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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
growing stock (stemwood)
tree species (56 classes)
regional demarcation: economic region
unit: 1000 m³
evaluation area: accessible forest without shrub forest
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 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%
n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
Abies alba	15416	8	1003	29	2287	22	7908	12	5327	14	3240	21	11587	10	6680	13	2754	21	2141	28	1273	30	1642	26	1397	24	2068	24	64723	4
Larix decidua, Larix kaempferi	75	64	81	47	326	39	137	50	611	26	25	81	19	94	192	48	423	36	0	.	274	52	9895	12	7503	10	6848	11	26409	6
Picea abies	15935	7	2497	19	4243	19	7957	12	11136	10	11562	12	18196	8	17721	10	13775	11	6430	17	6343	17	15460	9	31045	7	12778	12	175077	2
Pinus cembra	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	12	100	0	.	0	.	1082	21	1772	18	9	94	2875	13
Pinus mugo subsp. uncinata	0	.	0	.	0	.	0	.	0	.	0	.	221	81	8	100	80	48	89	67	0	.	182	40	465	25	93	76	1139	22
Pinus mugo subsp. mugo	0	.	0	.	0	.	0	.	0	.	0	.	2	71	0	.	43	81	12	71	1	100	13	60	47	32	0	.	117	34
Pinus nigra	63	81	93	84	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	157	60
Pinus strobus	88	92	0	.	16	89	85	65	19	100	0	.	37	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	246	44
Pinus sylvestris	1243	23	459	26	441	45	587	30	1333	19	0	.	463	58	103	66	0	0	245	55	58	60	1736	20	2298	19	72	54	9036	9
Pseudotsuga menziesii	0	.	318	82	62	91	791	41	503	70	0	.	81	100	0	.	0	.	0	.	0	.	0	.	0	.	81	100	1836	30
Taxus baccata	71	34	54	63	0	.	0	.	77	47	0	.	10	84	36	41	10	100	0	.	-17	117	1	100	0	.	1	100	243	25
other conifers	0	.	28	100	0	.	0	.	0	.	0	.	0	.	0	.	13	100	0	.	0	.	0	.	0	.	0	.	41	75
Acer campestre	79	32	47	50	16	73	0	.	11	84	0	.	14	100	0	.	18	74	0	.	9	100	22	57	7	76	7	84	232	20
Acer opalus	95	44	0	.	0	.	8	100	0	.	0	.	0	.	0	.	91	41	0	.	0	.	28	54	0	.	0	.	223	26
Acer platanoides	186	51	169	41	17	72	27	65	36	94	16	88	24	78	161	40	67	62	43	73	23	168	82	91	51	100	15	100	916	20
Acer pseudoplatanus	2525	11	709	20	340	27	690	18	2166	15	660	22	1349	17	1717	16	823	20	421	29	803	25	350	28	374	32	469	26	13396	5
Aesculus hippocastanum	11	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	11	100
Alnus glutinosa	110	76	43	71	255	54	177	45	369	35	0	.	0	.	2	100	0	.	0	.	0	.	0	.	0	.	302	42	1258	20
Alnus incana	30	65	0	.	6	100	21	72	20	87	90	49	78	55	172	44	60	62	109	65	62	69	145	49	443	40	160	42	1396	17
Alnus viridis	0	.	0	.	0	.	0	.	0	.	0	.	3	100	0	.	0	0	0	.	0	.	0	.	0	.	0	0	3	100
Betula pendula	0	0	-9	100	29	60	83	66	99	56	0	.	8	77	49	68	73	63	21	68	3	100	321	33	225	32	1865	17	2767	13
Betula pubescens	0	.	0	.	0	.	0	.	0	.	0	.	8	100	0	.	0	0	2	100	0	.	47	100	5	100	5	100	66	72
Carpinus betulus	211	46	92	50	20	70	120	45	330	30	0	.	0	.	16	100	0	.	0	.	0	.	7	100	0	.	8	100	802	19
Castanea sativa	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	6	100	0	.	0	.	165	51	23	82	5412	13	5605	12
Fagus sylvatica	14990	6	6063	12	4118	17	7562	11	10026	9	1823	23	7861	13	6571	12	2692	20	1758	23	2137	21	920	30	1310	27	6788	11	74620	3
Fraxinus excelsior	1451	18	897	24	1542	25	1568	25	2970	15	640	38	847	38	1638	21	553	31	504	38	405	32	485	30	274	40	869	31	14642	7
Fraxinus ornus	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	43	70	43	70
Ilex aquifolium	5	78	4	100	0	.	0	.	0	.	0	.	6	100	3	71	2	100	2	100	0	.	2	100	0	.	60	50	84	38
Juglans regia	0	0	10	83	0	.	6	77	11	72	0	.	4	70	0	.	2	100	0	.	0	.	13	92	37	52	8	100	91	30
Laburnum anagyroides	8	81	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	0	0	.	0	.	4	71	0	.	17	87	28	57
Malus sylvestris	0	.	0	.	0	.	5	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	5	100
Ostrya carpinifolia	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	540	38	540	38
Populus alba, Populus x canescens	0	.	0	.	151	100	0	.	0	.	0	.	0	.	0	.	283	100	0	.	0	.	0	0	0	.	0	.	435	74
Populus nigra s.l.	0	.	40	100	243	77	16	100	180	71	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	32	100	511	45
Populus (others)	0	.	0	.	119	77	66	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	185	61
Populus tremula	10	100	0	.	83	55	0	.	5	74	13	91	18	76	0	.	9	75	0	.	11	100	123	50	82	94	271	72	625	36
Prunus avium	57	40	45	61	24	58	219	33	165	28	11	62	27	56	43	50	41	57	8	100	31	56	78	32	22	62	256	29	1027	13
Prunus padus	0	.	0	.	2	100	6	100	43	55	0	.	0	.	0	.	0	.	0	.	0	.	0	.	3	72	3	100	57	44
Pyrus communis, Pyrus pyraster	0	.	0	.	2	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	2	100
Quercus cerris	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	102	63	102	63
Quercus petraea	862	27	414	43	578	39	219	42	667	29	0	.	63	91	13	71	85	53	86	72	2	100	72	44	149	71	681	26	3891	12
Quercus pubescens	33	100	0	.	0	.	21	100	5	100	0	.	0	.	0	.	0	.	0	.	0	.	171	47	0	.	112	43	341	30
Quercus robur	324	48	183	51	496	40	656	26	1214	37	62	67	61	72	68	71	0	.	19	100	0	.	33	100	0	.	122	51	3237	17
Quercus rubra	0	.	140	92	0	.	0	.	161	75	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	301	59
Robinia pseudoacacia	0	.	32	100	0	0	19	100	6	100	0	.	0	.	0	.	0	.	0	.	0	.	15	88	0	.	426	50	498	44
Salix (others)	96	43	1	100	24	76	41	60	91	39	60	48	21	61	20	100	24	53	1	100	3	74	109	38	155	41	128	34	774	15
Sorbus aria	197	30	46	47	0	.	5	100	32	56	33	45	17	57	4	71	32	51	32	43	52	72	75	30	20	56	103	24	648	14
Sorbus aucuparia	63	33	0	.	6	100	0	.	5	73	31	65	54	51	11	77	83	41	17	56	6	80	49	37	53	42	36	47	412	15
Sorbus torminalis	0	.	9	100	0	.	19	100	10	85	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	38	60
Tilia cordata	63	46	15	62	50	62	86	54	162	34	5	100	3	100	145	66	261	51	111	59	28	100	6	78	27	79	672	28	1634	17
Tilia platyphyllos	53	65	150	72	14	100	21	100	75	71	0	.	26	76	82	54	-3	100	10	100	93	64	201	47	19	100	9	87	750	24
Ulmus glabra	38	47	119	52	48	67	62	51	116	43	19	65	229	28	120	34	25	52	22	67	29	69	0	.	4	71	39	64	869	15
Ulmus minor	0	.	0	.	27	100	0	.	0	.	0	.	0	0	0	.	0	.	0	.	0	.	0	.	0	.	0	.	27	100
other broadleaves	74	80	0	.	0	.	2	100	0	.	0	.	0	.	0	.	0	0	0	.	6	100	5	100	0	.	36	75	122	53
other shrubs	8	55	4	76	8	84	6	78	9	55	10	100	0	.	2	100	18	69	0	.	0	.	11	52	14	53	82	32	172	20
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	54467	4	13755	10	15592	11	29195	7	37989	5	18300	10	41336	6	35578	7	22357	9	12082	13	11634	13	33548	6	47824	5	41627	4	415285	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. 1217694. Birmensdorf, Swiss Federal Research Institute WSL

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