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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)
aspect (9 classes)
regional demarcation: canton
unit: 1000 m³
evaluation area: accessible forest without shrub forest NFI1-NFI5
grid: 1.4 km grid, subgrids 1-5
state 2018/26
	canton
	AG		AI		AR		BE		BL/BS		FR		GE		GL		GR		JU		LU		NE		NW		OW		SG		SH		SO		SZ		TG		TI		UR		VD		VS		ZG		ZH		Switzerland
aspect (9 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	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%
n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
indetermined	2737	21	0	.	0	.	8485	14	940	44	1863	30	475	55	0	0	806	51	1211	37	2520	26	1479	33	0	.	197	81	1509	47	913	49	1152	37	223	71	4028	21	175	97	0	.	5013	18	123	72	336	63	4506	18	38693	6
N	2056	30	558	74	433	72	10608	13	841	42	2680	27	0	.	739	47	7254	16	3568	24	1561	31	1405	38	1035	52	681	50	3711	25	769	47	2197	26	1179	42	1038	40	4596	18	978	43	1671	29	4378	18	0	0	2908	25	56845	5
NE	916	32	0	.	868	55	5297	21	575	72	649	54	0	.	540	59	6903	15	401	58	3459	25	231	64	274	100	476	52	3173	27	350	71	472	51	1289	49	1115	35	3078	22	949	49	1017	36	1345	33	38	100	2180	26	35595	7
E	1026	39	322	91	981	65	5147	21	276	52	990	41	0	.	475	51	7932	15	682	58	2431	29	876	41	460	58	782	46	3339	28	338	76	679	53	381	65	651	62	4289	17	920	52	3026	25	4452	20	222	100	1507	34	42186	6
SE	1248	40	1251	44	412	78	8983	15	737	40	2482	28	0	.	321	71	4831	20	516	62	1840	31	3161	26	302	71	1153	44	2561	28	358	59	1915	29	1304	40	482	66	3584	19	632	77	7017	16	2870	23	0	.	1178	40	49139	6
S	592	44	880	71	184	100	6679	16	456	63	1880	32	0	.	1799	41	4873	19	1033	39	1100	52	1076	40	0	.	630	51	1398	46	397	61	1686	28	1348	35	538	57	2193	22	527	66	2792	27	3096	26	223	77	1496	37	36875	7
SW	820	44	0	.	198	100	4248	21	213	68	989	45	0	.	482	61	5215	18	1281	43	1545	40	639	52	42	100	1238	54	1820	35	209	75	33	100	1188	39	426	58	4162	20	479	62	1489	31	1780	33	148	73	700	39	29344	8
W	976	38	152	100	506	77	4662	20	770	47	1176	48	0	.	646	51	7222	15	992	54	1868	37	242	76	522	73	963	52	2194	34	1034	39	653	60	995	46	399	73	2485	22	1070	43	2550	27	5020	19	270	100	1452	41	38821	7
NW	1563	34	357	100	1168	46	10118	14	501	53	3641	27	0	.	422	50	6311	16	2278	29	2594	26	2253	29	528	66	1039	48	3289	25	375	63	803	41	2354	29	171	62	3782	37	1203	37	6157	19	7192	17	307	71	1181	34	59590	6
total	11935	11	3520	29	4750	24	64227	5	5310	17	16349	11	475	55	5426	19	51347	5	11963	12	18918	10	11363	11	3164	27	7159	18	22996	10	4744	18	9590	12	10261	14	8847	14	28344	7	6758	18	30732	7	30257	7	1544	33	17110	9	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. 1195681. Birmensdorf, Swiss Federal Research Institute WSL

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