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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 (10 classes)
regional demarcation: protection forest region
unit: 1000 m³
evaluation area: accessible forest without shrub forest NFI1-NFI5
grid: 1.4 km grid, subgrids 1-5
state 2018/26
		protection forest region
		Jura + Plateau		Northwestern Alps		Northeastern Alps		Southwestern Alps		Southeastern Alps		Southern Alps		Switzerland
altitudinal vegetation belts (NaiS; 6 classes)	diameter at breast height (10 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	.
	12-20 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	21-30 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	31-40 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	41-50 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	51-60 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	61-70 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	71-80 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	81-90 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	91-100 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	>100 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	.
	12-20 cm	0	.	0	.	0	.	211	52	240	26	30	49	481	26
	21-30 cm	0	.	0	.	0	.	299	31	423	23	132	41	853	17
	31-40 cm	0	.	0	.	0	.	483	31	665	22	156	47	1304	17
	41-50 cm	0	.	0	.	0	.	468	30	811	23	75	55	1355	17
	51-60 cm	0	.	0	.	0	.	238	37	635	24	50	51	923	19
	61-70 cm	0	.	0	.	0	.	186	39	293	31	0	.	479	24
	71-80 cm	0	.	0	.	0	.	167	38	241	39	0	.	408	28
	81-90 cm	0	.	0	.	0	.	46	100	232	54	0	.	278	48
	91-100 cm	0	.	0	.	0	.	30	100	48	100	0	.	78	73
	>100 cm	0	.	0	.	0	.	39	100	88	72	0	.	128	58
	total	0	.	0	.	0	.	2167	22	3676	17	443	40	6286	13
subalpine	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	3	100	405	24	129	43	590	21	657	21	210	26	1994	11
	21-30 cm	14	100	842	21	259	43	1059	18	1284	17	614	26	4072	9
	31-40 cm	0	100	1517	20	472	41	1333	20	2427	15	915	21	6664	9
	41-50 cm	14	100	1827	19	355	35	1893	20	2998	14	1065	21	8153	8
	51-60 cm	33	100	849	23	366	34	1817	18	2491	14	1110	21	6666	9
	61-70 cm	12	100	612	27	312	40	1369	21	1744	20	396	28	4445	11
	71-80 cm	0	.	474	29	144	60	666	40	782	25	318	32	2384	16
	81-90 cm	0	.	0	.	148	51	418	41	334	54	173	66	1072	27
	91-100 cm	0	.	57	100	38	100	143	58	170	58	0	.	408	36
	>100 cm	0	.	36	100	38	100	0	.	155	71	0	.	229	53
	total	77	100	6620	16	2261	29	9288	14	13041	11	4799	17	36086	7
high-montane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	62	65	838	17	284	25	1124	15	1500	13	496	19	4304	7
	21-30 cm	33	100	1562	17	752	22	2317	16	2658	13	1028	16	8349	7
	31-40 cm	80	59	2334	13	1013	23	2707	15	3210	12	1898	18	11243	6
	41-50 cm	43	71	2995	15	1291	28	2724	14	4289	12	2020	15	13362	7
	51-60 cm	62	63	3249	15	949	25	2695	15	3915	14	1977	16	12848	7
	61-70 cm	100	80	1816	21	636	31	1278	23	2163	18	1307	20	7300	9
	71-80 cm	81	74	1210	22	414	47	1012	25	1047	23	1011	30	4775	12
	81-90 cm	122	100	411	41	78	71	259	43	575	31	350	57	1795	20
	91-100 cm	71	100	167	58	172	58	188	50	152	58	145	71	895	25
	>100 cm	0	.	49	100	51	100	64	100	69	100	203	73	436	43
	total	655	45	14628	12	5641	19	14368	11	19580	9	10435	12	65306	5
lower and upper montane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	4756	7	2912	9	1762	11	266	27	218	25	1235	14	11149	4
	21-30 cm	9617	6	6231	8	4739	11	539	27	542	26	2253	16	23921	4
	31-40 cm	14214	6	8683	8	7431	9	683	28	833	25	2156	23	34000	4
	41-50 cm	17611	5	9849	7	8798	9	656	28	1007	24	1842	20	39762	3
	51-60 cm	15740	6	10387	7	9153	9	514	40	974	25	1481	29	38247	4
	61-70 cm	8506	8	6612	10	5646	12	230	42	848	23	807	23	22649	5
	71-80 cm	4494	12	3225	14	3763	15	90	58	513	36	364	35	12449	7
	81-90 cm	1720	20	1267	23	1047	24	0	0	146	58	303	40	4483	12
	91-100 cm	615	34	175	58	284	47	21	100	0	.	212	58	1308	23
	>100 cm	255	59	263	61	129	71	0	.	0	.	111	100	757	35
	total	77528	4	49604	5	42752	7	2998	24	5081	18	10762	15	188726	3
submontane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	5252	7	485	30	279	38	77	60	78	39	0	.	6172	6
	21-30 cm	9050	6	694	25	599	34	83	69	160	42	0	.	10586	6
	31-40 cm	11853	6	872	25	797	27	87	71	123	49	0	.	13732	5
	41-50 cm	13740	6	1118	26	772	28	26	72	160	43	0	.	15815	5
	51-60 cm	13269	6	980	25	506	34	42	100	198	46	0	.	14995	6
	61-70 cm	8451	8	430	43	205	53	16	100	24	100	0	.	9125	8
	71-80 cm	3896	12	427	37	83	71	0	.	33	100	0	.	4439	11
	81-90 cm	1689	20	0	.	196	52	0	.	0	.	0	.	1885	19
	91-100 cm	437	35	0	.	0	.	0	.	52	100	0	.	489	33
	>100 cm	415	56	0	.	0	.	0	.	0	.	0	.	415	56
	total	68052	4	5005	19	3436	24	332	47	829	37	0	.	77654	4
hyperinsubric and colline	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	67	46	0	.	0	.	219	29	3	100	1726	12	2014	11
	21-30 cm	212	44	0	.	0	.	289	30	11	100	2910	11	3422	10
	31-40 cm	234	42	0	.	0	.	242	33	9	100	2203	11	2688	10
	41-50 cm	195	41	0	.	0	.	170	38	27	100	1745	14	2137	12
	51-60 cm	90	65	0	.	0	.	155	71	30	100	928	20	1204	19
	61-70 cm	37	100	0	.	0	.	0	.	32	100	493	24	561	23
	71-80 cm	45	100	0	.	0	.	0	.	0	.	255	32	301	31
	81-90 cm	0	.	0	.	0	.	0	.	0	.	153	46	153	46
	91-100 cm	0	.	0	.	0	.	29	100	0	.	145	59	174	52
	>100 cm	0	.	0	.	0	.	0	.	0	.	374	60	374	60
	total	881	36	0	.	0	.	1104	28	113	100	10932	8	13029	8
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	10140	4	4640	7	2455	10	2487	10	2697	9	3697	7	26115	3
	21-30 cm	18926	4	9329	6	6349	9	4586	10	5077	9	6937	7	51203	2
	31-40 cm	26382	4	13406	6	9713	8	5534	9	7268	8	7329	8	69632	2
	41-50 cm	31604	3	15788	6	11216	8	5937	10	9293	7	6746	7	80585	2
	51-60 cm	29193	3	15465	6	10974	8	5462	10	8243	8	5545	10	74883	2
	61-70 cm	17106	5	9470	8	6799	11	3079	14	5103	11	3002	11	44559	3
	71-80 cm	8517	8	5336	10	4403	14	1934	19	2617	14	1948	17	24755	5
	81-90 cm	3531	14	1678	20	1469	20	723	29	1287	23	978	27	9667	8
	91-100 cm	1124	24	399	38	494	34	412	32	422	35	502	36	3352	13
	>100 cm	670	41	347	50	218	51	103	73	312	46	687	42	2338	20
	total	147193	2	75857	4	54090	6	30257	7	42320	6	37372	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. 1321309. Birmensdorf, Swiss Federal Research Institute WSL

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