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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.

NFI2
total number of stems
higher/lower altitude zone · tree state (living/dead)
regional demarcation: canton
unit: 1000 n
evaluation area: accessible forest without shrub forest
grid: 1.4-km grid
state 1993/95
		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
higher/lower altitude zone	tree state (living/dead)	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	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%
n/a	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	.
	living	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	62	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	62	100
	dead	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	10	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	10	100
	total	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	72	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	72	100
lower altitude zone	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	.
	living	19519	7	671	47	2428	27	41120	5	7790	12	11668	10	1206	38	2422	29	7754	13	12762	9	13958	10	3795	15	1581	32	2530	26	14970	10	5374	15	12280	9	3015	21	10362	11	36849	5	1294	32	23189	7	6923	13	1199	28	18812	7	263472	2
	dead	646	18	50	65	132	39	1103	16	325	22	378	27	69	55	240	38	534	25	911	17	329	26	116	38	8	100	162	47	442	20	103	30	672	21	126	41	178	36	3500	10	60	52	1443	16	720	23	52	60	714	22	13010	5
	total	20165	7	721	47	2560	26	42223	5	8115	12	12046	10	1275	38	2662	29	8287	13	13673	9	14287	10	3911	15	1589	32	2692	27	15412	10	5477	14	12952	9	3141	21	10539	11	40349	5	1354	31	24632	7	7642	13	1251	28	19527	7	276483	2
higher altitude zone	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	.
	living	0	.	2155	24	2592	24	34345	6	91	73	9616	13	0	.	4511	19	54827	4	3117	21	7650	13	7710	11	2041	27	6691	14	11452	11	0	.	1990	26	9377	12	0	.	10466	9	6070	15	17533	8	37264	5	1424	32	573	58	231496	2
	dead	0	.	199	43	125	41	2511	12	19	71	431	31	0	.	534	26	4976	8	131	36	400	25	89	39	235	31	533	21	1287	21	0	.	130	39	771	25	0	.	853	16	431	23	847	17	4369	10	37	60	20	71	18928	4
	total	0	.	2354	25	2717	24	36856	6	110	72	10047	13	0	.	5045	19	59803	4	3248	21	8051	13	7799	11	2275	26	7224	14	12739	11	0	.	2120	26	10147	12	0	.	11319	9	6501	15	18380	8	41633	5	1461	32	594	58	250423	2
total	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	.
	living	19519	7	2826	22	5020	18	75466	4	7881	12	21285	8	1206	38	6933	16	62643	4	15879	8	21609	8	11505	9	3622	21	9222	12	26422	7	5374	15	14270	9	12392	10	10362	11	47315	4	7363	13	40722	5	44187	5	2623	22	19386	7	495030	1
	dead	646	18	249	37	258	28	3614	10	345	21	808	21	69	55	773	22	5519	8	1042	16	729	18	205	28	242	30	694	20	1729	17	103	30	801	19	897	22	178	36	4353	8	491	21	2290	12	5089	9	89	43	735	21	31948	3
	total	20165	7	3075	22	5278	18	79080	4	8225	12	22093	8	1275	38	7707	16	68162	4	16921	8	22338	8	11710	9	3864	20	9916	12	28151	7	5477	14	15071	9	13288	10	10539	11	51668	4	7855	13	43013	5	49276	5	2712	21	20120	7	526978	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. 1379095. Birmensdorf, Swiss Federal Research Institute WSL

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