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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.

NFI2
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
state 1993/95
		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	.	105	73	389	57	0	.	576	42	112	71	47	100	5485	13	9745	9	1953	18	18412	7
	one visible damage	0	.	0	.	0	.	0	.	0	.	50	83	58	56	0	.	98	41	9	100	10	100	1772	13	2469	10	459	21	4926	7
	two or more visible damages	0	.	0	.	0	.	0	.	0	.	4	100	49	71	0	.	42	51	23	100	0	.	519	18	368	20	158	25	1162	12
	dead or lying tree	0	.	0	.	0	.	0	.	0	.	0	.	0	0	0	.	0	0	11	100	0	.	45	57	268	47	57	62	382	35
	total	0	.	0	.	0	.	0	.	0	.	160	76	495	54	0	.	716	39	155	75	58	100	7821	11	12850	9	2627	17	24881	6
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	.	769	39	1966	29	240	71	1994	22	383	53	767	34	5933	14	8739	10	3480	15	24270	6
	one visible damage	0	.	0	.	0	.	0	.	0	.	222	39	366	27	29	71	547	27	84	55	263	37	2125	15	1975	12	782	17	6392	7
	two or more visible damages	0	.	0	.	0	.	0	.	0	.	61	62	45	57	14	76	300	42	36	66	42	47	566	18	649	19	214	24	1927	11
	dead or lying tree	0	.	0	.	0	.	0	.	0	.	0	0	14	100	21	100	0	0	0	0	0	0	64	68	46	47	29	58	173	33
	total	0	.	0	.	0	.	0	.	0	.	1052	39	2391	27	304	71	2841	21	503	46	1072	33	8687	13	11409	10	4504	14	32763	6
1401-1600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	693	28	0	.	347	45	0	.	0	.	2828	22	4136	18	1209	28	3456	18	815	33	820	33	4666	13	7411	13	5195	13	31576	6
	one visible damage	197	32	0	.	76	43	0	.	0	.	844	25	809	19	369	40	1100	17	263	30	231	30	1480	14	1625	13	1167	15	8161	6
	two or more visible damages	47	51	0	.	18	72	0	.	0	.	139	37	162	31	68	43	501	24	98	38	82	32	549	18	446	18	303	23	2411	9
	dead or lying tree	0	0	0	.	0	0	0	.	0	.	15	100	40	90	0	0	31	75	0	0	0	0	122	35	31	58	66	46	305	24
	total	937	26	0	.	441	43	0	.	0	.	3826	21	5147	17	1645	29	5088	16	1176	30	1132	30	6817	12	9513	12	6730	12	42452	5
1201-1400 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	5532	11	0	.	253	54	80	100	0	.	4988	17	4552	14	3335	15	3727	17	1937	25	1886	24	5050	15	4627	14	6111	13	42076	5
	one visible damage	1316	15	0	.	18	100	33	100	0	.	1390	22	1306	17	1107	18	884	19	572	26	571	25	1445	16	1386	17	1344	16	11371	6
	two or more visible damages	362	21	0	.	12	75	0	.	0	.	514	35	596	22	388	28	405	40	222	34	221	48	452	25	393	22	360	20	3925	9
	dead or lying tree	0	0	0	.	0	0	0	.	0	.	0	0	28	73	41	62	0	0	40	62	35	71	61	46	0	0	4	100	209	27
	total	7209	10	0	.	283	53	113	100	0	.	6892	16	6481	13	4870	15	5016	16	2770	24	2713	22	7007	14	6407	13	7819	12	57582	4
1001-1200 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	14373	7	38	100	280	43	113	73	299	45	4392	17	6808	11	6230	13	2582	20	1796	24	2107	30	3500	17	3461	16	7518	12	53498	4
	one visible damage	3007	9	10	100	111	43	46	66	84	71	962	20	2174	13	1557	16	738	22	577	27	587	29	1191	21	1150	23	1475	13	13669	5
	two or more visible damages	740	14	10	100	15	78	0	.	14	77	298	25	860	18	422	21	257	32	154	31	255	29	400	28	442	26	585	19	4451	7
	dead or lying tree	25	61	0	0	0	0	0	.	0	.	0	0	30	76	9	100	28	58	40	79	10	100	20	71	31	58	97	44	291	23
	total	18145	7	57	100	405	41	159	67	397	46	5652	16	9872	11	8217	13	3605	18	2567	23	2959	27	5112	16	5084	16	9675	11	71908	4
801-1000 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	11666	9	1547	25	2639	21	1683	27	1310	27	3149	21	8916	10	8872	12	2062	28	1835	27	2338	24	3402	18	2523	19	5796	14	57737	4
	one visible damage	3380	9	320	33	436	25	356	27	429	30	628	23	2608	14	1902	16	588	25	665	30	793	23	998	23	705	20	1494	17	15302	5
	two or more visible damages	1456	15	165	34	48	45	113	34	80	39	159	31	987	18	526	21	153	36	175	42	649	25	391	24	265	32	651	19	5819	7
	dead or lying tree	19	71	0	0	0	0	0	0	0	0	0	0	43	51	4	100	9	100	0	0	10	100	10	100	63	54	34	73	192	27
	total	16520	8	2032	25	3123	20	2152	25	1819	26	3936	20	12554	10	11304	12	2812	25	2675	25	3790	21	4801	17	3556	17	7975	13	79050	4
601-800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	12119	8	3577	16	7454	12	8619	10	11343	10	1086	34	6033	13	5629	14	1916	27	379	39	1150	35	1525	23	1827	23	5418	14	68075	4
	one visible damage	3037	10	819	22	1499	14	1564	12	1694	11	96	56	1451	16	859	16	341	47	264	43	372	34	543	26	389	24	1692	17	14620	5
	two or more visible damages	891	15	235	36	364	21	350	20	395	19	43	56	528	21	257	32	34	64	134	42	161	36	235	29	135	56	1274	18	5037	7
	dead or lying tree	0	0	0	0	20	71	10	100	40	50	0	0	0	0	12	100	0	0	0	0	9	100	36	63	41	91	10	100	178	30
	total	16048	8	4630	15	9336	11	10542	10	13473	9	1225	33	8012	12	6756	14	2292	26	777	36	1693	32	2339	21	2392	21	8394	13	87910	3
=600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	7070	12	9875	10	7360	13	15339	9	26134	6	0	.	1474	33	2491	25	648	47	683	41	154	66	1142	32	298	54	7383	12	80054	3
	one visible damage	1589	15	1559	12	1057	19	2502	10	3576	8	0	.	156	38	592	39	108	51	303	41	21	68	405	44	19	82	2096	14	13981	5
	two or more visible damages	563	23	309	26	158	46	846	17	871	14	0	.	70	48	100	65	20	70	60	48	0	.	56	52	0	.	1187	17	4240	8
	dead or lying tree	9	100	22	61	83	79	14	76	31	100	0	.	0	0	0	0	0	0	10	100	0	.	0	0	0	0	39	84	209	40
	total	9232	11	11766	9	8658	12	18701	8	30612	5	0	.	1700	32	3183	25	776	45	1056	36	175	66	1603	31	317	54	10705	11	98484	3
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	51454	3	15037	7	18333	7	25835	6	39087	4	17316	8	34274	5	28004	6	16963	8	7940	12	9270	12	30703	5	38632	5	42853	4	375699	1
	one visible damage	12525	4	2707	10	3195	10	4501	7	5783	6	4194	11	8928	6	6414	8	4402	9	2737	13	2848	12	9960	6	9718	5	10508	5	88421	2
	two or more visible damages	4059	7	719	18	615	17	1309	12	1360	11	1218	17	3296	9	1775	11	1712	15	902	15	1410	15	3167	8	2698	9	4733	7	28973	3
	dead or lying tree	53	42	22	61	103	65	24	61	71	52	15	100	155	35	87	42	68	43	101	42	65	47	357	22	480	29	336	23	1938	11
	total	68091	3	18485	7	22246	7	31668	6	46301	4	22743	8	46653	5	36280	6	23145	7	11680	11	13593	11	44187	5	51528	4	58430	3	495030	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. 1198720. Birmensdorf, Swiss Federal Research Institute WSL

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