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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
number of stems
giant (yes/no) · main tree species
regional demarcation: economic region
unit: 1000 n
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
giant (yes/no)	main tree species	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	.
	spruce	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	fir	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	larch	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	beech	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	maple	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	ash	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	oak	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other 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	.
no	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	13540	8	2384	23	3719	20	9013	13	10210	11	10347	14	18748	10	12597	10	12989	11	6577	16	5339	18	19310	9	35964	7	13399	12	174136	3
	fir	14842	8	1020	30	1572	22	6678	13	3220	15	3079	21	9961	11	3831	15	1825	21	2098	22	641	25	1532	24	619	27	1604	24	52522	4
	pine	1160	24	499	28	260	38	497	33	648	22	0	.	883	57	37	55	215	53	538	43	179	80	4670	21	4788	19	338	53	14710	10
	larch	21	58	127	51	671	64	92	48	632	36	140	71	67	81	135	74	524	38	0	.	326	59	9469	12	6316	12	8661	12	27182	6
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	10	100	0	.	0	.	1818	22	3933	20	65	79	5825	15
	other conifers	419	40	287	48	47	72	336	27	672	38	0	.	68	50	170	40	364	64	144	72	82	64	173	56	696	32	44	70	3501	14
	beech	17443	7	6427	12	4115	18	6848	10	9254	9	2180	24	8822	11	6373	13	3263	19	2118	23	2608	23	2313	27	1669	23	12975	12	86407	3
	maple	5494	12	1772	19	1108	34	1404	19	3661	13	1268	23	2689	20	2700	17	2794	18	794	26	1321	24	1997	24	778	29	1817	26	29597	5
	ash	1867	17	1146	22	1300	23	1144	20	2331	14	832	32	1129	34	1412	20	985	28	804	33	581	33	1508	27	778	43	2433	22	18251	6
	oak	1948	32	544	30	1141	31	548	24	818	17	88	56	125	51	44	56	234	55	57	74	35	100	1142	32	91	72	2180	24	8994	11
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	7	100	0	.	0	.	231	69	45	72	10315	14	10599	13
	other broadleaves	3412	15	1128	19	1539	22	2401	20	3959	14	1490	26	2085	18	1803	23	2734	22	1269	37	1068	31	5314	14	4849	21	17040	10	50090	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	0
	total	60146	4	15332	10	15472	11	28960	7	35406	6	19422	11	44578	6	29101	8	25943	8	14399	13	12180	13	49475	6	60527	5	70871	4	481813	1
yes	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	68	46	0	.	24	59	34	45	67	37	67	36	76	32	103	30	89	31	23	58	86	33	72	32	219	22	118	37	1046	10
	fir	106	28	0	.	33	53	56	39	57	46	9	100	85	33	45	46	8	100	7	100	27	50	0	.	15	71	32	51	481	14
	pine	0	.	0	.	0	.	0	.	7	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	7	100	0	.	14	71
	larch	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	118	32	88	37	108	33	314	19
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	42	47	22	58	0	.	64	37
	other conifers	0	.	7	100	0	.	13	71	14	100	0	.	7	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	41	47
	beech	8	100	0	.	0	.	12	100	52	43	0	.	7	100	16	71	0	.	15	71	0	.	0	0	0	.	37	45	146	24
	maple	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	14	71	0	.	0	.	0	.	14	71
	ash	0	.	7	100	0	.	10	100	16	71	0	.	0	.	17	72	0	.	0	.	0	.	0	.	0	.	0	.	50	41
	oak	0	.	0	.	0	.	7	100	52	54	0	.	0	.	8	100	0	.	10	100	0	.	0	.	0	.	0	.	77	41
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	7	100	0	.	133	36	140	35
	other broadleaves	0	.	0	.	21	73	7	100	13	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	42	52
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	183	24	14	70	79	35	138	24	278	20	75	34	175	22	189	22	96	30	56	38	127	26	240	20	351	17	429	18	2431	6
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	13608	8	2384	23	3744	20	9047	13	10277	11	10413	14	18823	10	12700	10	13078	11	6600	16	5426	18	19382	9	36184	7	13518	12	175182	3
	fir	14949	8	1020	30	1605	22	6734	13	3277	14	3088	21	10047	11	3876	15	1833	21	2106	22	667	25	1532	24	634	26	1637	24	53003	4
	pine	1160	24	499	28	260	38	497	33	655	22	0	.	883	57	37	55	215	53	538	43	179	80	4670	21	4795	19	338	53	14724	10
	larch	21	58	127	51	671	64	92	48	632	36	140	71	67	81	135	74	524	38	0	.	326	59	9587	12	6404	12	8770	11	27496	6
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	10	100	0	.	0	.	1860	22	3954	20	65	79	5889	15
	other conifers	419	40	293	49	47	72	349	28	686	37	0	.	75	46	170	40	364	64	144	72	82	64	173	56	696	32	44	70	3543	14
	beech	17452	7	6427	12	4115	18	6860	10	9306	9	2180	24	8829	11	6388	13	3263	19	2133	23	2608	23	2313	27	1669	23	13012	12	86553	3
	maple	5494	12	1772	19	1108	34	1404	19	3661	13	1268	23	2689	20	2700	17	2794	18	794	26	1336	23	1997	24	778	29	1817	26	29611	5
	ash	1867	17	1153	22	1300	23	1154	20	2348	14	832	32	1129	34	1430	20	985	28	804	33	581	33	1508	27	778	43	2433	22	18301	6
	oak	1948	32	544	30	1141	31	555	23	870	17	88	56	125	51	52	50	234	55	67	68	35	100	1142	32	91	72	2180	24	9071	11
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	7	100	0	.	0	.	238	67	45	72	10448	13	10739	13
	other broadleaves	3412	15	1128	19	1560	22	2408	20	3972	14	1490	26	2085	18	1803	23	2734	22	1269	37	1068	31	5314	14	4849	21	17040	10	50132	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	0
	total	60329	4	15346	10	15551	11	29098	7	35684	6	19498	11	44753	6	29290	8	26039	8	14455	13	12307	13	49715	6	60878	5	71300	4	484244	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. 1353433. Birmensdorf, Swiss Federal Research Institute WSL

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