Southern Alps		Switzerland
tree species (56 classes)	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%
n/a	0	.	0	.	0	.	0	.	0	.	0	.
Abies alba	15727	7	11462	8	16768	8	6463	11	1563	25	51983	4
Larix decidua, Larix kaempferi	148	44	1395	35	342	44	11296	8	5302	15	18482	7
Picea abies	15516	8	22814	7	36987	6	69678	4	11014	13	156009	3
Pinus cembra	0	.	0	.	0	.	4183	18	49	100	4231	17
Pinus mugo subsp. uncinata	0	.	0	.	602	80	3123	24	156	100	3881	23
Pinus mugo subsp. mugo	0	.	0	.	17	100	778	31	0	.	795	31
Pinus nigra	96	53	0	.	0	.	0	.	0	.	96	53
Pinus strobus	70	71	93	51	7	100	0	.	0	.	170	40
Pinus sylvestris	1492	20	1318	18	311	49	6204	17	68	54	9393	12
Pseudotsuga menziesii	118	84	645	22	7	100	0	.	24	100	795	22
Taxus baccata	580	34	437	54	202	36	99	56	20	100	1338	24
other conifers	14	100	0	.	0	.	6	100	0	.	20	76
Acer campestre	366	27	59	52	63	100	188	36	58	76	734	20
Acer opalus	243	36	19	100	0	.	526	42	0	.	788	30
Acer platanoides	746	26	248	34	304	38	372	36	7	100	1677	16
Acer pseudoplatanus	5731	11	5680	11	5647	11	5107	12	1056	29	23221	5
Aesculus hippocastanum	7	100	0	.	0	.	0	.	0	.	7	100
Alnus glutinosa	162	55	1346	24	22	100	0	.	615	41	2144	20
Alnus incana	105	57	212	67	834	35	3272	27	528	43	4951	20
Alnus viridis	0	.	0	.	0	.	0	.	0	.	0	.
Betula pendula	19	100	511	30	136	45	1660	23	4178	20	6504	14
Betula pubescens	0	.	0	.	35	100	58	58	7	100	100	49
Carpinus betulus	890	29	978	19	35	100	55	100	80	100	2038	16
Castanea sativa	0	.	0	.	0	.	143	47	10308	14	10450	13
Fagus sylvatica	23618	5	19798	6	16948	7	11036	10	12090	13	83489	3
Fraxinus excelsior	2960	13	4535	10	3272	16	3356	16	1943	26	16066	7
Fraxinus ornus	0	.	0	.	0	.	0	.	298	72	298	72
Ilex aquifolium	70	61	0	.	87	64	59	58	443	52	659	37
Juglans regia	58	76	94	52	22	100	174	44	36	100	384	28
Laburnum anagyroides	36	71	0	.	0	.	20	100	29	100	85	51
Malus sylvestris	0	.	0	.	0	.	0	.	0	.	0	.
Ostrya carpinifolia	0	.	0	.	0	.	0	.	2518	36	2518	36
Populus alba, Populus x canescens	0	.	79	100	0	.	62	100	0	.	141	71
Populus nigra s.l.	9	100	41	69	0	.	0	.	0	.	49	60
Populus (others)	0	.	28	61	0	.	0	.	0	.	28	61
Populus tremula	8	100	77	45	66	63	491	34	137	53	779	24
Prunus avium	250	27	711	20	288	30	616	36	512	30	2377	14
Prunus padus	0	.	288	47	0	.	18	100	0	.	306	44
Pyrus communis, Pyrus pyraster	0	.	17	100	0	.	0	.	0	.	17	100
Quercus cerris	0	.	0	.	0	.	0	.	102	51	102	51
Quercus petraea	1611	30	1263	28	70	61	616	40	1391	33	4951	16
Quercus pubescens	390	100	55	75	0	.	776	38	415	52	1636	33
Quercus robur	370	33	1151	17	143	40	22	77	70	45	1755	14
Quercus rubra	121	94	27	71	0	.	0	.	0	.	148	79
Robinia pseudoacacia	24	100	52	100	0	.	76	71	1011	42	1163	37
Salix (others)	211	35	732	35	294	33	956	27	298	34	2491	16
Sorbus aria	985	22	223	43	229	35	836	26	862	25	3135	13
Sorbus aucuparia	399	35	107	69	382	29	1254	22	119	50	2261	15
Sorbus torminalis	7	100	41	61	0	.	0	.	0	.	48	54
Tilia cordata	255	36	805	26	255	74	557	31	1664	24	3536	15
Tilia platyphyllos	247	45	153	50	195	50	580	34	27	75	1202	22
Ulmus glabra	233	26	670	25	857	21	213	32	133	63	2107	13
Ulmus minor	0	.	17	100	0	0	0	.	0	.	17	100
other broadleaves	38	100	20	100	0	.	0	0	28	100	86	60
other shrubs	126	42	121	47	17	100	247	38	737	28	1249	19
indeterminable	0	0	0	0	0	0	0	0	0	0	0	0
total	74057	3	78322	3	85446	4	135175	3	59893	5	432892	2

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. 1355767. Birmensdorf, Swiss Federal Research Institute WSL

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