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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: economic region
unit: 1000 n
evaluation area: accessible forest without shrub forest NFI1-NFI5
grid: 1.4 km grid, subgrids 1-5
state 2018/26
	economic region
	Western Jura		Eastern Jura		Western Plateau		Central Plateau		Eastern Plateau		Western Pre-Alps		Central Pre-Alps		Eastern Pre-Alps		Northwestern Alps		Central Alps		Northeastern Alps		Southwestern Alps		Southeastern Alps		Southern Alps		Switzerland
tree species (56 classes)	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%
n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
Abies alba	14708	8	1020	30	1605	22	6616	13	3241	15	3048	22	10007	11	3714	15	1826	21	1923	24	579	27	1501	24	634	26	1563	25	51983	4
Larix decidua, Larix kaempferi	21	58	127	51	671	64	92	48	632	36	140	71	67	81	135	74	446	43	0	.	142	72	6942	12	3766	13	5302	15	18482	7
Picea abies	13142	8	2374	23	3614	21	8983	13	10216	11	8044	14	17484	10	11458	11	11287	11	5283	18	4893	19	17710	10	30504	7	11014	13	156009	3
Pinus cembra	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	10	100	0	.	0	.	1592	24	2581	24	49	100	4231	17
Pinus mugo subsp. uncinata	0	.	0	.	0	.	0	.	0	.	0	.	596	80	6	100	176	62	160	74	0	.	435	49	2353	30	156	100	3881	23
Pinus mugo subsp. mugo	0	.	0	.	0	.	0	.	0	.	0	.	17	100	0	.	0	.	87	100	18	100	156	62	518	40	0	.	795	31
Pinus nigra	49	73	48	77	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	96	53
Pinus strobus	70	71	0	.	56	76	30	64	7	100	0	.	7	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	170	40
Pinus sylvestris	1041	26	451	29	204	43	466	35	648	22	0	.	280	54	31	63	0	0	201	65	0	.	4187	23	1816	25	68	54	9393	12
Pseudotsuga menziesii	0	.	118	84	47	72	349	28	249	41	0	.	7	100	0	.	0	.	0	.	0	.	0	.	0	.	24	100	795	22
Taxus baccata	419	40	161	63	0	.	0	.	437	54	0	.	33	71	170	40	17	100	0	.	65	77	17	100	0	.	20	100	1338	24
other conifers	0	.	14	100	0	.	0	.	0	.	0	.	0	.	0	.	6	100	0	.	0	.	0	.	0	.	0	.	20	76
Acer campestre	289	31	77	51	34	71	0	.	24	77	0	.	63	100	0	.	64	58	0	.	15	100	53	74	55	74	58	76	734	20
Acer opalus	243	36	0	.	0	.	19	100	0	.	0	.	0	.	0	.	437	49	0	.	0	.	89	60	0	.	0	.	788	30
Acer platanoides	399	31	346	42	61	90	81	60	106	40	56	73	26	75	222	48	78	60	31	72	92	85	138	68	33	100	7	100	1677	16
Acer pseudoplatanus	4484	13	1247	20	993	38	1291	20	3396	13	1177	24	2186	19	2283	18	2088	21	514	31	1005	27	925	30	575	35	1056	29	23221	5
Aesculus hippocastanum	7	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	7	100
Alnus glutinosa	85	81	76	75	176	59	443	46	727	33	0	.	0	.	22	100	0	.	0	.	0	.	0	.	0	.	615	41	2144	20
Alnus incana	105	57	0	.	34	100	24	76	153	89	221	64	293	62	320	58	254	74	96	83	305	73	637	49	1980	39	528	43	4951	20
Alnus viridis	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
Betula pendula	0	0	19	100	54	73	153	58	304	40	0	.	35	70	101	55	60	76	87	66	17	100	934	29	561	48	4178	20	6504	14
Betula pubescens	0	.	0	.	0	.	0	.	0	.	0	.	35	100	0	.	0	0	17	100	0	.	23	100	18	100	7	100	100	49
Carpinus betulus	560	41	330	38	103	62	161	43	714	22	0	.	0	.	35	100	0	.	0	.	0	.	55	100	0	.	80	100	2038	16
Castanea sativa	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	7	100	0	.	0	.	90	65	45	72	10308	14	10450	13
Fagus sylvatica	17324	7	6294	12	4115	18	6656	10	9027	9	2154	24	8580	11	6213	13	3113	20	1735	25	2356	24	2216	28	1615	24	12090	13	83489	3
Fraxinus excelsior	1826	17	1134	22	1284	23	1154	20	2098	14	832	32	1129	34	1311	20	778	29	720	36	357	33	912	29	589	52	1943	26	16066	7
Fraxinus ornus	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	298	72	298	72
Ilex aquifolium	51	74	19	100	0	.	0	.	0	.	0	.	49	100	38	71	18	100	23	100	0	.	18	100	0	.	443	52	659	37
Juglans regia	0	0	58	76	0	.	59	72	34	71	0	.	22	100	0	.	18	100	0	.	0	.	18	100	138	52	36	100	384	28
Laburnum anagyroides	36	71	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	0	0	.	0	.	20	100	0	.	29	100	85	51
Malus sylvestris	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
Ostrya carpinifolia	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	2518	36	2518	36
Populus alba, Populus x canescens	0	.	0	.	79	100	0	.	0	.	0	.	0	.	0	.	62	100	0	.	0	.	0	0	0	.	0	.	141	71
Populus nigra s.l.	0	.	9	100	8	100	7	100	26	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	49	60
Populus (others)	0	.	0	.	20	75	7	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	28	61
Populus tremula	8	100	0	.	38	55	0	.	39	70	31	100	35	80	0	.	88	72	0	.	6	100	379	40	18	100	137	53	779	24
Prunus avium	191	30	60	66	98	49	432	29	180	30	57	58	87	61	143	42	51	58	18	100	73	47	371	56	102	62	512	30	2377	14
Prunus padus	0	.	0	.	17	100	67	100	204	57	0	.	0	.	0	.	0	.	0	.	0	.	0	.	18	100	0	.	306	44
Pyrus communis, Pyrus pyraster	0	.	0	.	17	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	17	100
Quercus cerris	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	102	51	102	51
Quercus petraea	1344	36	267	34	818	40	138	57	306	26	0	.	42	87	28	79	176	65	61	75	0	.	288	71	91	72	1391	33	4951	16
Quercus pubescens	390	100	0	.	0	.	37	100	17	100	0	.	0	.	0	.	0	.	0	.	0	.	776	38	0	.	415	52	1636	33
Quercus robur	214	45	155	49	323	37	347	27	481	25	88	56	39	71	17	71	0	.	6	100	0	.	16	100	0	.	70	45	1755	14
Quercus rubra	0	.	121	94	0	.	0	.	27	71	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	148	79
Robinia pseudoacacia	0	.	24	100	0	.	0	.	52	100	0	.	0	.	0	.	0	.	0	.	0	.	76	71	0	.	1011	42	1163	37
Salix (others)	194	37	17	100	127	63	301	68	304	45	170	44	116	53	8	100	124	67	17	100	35	71	415	40	366	48	298	34	2491	16
Sorbus aria	868	24	117	44	0	.	33	100	190	47	136	50	55	58	38	71	143	53	107	53	195	84	318	33	73	61	862	25	3135	13
Sorbus aucuparia	399	35	0	.	69	100	0	.	38	71	157	49	189	41	37	72	494	38	91	64	51	76	457	41	161	37	119	50	2261	15
Sorbus torminalis	0	.	7	100	0	.	17	100	24	77	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	48	54
Tilia cordata	146	43	109	62	221	62	217	44	368	36	18	100	8	100	228	82	347	45	83	60	12	100	36	71	78	71	1664	24	3536	15
Tilia platyphyllos	108	69	139	61	18	100	46	100	90	65	0	.	110	73	86	67	15	100	22	100	78	61	431	44	33	100	27	75	1202	22
Ulmus glabra	150	34	83	42	216	57	247	39	208	34	42	63	526	29	289	31	83	52	40	61	36	71	0	.	54	74	133	63	2107	13
Ulmus minor	0	.	0	.	17	100	0	.	0	.	0	.	0	0	0	.	0	.	0	.	0	.	0	.	0	.	0	.	17	100
other broadleaves	38	100	0	.	0	.	20	100	0	.	0	.	0	.	0	.	0	0	0	.	0	.	0	.	0	.	28	100	86	60
other shrubs	90	52	35	71	17	100	17	100	87	59	0	.	0	.	17	100	50	73	0	.	0	.	91	60	106	64	737	28	1249	19
indeterminable	0	0	0	0	0	.	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
total	59000	4	15057	10	15157	11	28510	8	34655	6	16373	11	42123	6	26950	8	22317	9	11322	15	10333	14	42322	7	48881	6	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. 1355765. Birmensdorf, Swiss Federal Research Institute WSL

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