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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: production region
unit: 1000 m³
evaluation area: accessible forest without shrub forest
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 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%
n/a	0	.	0	.	0	.	0	.	0	.	0	.
Abies alba	16419	7	15522	8	21507	7	9207	11	2068	24	64723	4
Larix decidua, Larix kaempferi	156	39	1074	20	236	40	18095	7	6848	11	26409	6
Picea abies	18432	6	23336	6	47480	5	73052	4	12778	12	175077	2
Pinus cembra	0	.	0	.	0	.	2866	13	9	94	2875	13
Pinus mugo subsp. uncinata	0	.	0	.	229	79	817	19	93	76	1139	22
Pinus mugo subsp. mugo	0	.	0	.	2	71	115	34	0	.	117	34
Pinus nigra	157	60	0	.	0	.	0	.	0	.	157	60
Pinus strobus	88	92	121	50	37	100	0	.	0	.	246	44
Pinus sylvestris	1701	18	2361	15	566	49	4336	13	72	54	9036	9
Pseudotsuga menziesii	318	82	1357	35	81	100	0	.	81	100	1836	30
Taxus baccata	125	33	77	47	46	37	-6	394	1	100	243	25
other conifers	28	100	0	.	0	.	13	100	0	.	41	75
Acer campestre	127	27	27	55	14	100	57	38	7	84	232	20
Acer opalus	95	44	8	100	0	.	120	34	0	.	223	26
Acer platanoides	354	33	80	50	200	34	266	41	15	100	916	20
Acer pseudoplatanus	3234	9	3195	11	3727	10	2771	11	469	26	13396	5
Aesculus hippocastanum	11	100	0	.	0	.	0	.	0	.	11	100
Alnus glutinosa	153	58	801	25	2	100	0	.	302	42	1258	20
Alnus incana	30	65	48	51	340	28	818	26	160	42	1396	17
Alnus viridis	0	.	0	.	3	100	0	0	0	0	3	100
Betula pendula	-9	100	211	38	57	60	643	21	1865	17	2767	13
Betula pubescens	0	.	0	.	8	100	53	88	5	100	66	72
Carpinus betulus	302	35	470	24	16	100	7	100	8	100	802	19
Castanea sativa	0	.	0	.	0	.	193	45	5412	13	5605	12
Fagus sylvatica	21053	5	21707	6	16255	7	8818	9	6788	11	74620	3
Fraxinus excelsior	2348	14	6080	11	3125	16	2220	15	869	31	14642	7
Fraxinus ornus	0	.	0	.	0	.	0	.	43	70	43	70
Ilex aquifolium	10	62	0	.	9	71	6	59	60	50	84	38
Juglans regia	10	83	16	54	4	70	52	44	8	100	91	30
Laburnum anagyroides	8	81	0	.	0	.	4	71	17	87	28	57
Malus sylvestris	0	.	5	100	0	.	0	.	0	.	5	100
Ostrya carpinifolia	0	.	0	.	0	.	0	.	540	38	540	38
Populus alba, Populus x canescens	0	.	151	100	0	.	283	100	0	.	435	74
Populus nigra s.l.	40	100	439	51	0	.	0	.	32	100	511	45
Populus (others)	0	.	185	61	0	.	0	.	0	.	185	61
Populus tremula	10	100	88	52	31	58	226	44	271	72	625	36
Prunus avium	102	35	408	21	81	33	181	23	256	29	1027	13
Prunus padus	0	.	51	49	0	.	3	72	3	100	57	44
Pyrus communis, Pyrus pyraster	0	.	2	100	0	.	0	.	0	.	2	100
Quercus cerris	0	.	0	.	0	.	0	.	102	63	102	63
Quercus petraea	1276	22	1463	21	77	76	394	34	681	26	3891	12
Quercus pubescens	33	100	25	84	0	.	171	47	112	43	341	30
Quercus robur	507	36	2365	22	191	40	52	73	122	51	3237	17
Quercus rubra	140	92	161	75	0	.	0	.	0	.	301	59
Robinia pseudoacacia	32	100	25	80	0	.	15	88	426	50	498	44
Salix (others)	97	42	155	30	102	37	292	26	128	34	774	15
Sorbus aria	243	26	37	51	54	33	211	23	103	24	648	14
Sorbus aucuparia	63	33	11	63	96	37	208	22	36	47	412	15
Sorbus torminalis	9	100	30	72	0	.	0	.	0	.	38	60
Tilia cordata	78	39	298	26	153	62	433	35	672	28	1634	17
Tilia platyphyllos	203	56	110	54	109	45	319	35	9	87	750	24
Ulmus glabra	157	41	227	30	368	21	79	35	39	64	869	15
Ulmus minor	0	.	27	100	0	0	0	.	0	.	27	100
other broadleaves	74	80	2	100	0	.	11	71	36	75	122	53
other shrubs	12	45	23	41	11	88	43	36	82	32	172	20
indeterminable	0	0	0	0	0	0	0	0	0	0	0	0
total	68222	3	82776	3	95214	3	127445	2	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. 1217699. Birmensdorf, Swiss Federal Research Institute WSL

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