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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
total number of stems
altitudinal vegetation belts (NaiS, 3 classes) · diameter at breast height (10 classes)
regional demarcation: biogeographical region
unit: 1000 n
evaluation area: accessible forest without shrub forest NFI4/NFI5
grid: 1.4 km grid, subgrids 1-5
state 2018/26
		biogeographical region
		Jura		Plateau		Northern Alps		Western Central-Alps		Eastern Central-Alps		Southern Alps		Switzerland
altitudinal vegetation belts (NaiS, 3 classes)	diameter at breast height (10 classes)	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	.
	12-20 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	21-30 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	31-40 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	41-50 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	51-60 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	61-70 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	71-80 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	81-90 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	91-100 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	>100 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	.	0	.	0	.	0	.	0	.	0	.	0	.
subalpine	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	50	100	0	.	6822	17	7505	13	13415	11	6176	15	33968	7
	21-30 cm	67	100	0	.	4005	16	4071	14	7235	11	3645	15	19023	7
	31-40 cm	64	100	0	.	2782	17	2686	14	4681	10	1834	15	12047	7
	41-50 cm	33	100	0	.	1753	14	1717	15	2914	10	981	17	7399	6
	51-60 cm	27	100	0	.	709	17	905	15	1558	11	657	17	3856	7
	61-70 cm	7	100	0	.	342	20	488	19	574	16	187	22	1597	9
	71-80 cm	0	.	0	.	207	21	191	28	234	20	92	29	724	12
	81-90 cm	0	.	0	.	36	45	78	40	122	31	113	33	349	18
	91-100 cm	0	.	0	.	16	71	36	45	35	53	15	71	102	28
	>100 cm	0	.	0	.	14	71	7	100	28	50	7	100	57	35
	total	247	100	0	.	16684	14	17685	11	30796	9	13708	12	79120	5
montane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	26382	6	12914	11	55183	5	14123	11	16376	9	18599	9	143578	3
	21-30 cm	14918	6	7493	10	32273	5	7996	12	9912	9	10344	9	82936	3
	31-40 cm	10263	6	4685	10	19978	4	3925	12	5066	9	5277	10	49193	3
	41-50 cm	6504	5	3372	9	12221	4	2019	12	3222	9	2648	9	29985	3
	51-60 cm	3404	6	2373	9	7693	4	1150	13	1948	10	1500	17	18069	3
	61-70 cm	1311	10	912	12	3507	6	346	19	783	13	645	13	7505	4
	71-80 cm	461	14	498	15	1520	8	163	28	314	18	305	20	3262	6
	81-90 cm	97	31	220	20	341	16	54	38	118	24	143	27	973	9
	91-100 cm	44	41	43	46	131	24	37	45	31	51	58	38	343	15
	>100 cm	28	50	7	100	50	38	7	100	16	71	32	59	142	24
	total	63414	4	32517	8	132899	3	29820	10	37787	8	39551	8	335987	2
hyperinsubric, colline, submontane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	8646	13	30696	6	4589	20	3022	27	726	37	17913	10	65590	5
	21-30 cm	4297	12	15323	6	2565	20	1091	27	491	40	9139	9	32904	4
	31-40 cm	2648	13	8384	6	1314	19	407	29	208	45	3347	11	16309	5
	41-50 cm	1578	12	5734	6	668	21	135	35	116	40	1395	12	9626	5
	51-60 cm	757	14	3582	6	385	21	59	66	87	42	530	17	5400	5
	61-70 cm	331	19	1510	8	141	32	0	.	6	100	191	20	2179	7
	71-80 cm	85	31	640	12	47	42	0	.	6	100	127	29	906	10
	81-90 cm	7	100	215	19	28	58	0	.	0	.	53	47	302	17
	91-100 cm	0	.	61	33	0	.	7	100	7	100	38	60	113	28
	>100 cm	0	.	58	44	0	.	0	.	0	.	50	51	108	33
	total	18349	10	66203	4	9735	17	4721	24	1647	36	32782	8	133437	3
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	35078	5	43610	5	66593	4	24650	8	30517	7	42688	6	243136	2
	21-30 cm	19282	5	22816	5	38843	4	13157	9	17637	7	23127	5	134863	2
	31-40 cm	12975	5	13069	5	24073	4	7018	8	9955	6	10458	6	77548	2
	41-50 cm	8116	4	9106	4	14641	4	3871	9	6252	6	5024	6	47010	2
	51-60 cm	4188	5	5955	5	8786	4	2114	9	3593	7	2688	10	27325	2
	61-70 cm	1649	8	2422	6	3990	6	834	13	1363	10	1022	9	11281	3
	71-80 cm	546	12	1139	9	1775	8	355	20	554	13	524	14	4892	4
	81-90 cm	104	30	435	13	404	15	132	28	240	20	309	19	1624	7
	91-100 cm	44	41	103	27	148	22	80	30	73	35	110	30	558	12
	>100 cm	28	50	65	40	64	33	14	71	44	41	90	37	306	17
	total	82010	3	98720	3	159318	3	52226	7	70230	5	86040	4	548544	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. 1318930. Birmensdorf, Swiss Federal Research Institute WSL

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