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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)
development stage
regional demarcation: canton
unit: 1000 m³
evaluation area: accessible forest without shrub forest
grid: 1.4 km grid, subgrids 1-5
state 2018/26
	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
development stage	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	.	36	100	277	64	0	.	34	100	0	.	19	90	645	35	17	100	4	100	0	.	0	.	0	.	68	100	0	.	111	88	11	100	140	83	59	81	0	.	289	64	54	55	0	.	3	100	1766	22
young growth/ thicket	310	45	0	0	133	72	2180	24	74	68	452	42	24	71	46	100	2358	25	98	56	544	46	104	69	0	.	44	60	190	43	80	85	57	70	227	50	117	100	185	47	70	65	509	38	184	36	78	71	420	41	8485	11
pole timber	1402	23	0	.	266	88	3905	15	771	32	994	35	0	.	448	64	4018	14	682	51	2001	25	602	36	187	76	379	53	1215	33	318	52	613	36	1069	34	941	31	4429	12	894	37	2907	19	2888	16	120	71	2213	21	33263	5
young timber	1473	30	218	100	284	71	5615	16	602	47	2491	26	0	.	408	52	5436	16	1177	39	1618	31	280	81	698	57	1216	40	2129	30	889	38	875	34	218	72	1019	37	6180	13	1022	40	3515	19	4105	19	222	100	2816	23	44507	6
medium timber	2208	25	812	59	1000	60	9849	14	1692	32	4352	23	301	71	1502	36	10333	13	1988	28	2705	28	1331	36	1029	51	657	59	4771	22	1518	32	3608	22	2193	29	891	36	4199	19	1748	43	6871	15	4027	22	632	50	4069	20	74285	5
old timber	5715	18	2430	36	2831	33	29038	9	1875	34	6833	19	160	94	1870	39	20694	10	5129	21	7209	18	3948	24	1198	43	3029	31	11675	15	1482	39	3767	23	6079	20	4982	20	6904	16	2009	32	11734	14	11081	14	734	60	5923	19	158328	3
mixed	1020	30	291	100	200	71	17414	10	629	41	2239	27	0	0	1721	31	14521	9	2872	26	5433	18	5303	16	227	87	2153	27	5511	20	457	58	1260	33	1409	30	882	37	9490	17	1703	34	6671	16	11209	11	251	73	1784	28	94649	4
total	12128	11	3751	28	4750	24	68278	5	5643	16	17394	11	485	54	6015	18	58007	5	11963	12	19513	10	11568	11	3339	26	7478	17	25559	9	4744	18	10291	12	11207	13	8970	13	31445	6	7447	17	32496	7	33548	6	2036	30	17228	9	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. 1370856. Birmensdorf, Swiss Federal Research Institute WSL

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