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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 NFI1-NFI5
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	.	0	.	69	100	0	.	730	52	0	.	0	.	5152	17	8606	14	1706	27	16263	10
	one visible damage	0	.	0	.	0	.	0	.	0	.	0	.	7	100	0	.	229	50	0	.	0	.	1527	18	2837	15	512	34	5112	11
	two or more visible damages	0	.	0	.	0	.	0	.	0	.	0	.	66	100	0	.	88	55	0	.	0	.	1015	25	1112	20	384	34	2665	14
	dead or lying tree	0	.	0	.	0	.	0	.	0	.	0	.	0	0	0	.	0	0	0	.	0	.	104	71	346	48	0	0	450	40
	total	0	.	0	.	0	.	0	.	0	.	0	.	142	100	0	.	1047	48	0	.	0	.	7798	16	12901	13	2602	25	24491	9
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	.	764	51	2811	39	272	100	1719	27	262	48	1022	55	5806	19	6259	16	4120	19	23034	9
	one visible damage	0	.	0	.	0	.	0	.	0	.	203	59	489	34	0	.	658	31	255	47	101	46	1921	20	1748	18	989	21	6365	10
	two or more visible damages	0	.	0	.	0	.	0	.	0	.	126	61	297	53	0	.	393	42	137	69	14	71	866	21	1021	21	432	27	3287	12
	dead or lying tree	0	.	0	.	0	.	0	.	0	.	0	0	79	92	22	100	0	0	0	0	0	0	49	54	0	0	0	0	151	53
	total	0	.	0	.	0	.	0	.	0	.	1094	53	3677	36	294	100	2770	25	655	47	1137	52	8642	18	9027	15	5540	18	32836	9
1401-1600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	571	39	0	.	386	53	0	.	0	.	2195	37	2986	23	1513	36	3766	21	1556	37	826	36	5378	18	8388	15	5943	19	33509	7
	one visible damage	183	40	0	.	61	61	0	.	0	.	654	30	1076	21	267	47	964	23	470	36	276	39	1417	19	2051	16	1537	21	8956	8
	two or more visible damages	91	55	0	.	0	.	0	.	0	.	375	41	391	27	59	51	707	25	149	43	170	53	849	23	1265	19	590	22	4646	9
	dead or lying tree	0	0	0	.	0	0	0	.	0	.	37	72	0	0	0	0	18	100	0	0	35	71	181	65	53	58	18	100	341	38
	total	845	37	0	.	446	53	0	.	0	.	3260	31	4453	20	1840	36	5456	19	2174	36	1306	36	7826	17	11758	14	8088	18	47452	7
1201-1400 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	5032	16	0	.	207	78	0	.	0	.	3484	21	3462	22	2796	20	3028	25	1457	34	1126	35	5094	20	3397	22	4695	20	33778	7
	one visible damage	1126	19	0	.	39	82	0	.	0	.	683	23	1064	22	849	23	797	25	351	32	401	32	899	23	1328	21	1572	17	9109	7
	two or more visible damages	375	25	0	.	27	100	0	.	0	.	712	32	425	31	395	29	389	30	179	48	532	37	521	31	691	31	817	23	5062	10
	dead or lying tree	0	0	0	.	0	0	0	.	0	.	0	0	36	71	6	100	0	0	35	100	90	60	60	53	0	0	108	43	334	27
	total	6533	15	0	.	273	75	0	.	0	.	4879	20	4986	20	4046	19	4215	23	2022	33	2149	30	6573	19	5416	20	7191	17	48282	6
1001-1200 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	12295	10	0	.	575	58	198	74	140	67	2895	25	6595	15	3456	20	2334	27	1951	30	1640	37	3215	21	2226	29	5567	19	43088	6
	one visible damage	2315	12	0	.	53	88	7	100	63	75	551	24	1528	19	1003	21	667	29	758	35	628	31	761	24	692	34	1669	18	10695	7
	two or more visible damages	995	17	0	.	76	92	0	.	13	100	231	32	786	22	532	31	256	40	445	36	309	40	442	35	683	33	1002	22	5771	9
	dead or lying tree	0	0	0	.	0	0	0	0	0	.	15	100	37	100	61	76	18	100	0	0	0	0	122	74	18	100	43	71	314	37
	total	15604	9	0	.	704	56	205	73	216	63	3692	24	8946	14	5052	18	3275	25	3155	29	2577	32	4539	21	3619	26	8282	17	59867	5
801-1000 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	11227	11	1258	32	1671	30	2445	30	1317	43	1797	32	8467	15	6638	16	1958	26	969	44	886	32	2645	27	1959	28	5562	26	48799	6
	one visible damage	2786	15	214	42	241	40	421	33	188	59	322	39	1712	17	1280	19	440	31	411	42	453	30	715	31	732	26	2069	23	11984	7
	two or more visible damages	1472	17	76	46	163	44	96	38	138	42	156	35	803	24	517	24	115	40	226	61	442	34	450	41	398	28	985	26	6038	9
	dead or lying tree	0	0	0	0	0	0	0	0	0	0	0	0	94	55	0	0	8	100	0	0	22	77	18	100	18	100	188	63	348	38
	total	15486	11	1549	32	2076	31	2961	29	1642	40	2275	29	11076	14	8435	16	2520	26	1607	39	1803	26	3829	25	3107	25	8804	23	67170	6
601-800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	10625	13	2142	23	5283	21	9388	14	7951	13	923	46	5778	17	3857	22	1459	29	520	60	884	45	1137	48	2132	25	4497	20	56576	5
	one visible damage	1997	14	527	29	1049	24	1585	19	1633	17	224	61	1441	22	1088	23	509	38	199	57	220	52	269	38	655	28	2513	22	13911	7
	two or more visible damages	823	18	339	49	344	26	738	20	761	19	25	100	759	27	476	25	132	40	96	58	86	60	210	49	232	41	1697	22	6719	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	13445	12	3043	22	6676	19	11711	13	10396	12	1173	45	8014	16	5482	20	2100	29	816	56	1206	46	1652	39	3019	23	8805	17	77536	5
=600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	5135	16	8058	14	3914	19	11469	11	17200	8	0	.	699	56	994	38	648	62	763	56	102	74	1243	37	35	100	6220	18	56479	5
	one visible damage	1319	21	1665	16	676	24	1451	14	3335	10	0	.	97	90	408	48	186	54	104	54	52	72	98	47	0	.	2168	16	11558	6
	two or more visible damages	572	22	652	18	392	24	713	18	1768	15	0	.	34	62	380	52	85	64	26	76	0	.	103	48	0	.	1869	21	6595	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	7087	15	10465	13	4982	18	13633	11	22401	8	0	.	830	58	1803	41	935	55	893	54	154	71	1462	36	35	100	10580	15	75259	4
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	44884	4	11458	11	12036	12	23500	8	26609	6	12059	12	30867	7	19526	9	15642	10	7478	16	6486	16	29671	7	33001	7	38310	6	311526	2
	one visible damage	9727	6	2406	13	2119	15	3463	11	5219	8	2637	13	7414	8	4895	10	4451	11	2550	16	2132	15	7606	8	10043	7	13029	6	77689	2
	two or more visible damages	4328	8	1068	19	1002	16	1546	13	2681	11	1625	18	3561	11	2360	13	2166	14	1260	20	1554	19	4456	11	5402	9	7775	8	40782	3
	dead or lying tree	62	53	125	42	0	0	0	0	147	34	52	59	281	36	170	37	58	52	35	100	162	39	589	29	436	39	779	24	2895	12
	total	59000	4	15057	10	15157	11	28510	8	34655	6	16373	11	42123	6	26950	8	22317	9	11322	15	10333	14	42322	7	48881	6	59893	5	432892	2

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. 1198798. Birmensdorf, Swiss Federal Research Institute WSL

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