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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 NFI4/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	31110	5	15954	8	9276	11	1311	28	1341	24	1771	25	60763	4
Larix decidua, Larix kaempferi	1185	19	360	33	479	34	8917	11	6604	12	5930	11	23475	6
Picea abies	48063	4	44386	6	30810	7	14247	9	28423	7	11670	10	177599	2
Pinus cembra	0	.	-7	100	0	.	958	22	1532	18	5	100	2489	13
Pinus mugo subsp. uncinata	0	.	226	67	72	58	175	39	443	27	85	75	1002	22
Pinus mugo subsp. mugo	0	.	38	96	6	100	15	58	45	35	0	.	104	39
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	431	36	1845	20	2163	21	106	55	9594	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	20	100	0	.	0	.	0	.	53	63
Acer campestre	82	33	21	71	0	6505	8	52	8	77	9	71	127	28
Acer opalus	111	39	104	40	0	.	26	70	0	.	0	.	241	26
Acer platanoides	381	31	118	46	210	37	54	87	38	89	20	100	821	20
Acer pseudoplatanus	5192	8	2699	12	2423	13	234	30	360	47	318	27	11227	5
Aesculus hippocastanum	8	100	0	.	0	.	0	.	0	.	0	.	8	100
Alnus glutinosa	988	27	0	.	0	0	0	.	0	.	226	51	1214	24
Alnus incana	118	41	178	33	358	33	148	44	412	39	177	35	1392	17
Alnus viridis	0	.	11	90	0	.	0	.	0	.	0	.	11	90
Betula pendula	86	45	68	63	70	53	301	30	209	35	1810	17	2542	13
Betula pubescens	0	.	9	100	2	100	36	100	3	100	0	.	50	75
Carpinus betulus	799	20	0	.	21	78	3	100	0	.	9	81	831	19
Castanea sativa	8	82	7	100	0	.	194	59	18	100	5342	12	5569	12
Fagus sylvatica	44017	4	11731	9	9708	10	958	29	1304	27	5569	12	73286	3
Fraxinus excelsior	10015	8	2075	19	2886	15	437	31	244	37	708	27	16367	6
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.	704	63	0	.	101	100	0	.	0	.	0	.	805	56
Populus (others)	398	62	0	.	0	.	0	.	5	100	0	.	404	62
Populus tremula	68	51	29	70	16	100	105	39	81	59	223	53	522	27
Prunus avium	502	20	63	43	89	40	32	36	15	62	194	29	895	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	.	85	56	85	56
Quercus petraea	3030	15	84	48	82	58	47	41	130	71	604	26	3978	12
Quercus pubescens	53	66	0	.	0	.	137	52	0	.	94	46	284	32
Quercus robur	2635	18	95	49	90	46	21	100	0	.	173	49	3014	16
Quercus rubra	254	61	0	.	0	.	0	.	0	.	0	.	254	61
Robinia pseudoacacia	55	58	0	.	0	.	21	72	0	.	226	57	301	44
Salix (others)	189	44	140	66	20	84	95	40	88	43	129	40	661	22
Sorbus aria	295	20	80	30	93	41	49	34	29	55	74	28	620	13
Sorbus aucuparia	83	27	140	28	38	39	43	35	38	42	30	52	371	15
Sorbus torminalis	57	51	0	.	0	.	0	.	0	.	0	.	57	51
Tilia cordata	265	27	308	45	233	45	17	92	40	77	673	28	1535	18
Tilia platyphyllos	343	38	211	95	147	40	166	52	10	100	17	100	894	29
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	.	27	86	50	66
other shrubs	21	33	26	52	8	83	5	50	13	55	53	28	128	19
indeterminable	0	0	0	0	0	0	0	0	0	0	0	0	0	0
total	158121	2	80247	4	57842	5	30572	7	43639	5	37041	4	407462	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. 1217648. Birmensdorf, Swiss Federal Research Institute WSL

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