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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)
altitudinal vegetation belts (NaiS; 6 classes) · diameter at breast height (main diameter classes)
regional demarcation: biogeographical region
unit: 1000 m³
evaluation area: accessible forest without shrub forest NFI1-NFI5
grid: 1.4 km grid, subgrids 1-5
state 2018/26
		biogeographical region
		Jura		Plateau		Northern Alps		Western Central-Alps		Eastern Central-Alps		Southern Alps		Switzerland
altitudinal vegetation belts (NaiS; 6 classes)	diameter at breast height (main diameter classes)	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	.
	12-15 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	16-23 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	24-35 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	36-51 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	=52 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	.	0	.	0	.	0	.	0	.	0	.	0	.
upper subalpine	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	0	.	0	.	0	.	70	49	102	34	10	46	182	27
	16-23 cm	0	.	0	.	0	.	243	47	249	24	51	43	543	24
	24-35 cm	0	.	0	.	0	.	430	28	640	22	218	40	1288	16
	36-51 cm	0	.	0	.	0	.	748	30	1157	21	163	42	2068	16
	=52 cm	0	.	0	.	0	.	675	30	1372	24	158	81	2206	18
	total	0	.	0	.	0	.	2167	22	3519	17	600	39	6286	13
subalpine	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	3	100	0	.	160	22	213	27	233	27	47	28	656	14
	16-23 cm	5	100	0	.	623	22	559	20	795	19	284	23	2266	10
	24-35 cm	1	100	0	.	1907	19	1275	20	2222	16	960	22	6365	9
	36-51 cm	22	100	0	.	3368	16	2545	19	4520	13	1722	19	12177	8
	=52 cm	45	100	0	.	3159	17	3822	18	5381	15	2214	19	14621	8
	total	77	100	0	.	9218	14	8414	15	13150	11	5227	16	36086	7
high-montane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	29	82	0	.	442	16	387	16	565	19	149	19	1572	9
	16-23 cm	47	59	0	.	1343	13	1423	17	1625	13	691	19	5130	7
	24-35 cm	35	100	0	.	3445	13	3057	15	3184	14	1788	16	11509	7
	36-51 cm	107	56	0	.	6228	12	4041	14	6468	11	3310	15	20154	6
	=52 cm	437	55	0	.	9535	12	4600	14	7453	13	4916	15	26942	6
	total	655	45	0	.	20994	10	13509	11	19295	9	10854	12	65306	5
lower and upper montane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	1139	10	695	17	1423	9	59	30	79	24	454	20	3849	6
	16-23 cm	3959	7	2133	12	5123	8	272	35	387	24	1291	15	13165	4
	24-35 cm	9680	7	5353	11	15054	6	337	35	1137	23	3072	19	34633	4
	36-51 cm	18687	5	11123	9	25995	5	624	31	1905	20	2796	19	61131	3
	=52 cm	17567	7	16376	9	35690	5	236	52	2930	19	3150	21	75948	4
	total	51033	4	35681	7	83285	4	1528	29	6438	16	10762	15	188726	3
submontane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	361	23	1660	9	238	31	19	100	28	46	0	.	2306	8
	16-23 cm	1012	14	4814	8	734	22	21	100	104	42	0	.	6686	6
	24-35 cm	2478	15	10305	6	1481	23	20	100	241	42	0	.	14525	6
	36-51 cm	4558	12	17513	6	1871	20	0	.	279	41	0	.	24220	5
	=52 cm	3830	15	23734	6	2000	24	0	.	353	40	0	.	29918	5
	total	12239	10	58026	4	6324	17	60	100	1005	35	0	.	77654	4
hyperinsubric and colline	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	0	.	33	41	0	.	88	30	0	.	604	16	725	14
	16-23 cm	0	.	112	57	0	.	254	29	0	.	1955	11	2321	10
	24-35 cm	0	.	218	39	0	.	273	38	0	.	3388	11	3879	10
	36-51 cm	0	.	385	40	0	.	305	33	0	.	2817	11	3508	10
	=52 cm	0	.	132	87	0	.	185	62	0	.	2280	18	2596	17
	total	0	.	881	36	0	.	1104	28	0	.	11045	8	13029	8
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	1532	9	2389	7	2263	7	835	11	1006	13	1264	10	9290	4
	16-23 cm	5023	6	7060	6	7823	6	2772	11	3159	9	4272	7	30110	3
	24-35 cm	12194	6	15876	5	21888	5	5393	10	7424	8	9425	8	72200	2
	36-51 cm	23375	4	29021	4	37462	4	8262	9	14329	7	10809	7	123258	2
	=52 cm	21879	6	40242	5	50384	4	9519	10	17488	8	12718	8	152231	2
	total	64003	3	94588	3	119820	3	26782	7	43407	6	38488	5	387089	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. 1234292. Birmensdorf, Swiss Federal Research Institute WSL

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