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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.

NFI4
growing stock (stemwood)
altitudinal vegetation belts (NaiS; 6 classes) · diameter at breast height (main diameter classes)
regional demarcation: economic region
unit: 1000 m³
evaluation area: accessible forest without shrub forest
grid: 1.4-km grid
state 2009/17
		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
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	±%	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	.
	12-15 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	16-23 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	24-35 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	36-51 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	=52 cm	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	.
upper subalpine	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	3	100	0	.	61	24	111	18	50	25	225	12
	16-23 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	4	100	0	.	282	23	330	17	127	23	742	12
	24-35 cm	0	.	0	.	0	.	0	.	0	.	0	.	7	100	0	.	0	.	26	100	0	.	597	18	801	15	294	22	1726	10
	36-51 cm	0	.	0	.	0	.	0	.	0	.	0	.	10	100	0	.	0	.	6	100	0	.	882	16	1172	15	348	29	2418	10
	=52 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	0	0	.	964	19	1427	20	386	25	2778	13
	total	0	.	0	.	0	.	0	.	0	.	0	.	17	100	0	.	0	.	39	100	0	.	2786	14	3842	13	1205	18	7889	8
subalpine	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	0	.	0	.	2	100	0	.	0	.	8	61	45	37	11	61	65	22	18	45	26	29	212	20	392	15	114	24	893	9
	16-23 cm	0	.	0	.	2	100	0	.	0	.	49	56	174	32	26	59	190	23	49	51	92	36	648	13	1257	12	337	18	2825	7
	24-35 cm	0	.	0	.	23	100	0	.	0	.	157	37	548	24	29	64	671	22	141	39	232	37	1888	13	2906	10	910	17	7505	6
	36-51 cm	0	.	0	.	35	100	0	.	0	.	416	35	741	20	24	76	1261	21	186	43	413	35	3402	11	5547	9	1713	15	13738	5
	=52 cm	0	.	0	.	7	100	0	.	0	.	454	42	635	33	39	77	1181	21	222	54	558	33	3880	12	6185	13	2032	14	15195	7
	total	0	.	0	.	69	100	0	.	0	.	1084	32	2144	19	130	54	3369	18	616	35	1321	27	10030	10	16287	8	5106	12	40155	5
high-montane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	4	53	0	.	2	72	0	.	0	.	59	23	90	23	54	40	186	18	51	24	28	35	440	11	626	12	300	25	1839	7
	16-23 cm	1	266	0	.	18	68	0	.	0	.	250	22	295	20	136	25	422	16	188	25	49	35	1592	11	1762	10	761	12	5475	5
	24-35 cm	41	62	0	.	48	84	0	.	0	.	901	25	930	18	279	30	1166	17	579	25	152	42	3125	10	3680	9	1995	12	12895	5
	36-51 cm	172	42	0	.	110	46	0	.	0	.	1466	19	1534	17	811	24	2257	16	967	25	293	42	4105	10	6844	8	3288	11	21848	4
	=52 cm	350	40	0	.	58	77	0	.	0	.	1901	20	1409	21	817	27	3266	15	1019	30	677	38	5601	12	8536	9	4332	12	27968	5
	total	569	35	0	.	236	49	0	.	0	.	4577	17	4258	15	2097	21	7297	13	2804	21	1200	31	14863	8	21448	7	10677	8	70025	3
lower and upper montane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	1074	7	99	22	177	26	186	24	226	24	247	16	682	11	367	13	253	17	196	24	167	22	145	27	142	20	534	10	4496	4
	16-23 cm	3500	6	289	21	456	21	670	18	813	14	923	14	2080	8	1710	9	673	16	525	17	611	16	471	20	389	21	1658	10	14770	3
	24-35 cm	9861	5	1036	16	1235	20	1412	17	2386	12	2656	13	5427	7	5203	8	1535	14	1113	18	1639	16	895	20	953	19	2819	10	38169	3
	36-51 cm	18680	4	1816	16	1917	18	2498	14	4715	10	4670	11	10507	6	10315	7	2653	13	1669	17	3270	13	1125	20	1812	15	2602	10	68251	2
	=52 cm	15795	6	1757	21	2434	19	3591	15	4716	13	4906	14	14277	7	12904	8	3381	16	2438	20	3195	15	801	25	1839	18	2997	14	75031	3
	total	48911	3	4997	15	6219	14	8357	12	12856	9	13402	10	32972	6	30500	6	8494	11	5941	15	8883	12	3437	17	5136	13	10610	8	200716	2
submontane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	228	16	245	17	302	21	459	12	838	12	-3	359	98	24	72	31	67	30	34	54	23	65	43	39	15	48	0	.	2421	6
	16-23 cm	721	14	773	13	856	16	1313	11	2471	9	24	60	261	22	206	31	187	27	80	43	36	56	147	34	41	45	0	.	7117	5
	24-35 cm	1976	12	2025	12	1943	12	3032	10	5296	8	15	99	722	23	392	27	442	31	287	41	54	66	233	34	61	54	0	.	16478	4
	36-51 cm	4029	10	4229	10	3776	11	6196	9	8515	7	148	66	1117	24	866	25	460	31	318	37	96	43	117	37	145	46	0	.	30013	3
	=52 cm	2744	14	4017	12	4026	13	7821	10	11509	8	196	67	1245	26	980	28	403	42	135	57	92	56	62	56	131	51	0	.	33360	4
	total	9699	9	11289	8	10903	10	18821	7	28628	5	380	65	3443	20	2516	22	1559	25	856	35	301	43	602	30	393	37	0	.	89390	3
hyperinsubric and colline	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	1	100	0	.	18	40	0	.	4	86	0	.	0	.	0	.	0	.	0	.	0	.	92	23	5	86	635	12	757	10
	16-23 cm	7	72	0	.	63	44	0	.	15	100	0	.	0	.	0	.	0	.	0	.	0	.	221	21	25	82	2028	8	2359	8
	24-35 cm	63	71	0	.	151	44	0	.	63	68	0	.	0	.	0	.	0	.	0	.	0	.	286	26	34	60	3030	8	3627	7
	36-51 cm	33	71	0	.	251	42	0	.	79	64	0	.	0	.	0	.	0	.	0	.	0	.	271	30	37	90	2555	9	3226	8
	=52 cm	0	.	0	.	94	62	0	.	55	80	0	.	0	.	0	.	0	.	0	.	0	.	194	40	39	61	2527	15	2909	14
	total	104	71	0	.	577	37	0	.	217	57	0	.	0	.	0	.	0	.	0	.	0	.	1065	20	140	59	10775	6	12878	6
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	1308	6	344	13	501	15	645	11	1068	10	311	14	915	9	504	11	571	10	301	17	244	17	993	8	1293	8	1632	7	10631	3
	16-23 cm	4230	5	1063	11	1395	12	1983	9	3300	7	1247	11	2810	6	2079	8	1472	10	847	13	787	14	3361	7	3803	6	4912	5	33289	2
	24-35 cm	11941	5	3061	9	3400	10	4444	8	7745	6	3728	11	7634	6	5903	7	3814	9	2146	13	2078	14	7023	6	8435	5	9048	4	80400	2
	36-51 cm	22915	3	6045	8	6089	9	8694	7	13309	5	6699	9	13909	5	12016	6	6632	8	3146	12	4073	11	9902	6	15557	5	10507	4	139493	1
	=52 cm	18890	5	5774	10	6619	11	11413	8	16279	6	7457	10	17565	6	14740	7	8232	9	3815	15	4522	13	11503	7	18158	6	12274	6	157240	2
	total	59284	3	16287	7	18004	7	27179	6	41701	4	19443	8	42834	5	35243	5	20720	7	10256	11	11704	10	32783	5	47246	4	38372	3	421054	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. 1234281. Birmensdorf, Swiss Federal Research Institute WSL

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