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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)
site quality · conifers and broadleaves
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
site quality	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	±%	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	.	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	.	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	.	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	.	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	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
low	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	.
	conifers	96	79	352	71	0	.	5190	16	156	51	1130	44	0	.	1721	37	10832	11	806	35	823	47	718	39	538	52	2222	28	1799	32	0	.	299	39	1647	29	206	100	1108	30	1410	34	2321	24	4465	18	0	.	159	100	37999	6
	broadleaves	270	51	16	100	0	.	2898	21	582	42	754	47	0	.	305	46	6	59	1226	33	376	81	173	39	67	68	619	50	455	64	121	100	1460	31	346	48	2	100	4	72	242	95	787	31	681	36	0	.	223	83	11614	10
	indeterminable	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	.	0	0
	total	367	56	368	71	0	.	8088	14	738	39	1885	34	0	.	2026	33	10838	11	2032	30	1199	45	891	38	606	47	2841	25	2255	30	121	100	1759	29	1993	28	208	100	1112	30	1652	35	3109	22	5146	17	0	.	382	68	49613	5
moderate	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	.
	conifers	0	.	685	51	104	100	14270	11	0	.	3212	24	0	.	984	45	33272	7	779	59	1012	40	2835	25	401	63	1494	47	3265	24	0	.	271	53	2153	29	0	.	10390	11	1662	37	7807	16	24538	8	312	71	0	.	109447	3
	broadleaves	0	.	183	74	6	100	2438	20	0	.	461	35	0	.	665	45	2623	17	147	62	162	82	629	30	332	57	184	52	1284	28	0	.	179	59	392	39	0	.	3843	14	401	64	1814	20	2077	16	0	.	7	100	17830	7
	indeterminable	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	.	0	0
	total	0	.	867	51	110	100	16709	11	0	.	3674	22	0	.	1649	36	35895	6	926	55	1174	38	3465	24	733	56	1678	43	4549	22	0	.	450	50	2545	28	0	.	14234	9	2063	34	9621	14	26616	8	312	71	7	100	127277	3
good	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	.
	conifers	1377	30	2367	37	3057	28	16705	10	435	39	5315	19	0	.	1232	40	8387	15	2125	31	7334	16	4750	19	791	50	1471	34	6870	16	847	33	782	36	3692	23	822	35	2487	47	2444	28	7306	14	1006	43	994	45	3279	22	85877	4
	broadleaves	2069	27	149	63	987	32	7736	13	1221	31	1814	24	0	.	481	45	2887	19	1513	26	3149	21	802	26	702	52	644	42	4892	17	1151	30	1720	24	1805	27	1106	35	13285	8	885	32	5050	16	531	45	281	44	2948	19	57809	4
	indeterminable	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	.	0	.	0	.	0	.	0	0
	total	3447	22	2516	37	4043	26	24442	9	1656	28	7129	16	0	.	1713	34	11274	12	3638	23	10483	14	5552	18	1493	40	2116	31	11762	14	1998	26	2502	23	5497	19	1928	30	15772	11	3329	24	12356	12	1537	35	1275	41	6227	17	143686	3
very good	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	.
	conifers	3169	20	0	.	500	76	11947	12	1303	38	1700	32	75	91	295	59	0	.	2835	25	4831	18	1116	33	362	100	489	52	3961	24	1157	35	2300	23	336	47	3400	20	0	.	102	98	2925	21	0	.	171	73	5603	15	48576	5
	broadleaves	5146	15	0	.	97	75	7093	12	1947	24	3007	25	410	57	332	50	0	.	2532	22	1826	24	545	31	145	93	354	62	3032	23	1468	28	3280	21	836	48	3434	19	327	62	301	72	4485	17	249	60	278	65	5009	14	46133	5
	indeterminable	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	0	0
	total	8314	13	0	.	597	75	19040	10	3250	24	4707	22	485	54	627	48	0	.	5367	19	6657	16	1661	27	506	76	843	47	6993	19	2624	27	5580	18	1172	44	6835	15	327	62	403	71	7410	15	249	60	449	58	10611	11	94709	4
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	.
	conifers	4642	16	3404	29	3661	26	48113	6	1893	28	11358	13	75	91	4232	22	52491	5	6544	16	14000	11	9419	12	2093	31	5676	19	15896	11	2004	24	3652	17	7828	15	4428	17	13985	11	5618	18	20359	9	30010	7	1477	35	9041	12	281899	2
	broadleaves	7485	13	347	47	1090	30	20166	7	3750	17	6037	16	410	57	1783	24	5516	13	5419	14	5513	15	2149	15	1246	35	1802	26	9664	12	2739	20	6639	14	3379	20	4542	16	17460	6	1829	27	12137	10	3538	14	559	39	8187	11	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	0	.	0	.	0	.	0	.	0	.	0	0	0	.	0	0	0	0
	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. 1371931. Birmensdorf, Swiss Federal Research Institute WSL

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