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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)
diameter at breast height (main diameter classes) · conifers and broadleaves
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
diameter at breast height (main diameter classes)	conifers and broadleaves	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	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	broadleaves	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
12-15 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	577	15	104	27	121	24	625	19	254	21	225	24	651	15	221	19	252	15	135	23	76	28	636	13	970	13	331	17	5178	5
	broadleaves	674	14	342	17	253	21	370	18	540	13	142	25	286	14	167	16	270	16	152	34	150	31	422	14	227	19	1144	10	5140	4
	indeterminable	0	0	0	.	0	.	0	.	0	.	0	.	0	0	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	0
	total	1251	10	446	15	374	17	995	14	794	12	367	18	938	11	388	14	522	12	286	24	227	23	1058	10	1197	11	1475	9	10318	3
16-23 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	2109	9	244	28	548	37	1354	15	1323	16	654	30	2069	11	850	15	798	14	644	20	389	27	2519	11	3106	9	1140	12	17749	4
	broadleaves	2116	9	777	15	777	19	949	13	1305	11	574	25	1102	14	990	16	675	21	400	24	408	22	958	14	687	19	3651	7	15368	4
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	4225	7	1021	14	1325	19	2302	11	2628	10	1228	20	3171	9	1840	12	1473	13	1044	17	797	19	3477	9	3793	8	4792	6	33117	3
24-35 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	5136	9	834	23	1129	22	2599	15	3161	13	2621	17	4929	10	3407	14	2523	12	1477	19	927	29	5943	10	7960	8	3904	12	46548	3
	broadleaves	5248	8	1674	16	1452	18	1855	14	3663	11	1096	22	2779	12	2722	14	1267	18	986	25	708	26	1079	17	732	19	6667	8	31929	3
	indeterminable	0	0	0	.	0	.	0	.	0	0	0	.	0	.	0	.	0	0	0	.	0	.	0	0	0	0	0	.	0	0
	total	10383	6	2508	14	2581	14	4454	11	6824	8	3718	14	7709	8	6129	11	3790	10	2463	17	1634	21	7022	9	8692	8	10571	7	78478	2
36-51 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	10855	7	1466	18	2403	19	4687	13	5896	10	4863	13	8980	8	7516	10	5508	12	2933	19	2403	20	9195	9	14706	7	6751	10	88161	2
	broadleaves	8941	7	3457	13	2982	16	3766	11	5256	9	957	24	3781	14	4309	12	1625	19	784	26	1417	19	704	24	820	23	4811	8	43611	3
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	19796	5	4923	12	5384	13	8454	9	11153	7	5820	11	12761	8	11824	8	7133	11	3716	16	3821	15	9899	8	15527	6	11562	6	131773	2
=52 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	14213	8	1885	26	3175	20	8199	12	8372	11	6464	13	13986	8	12747	10	8031	12	3729	20	4136	18	11717	9	17785	8	9822	10	124263	3
	broadleaves	4598	11	2972	16	2752	17	4790	14	8218	11	704	32	2772	19	2650	17	1409	28	843	30	1019	28	374	35	831	28	3405	13	37336	4
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	18811	6	4857	14	5928	14	12990	10	16590	8	7168	13	16758	8	15397	9	9439	12	4572	18	5155	16	12092	9	18616	7	13227	7	161599	2
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	32890	5	4533	16	7376	14	17464	9	19006	8	14827	11	30616	7	24741	8	17111	10	8917	15	7932	15	30010	7	44527	5	21949	8	281899	2
	broadleaves	21577	5	9222	10	8216	13	11731	10	18983	7	3473	18	10720	11	10837	10	5246	15	3165	20	3702	17	3538	14	3297	15	19678	5	133386	2
	indeterminable	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. 1234721. Birmensdorf, Swiss Federal Research Institute WSL

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