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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)
forest type (12 classes)
regional demarcation: canton
unit: 1000 m³
evaluation area: accessible forest without shrub forest
grid: 1.4-km grid
state 2009/17
	canton
	AG		AI		AR		BE		BL/BS		FR		GE		GL		GR		JU		LU		NE		NW		OW		SG		SH		SO		SZ		TG		TI		UR		VD		VS		ZG		ZH		Switzerland
forest type (12 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	±%	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	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
inaccessible forest	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	.
shrub forest	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	.
permanently unstocked forest area	404	49	0	.	59	100	2358	29	497	51	575	47	0	.	280	51	793	41	590	44	610	59	77	87	0	.	54	77	552	61	204	62	204	69	390	58	127	76	521	51	5	100	944	45	896	44	130	100	449	42	10720	12
forest aisle, embankment	126	100	41	100	0	.	0	.	0	.	6	100	0	.	176	78	223	44	68	100	0	.	0	.	0	.	84	100	0	.	148	73	0	.	0	.	151	71	175	67	129	100	105	71	61	95	0	.	25	100	1518	23
permanently open stand	0	.	30	100	94	71	663	26	7	100	38	100	10	100	203	44	2499	15	137	63	13	100	184	52	75	74	239	43	410	42	83	100	-3	100	441	50	0	.	898	22	145	59	1395	18	1760	17	0	.	0	0	9320	8
(nut) orchard, plantation	103	100	0	.	0	.	0	.	0	.	147	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	696	40	0	.	268	72	0	.	0	.	0	.	1215	32
coppice forest	22	100	0	.	0	.	73	51	0	.	23	100	56	100	11	86	979	25	102	94	2	100	0	.	0	.	22	100	82	65	0	.	146	71	0	.	69	100	6001	10	109	75	652	41	643	35	0	.	0	.	8993	8
coppice with standards	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	146	73	102	100	0	.	0	.	0	.	0	.	84	100	205	60	0	.	0	.	0	.	569	33	0	.	54	100	7	100	0	.	0	.	1167	25
selection type high forest	169	69	0	100	0	.	6501	13	0	.	595	36	0	.	207	68	4927	12	835	33	772	32	2616	18	114	100	589	37	604	36	0	.	112	59	214	67	169	75	1776	20	818	32	893	27	3753	14	165	72	517	41	26343	6
non-uniform high forest	1338	28	92	72	173	60	10208	10	543	36	1549	25	0	.	927	34	8635	10	2390	19	3250	19	1493	24	255	70	1566	25	3485	19	0	.	1174	27	772	34	742	35	5068	12	810	34	6186	13	6499	12	289	51	824	30	58268	4
incomplete survey	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	.
uniform high forest	13753	8	2670	23	5715	18	49599	5	5988	13	14890	9	473	43	4485	17	38664	5	9579	10	13315	10	7547	13	1779	23	4867	16	18918	8	4236	15	9937	10	9499	11	7773	13	13047	7	3606	18	25289	6	19164	7	1734	25	16981	8	303510	1
total	15915	8	2832	22	6041	17	69403	4	7035	12	17824	8	539	39	6288	14	56866	4	13802	8	17964	8	11917	9	2223	21	7420	12	24134	7	4876	14	11570	9	11316	10	9031	11	28752	4	5622	14	35787	5	32783	5	2317	21	18797	7	421054	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. 1280045. Birmensdorf, Swiss Federal Research Institute WSL

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