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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
altitude (in 200 m classes) · number of cases of damage
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
altitude (in 200 m classes)	number of cases of damage	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	.
	no visible damage	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	one visible damage	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	two or more visible damages	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	dead or lying tree	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	.
>1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	0	.	0	.	0	.	0	.	496	100	69	100	0	.	769	50	255	100	71	100	5873	16	11624	12	3932	17	23089	8
	one visible damage	0	.	0	.	0	.	0	.	0	.	15	100	7	100	0	.	236	49	55	100	88	100	1840	16	4069	13	1582	25	7891	9
	two or more visible damages	0	.	0	.	0	.	0	.	0	.	0	.	66	100	0	.	126	44	0	.	18	100	1360	20	1421	17	822	23	3813	11
	dead or lying tree	0	.	0	.	0	.	0	.	0	.	0	.	0	0	0	.	0	0	0	0	0	.	140	56	452	39	93	49	684	29
	total	0	.	0	.	0	.	0	.	0	.	511	100	142	100	0	.	1131	44	309	100	176	100	9212	14	17566	11	6428	16	35477	8
1601-1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	0	.	0	.	0	.	0	.	771	51	3174	35	272	100	2396	22	262	48	1073	52	6720	18	8683	14	4947	17	28298	8
	one visible damage	0	.	0	.	0	.	0	.	0	.	210	57	569	30	0	.	874	27	274	45	239	44	2151	19	2515	15	1207	20	8040	9
	two or more visible damages	0	.	0	.	0	.	0	.	0	.	144	55	379	44	0	.	547	34	163	60	159	83	1051	18	1294	18	612	24	4349	10
	dead or lying tree	0	.	0	.	0	.	0	.	0	.	0	0	101	75	22	100	35	100	0	0	0	0	68	48	53	74	16	100	294	34
	total	0	.	0	.	0	.	0	.	0	.	1126	52	4224	32	294	100	3851	21	699	45	1471	44	9990	16	12545	13	6783	16	40982	7
1401-1600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	680	34	0	.	386	53	0	.	0	.	2465	34	3260	22	1622	34	4523	19	1923	31	923	34	6067	17	9563	14	7423	17	38834	7
	one visible damage	225	35	0	.	61	61	0	.	0	.	720	28	1174	20	298	43	1161	20	574	32	282	38	2018	25	2332	15	1905	19	10749	8
	two or more visible damages	97	51	0	.	0	.	0	.	0	.	384	40	483	28	68	47	1070	25	284	37	205	47	1048	21	1451	18	740	19	5830	9
	dead or lying tree	0	0	0	.	0	0	0	.	0	.	37	72	0	0	0	0	18	100	58	100	104	71	198	60	88	53	102	52	605	28
	total	1002	33	0	.	446	53	0	.	0	.	3606	29	4917	19	1987	33	6772	17	2838	30	1514	33	9331	16	13434	13	10169	15	56017	6
1201-1400 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	5587	17	0	.	253	66	40	100	0	.	4035	20	3635	21	3234	19	3347	24	1953	29	1403	30	5803	19	3871	21	5148	18	38309	6
	one visible damage	1134	19	0	.	39	82	109	100	0	.	904	23	1193	20	995	21	797	25	692	38	568	31	1089	21	1441	20	1778	16	10740	7
	two or more visible damages	375	25	0	.	27	100	53	100	0	.	801	29	541	29	413	28	443	29	300	38	638	35	973	35	747	29	921	21	6232	10
	dead or lying tree	0	0	0	.	0	0	0	0	0	.	0	0	36	71	6	100	0	0	158	81	90	60	78	47	0	0	125	39	493	31
	total	7096	15	0	.	320	65	202	100	0	.	5740	19	5405	19	4647	18	4587	22	3103	29	2698	27	7944	18	6059	19	7972	15	55774	6
1001-1200 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	12302	10	0	.	575	58	198	74	140	67	3494	23	7162	15	3920	18	2521	26	2075	29	1640	37	4041	19	2940	24	6511	17	47520	6
	one visible damage	2352	11	0	.	53	88	7	100	63	75	774	24	1604	18	1176	19	764	27	901	32	659	30	941	22	1154	29	1956	16	12403	6
	two or more visible damages	995	17	0	.	76	92	0	.	13	100	541	40	873	21	610	28	301	35	463	35	334	38	509	32	813	29	1128	20	6655	8
	dead or lying tree	0	0	0	.	0	0	0	0	0	.	15	100	37	100	61	76	18	100	71	100	0	0	139	66	18	100	169	60	527	32
	total	15649	9	0	.	704	56	205	73	216	63	4824	22	9675	15	5767	17	3604	23	3509	27	2633	31	5630	19	4926	21	9763	15	67105	5
801-1000 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	11430	11	1445	31	1824	29	2445	30	1679	37	1971	31	8843	15	7180	16	2171	25	1291	37	1007	29	2952	25	2055	27	6609	23	52901	6
	one visible damage	2786	15	245	38	241	40	421	33	310	49	374	36	1712	17	1375	18	629	37	534	36	691	29	756	30	749	26	2241	21	13064	7
	two or more visible damages	1506	17	96	39	163	44	96	38	192	41	174	33	803	24	756	24	139	37	251	55	657	30	498	38	472	27	1097	24	6901	8
	dead or lying tree	0	0	0	0	0	0	0	0	0	0	0	0	94	55	0	0	8	100	18	100	22	77	18	100	18	100	204	58	382	35
	total	15722	11	1786	30	2229	29	2961	29	2181	35	2518	28	11451	14	9310	15	2947	27	2094	34	2376	24	4225	23	3295	24	10151	20	73248	5
601-800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	10686	13	2142	23	5283	21	9513	14	8036	13	923	46	5872	16	3857	22	1526	28	520	60	884	45	1196	46	2132	25	4541	19	57111	5
	one visible damage	2038	14	580	28	1049	24	1585	19	1633	17	224	61	1441	22	1088	23	547	35	199	57	220	52	286	37	655	28	2513	22	14059	7
	two or more visible damages	841	18	339	49	344	26	738	20	761	19	25	100	759	27	476	25	140	38	96	58	86	60	210	49	232	41	1719	21	6767	8
	dead or lying tree	0	0	35	100	0	0	0	0	50	58	0	0	36	71	60	57	0	0	0	.	15	100	36	71	0	0	98	44	330	25
	total	13565	12	3095	22	6676	19	11835	13	10480	12	1173	45	8108	16	5482	20	2213	27	816	56	1206	46	1729	37	3019	23	8872	17	78268	5
=600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	5254	15	8058	14	4058	19	11589	11	17558	8	0	.	699	56	994	38	648	62	896	48	180	60	1289	36	35	100	6550	18	57810	5
	one visible damage	1372	20	1665	16	712	23	1580	14	3375	10	0	.	97	90	408	48	186	54	165	50	52	72	144	45	0	.	2227	16	11982	6
	two or more visible damages	607	22	652	18	405	24	725	18	1775	15	0	.	34	62	380	52	85	64	26	76	0	.	203	48	0	.	2061	19	6954	8
	dead or lying tree	62	53	90	44	0	0	0	0	97	41	0	.	0	0	21	74	15	100	0	0	0	0	18	100	0	.	323	41	627	24
	total	7294	15	10465	13	5176	18	13895	10	22806	7	0	.	830	58	1803	41	935	55	1086	46	233	58	1655	33	35	100	11162	15	77373	4
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	45940	4	11645	11	12380	12	23785	8	27414	6	14156	12	32715	7	21078	8	17901	9	9174	14	7180	15	33941	7	40903	6	45661	5	343872	2
	one visible damage	9908	6	2489	13	2155	15	3702	11	5381	8	3221	12	7798	8	5339	9	5193	10	3393	15	2800	14	9225	8	12915	7	15409	6	88928	2
	two or more visible damages	4420	8	1087	19	1016	16	1611	12	2742	11	2068	17	3938	11	2703	13	2852	13	1583	18	2096	17	5853	10	6432	8	9099	7	47500	3
	dead or lying tree	62	53	125	42	0	0	0	0	147	34	52	59	303	34	170	37	93	49	304	52	231	40	696	26	629	30	1132	20	3943	11
	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. 1198812. Birmensdorf, Swiss Federal Research Institute WSL

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