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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: production region
unit: 1000 n
evaluation area: accessible forest without shrub forest
grid: 1.4 km grid, subgrids 1-5
state 2018/26
		production region
		Jura		Plateau		Pre-Alps		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	±%
n/a	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	0	.	0	.	0	.	0	.	0	.
	one visible damage	0	.	0	.	0	.	0	.	0	.	0	.
	two or more visible damages	0	.	0	.	0	.	0	.	0	.	0	.
	dead or lying tree	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	.	0	.	0	.	0	.	0	.	0	.
>1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	0	.	566	89	18592	9	3932	17	23089	8
	one visible damage	0	.	0	.	22	75	6287	10	1582	25	7891	9
	two or more visible damages	0	.	0	.	66	100	2925	13	822	23	3813	11
	dead or lying tree	0	.	0	.	0	0	591	32	93	49	684	29
	total	0	.	0	.	654	81	28395	8	6428	16	35477	8
1601-1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	0	.	4217	29	19134	9	4947	17	28298	8
	one visible damage	0	.	0	.	780	27	6053	10	1207	20	8040	9
	two or more visible damages	0	.	0	.	523	35	3214	12	612	24	4349	10
	dead or lying tree	0	.	0	.	123	64	155	39	16	100	294	34
	total	0	.	0	.	5643	26	28556	9	6783	16	40982	7
1401-1600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	680	34	386	53	7347	16	22999	8	7423	17	38834	7
	one visible damage	225	35	61	61	2192	15	6366	11	1905	19	10749	8
	two or more visible damages	97	51	0	.	935	22	4059	11	740	19	5830	9
	dead or lying tree	0	0	0	0	37	72	465	34	102	52	605	28
	total	1002	33	446	53	10511	14	33889	8	10169	15	56017	6
1201-1400 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	5587	17	293	59	10904	11	16376	10	5148	18	38309	6
	one visible damage	1134	19	148	77	3092	12	4588	11	1778	16	10740	7
	two or more visible damages	375	25	80	74	1755	17	3101	16	921	21	6232	10
	dead or lying tree	0	0	0	0	42	62	326	44	125	39	493	31
	total	7096	15	522	56	15793	10	24391	9	7972	15	55774	6
1001-1200 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	12302	10	913	41	14576	10	13218	11	6511	17	47520	6
	one visible damage	2352	11	123	54	3554	11	4418	12	1956	16	12403	6
	two or more visible damages	995	17	89	79	2023	16	2420	15	1128	20	6655	8
	dead or lying tree	0	0	0	0	113	54	245	48	169	60	527	32
	total	15649	9	1125	39	20266	10	20302	10	9763	15	67105	5
801-1000 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	12875	10	5948	18	17994	10	9475	12	6609	23	52901	6
	one visible damage	3031	14	972	23	3461	11	3359	13	2241	21	13064	7
	two or more visible damages	1602	16	451	25	1732	15	2018	16	1097	24	6901	8
	dead or lying tree	0	0	0	0	94	55	84	43	204	58	382	35
	total	17508	10	7372	18	23280	9	14937	11	10151	20	73248	5
601-800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	12827	11	22832	8	10653	12	6258	16	4541	19	57111	5
	one visible damage	2618	12	4267	11	2754	15	1907	17	2513	22	14059	7
	two or more visible damages	1180	19	1843	12	1260	18	765	21	1719	21	6767	8
	dead or lying tree	35	100	50	58	96	44	52	58	98	44	330	25
	total	16660	10	28992	8	14763	11	8982	14	8872	17	78268	5
=600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	13312	10	33206	5	1693	32	3047	24	6550	18	57810	5
	one visible damage	3037	12	5667	7	504	43	547	27	2227	16	11982	6
	two or more visible damages	1259	14	2905	10	414	48	314	36	2061	19	6954	8
	dead or lying tree	152	34	97	41	21	74	34	71	323	41	627	24
	total	17759	9	41876	5	2633	34	3943	22	11162	15	77373	4
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	57584	3	63579	3	67949	4	109099	3	45661	5	343872	2
	one visible damage	12396	5	11238	5	16358	4	33527	4	15409	6	88928	2
	two or more visible damages	5507	7	5369	7	8708	7	18816	5	9099	7	47500	3
	dead or lying tree	186	33	147	34	525	24	1953	16	1132	20	3943	11
	total	75674	3	80333	3	93541	3	163395	2	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. 1198815. Birmensdorf, Swiss Federal Research Institute WSL

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