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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)
diameter at breast height (10 classes) · conifers and broadleaves
regional demarcation: protection forest region
unit: 1000 m³
evaluation area: accessible forest without shrub forest
grid: 1.4 km grid, subgrids 1-5
state 2018/26
		protection forest region
		Jura + Plateau		Northwestern Alps		Northeastern Alps		Southwestern Alps		Southeastern Alps		Southern Alps		Switzerland
diameter at breast height (10 classes)	conifers and broadleaves	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%
n/a	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	broadleaves	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	.	0	.	0	.	0	.	0	.	0	.	0	.
12-20 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	4786	7	3193	9	1435	11	1957	12	2679	9	974	12	15024	4
	broadleaves	5522	5	2001	10	1406	12	950	12	633	17	3304	7	13817	3
	indeterminable	0	0	0	0	0	.	0	.	0	.	0	.	0	0
	total	10309	4	5194	7	2841	9	2907	9	3312	8	4278	6	28841	3
21-30 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	9449	6	6442	7	3904	10	4203	10	5680	8	2444	11	32122	3
	broadleaves	9793	5	3883	10	3155	11	1162	16	804	20	5587	8	24386	3
	indeterminable	0	0	0	.	0	.	0	0	0	.	0	.	0	0
	total	19242	4	10325	6	7060	8	5365	9	6485	8	8031	6	56508	2
31-40 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	12677	6	10344	7	6672	9	5627	10	7698	8	3955	12	46974	3
	broadleaves	14035	5	4242	10	4045	10	715	20	502	18	4175	9	27714	3
	indeterminable	0	0	0	0	0	.	0	.	0	0	0	.	0	0
	total	26712	4	14585	5	10718	7	6342	9	8200	7	8131	8	74688	2
41-50 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	16853	5	13091	6	8112	9	6083	9	9801	7	4355	11	58296	3
	broadleaves	15438	4	4051	11	4277	11	322	32	510	28	2987	10	27586	4
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	32292	3	17142	6	12389	7	6405	9	10311	7	7343	7	85882	2
51-60 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	16244	5	13171	7	9166	8	5558	10	8484	8	4390	12	57013	3
	broadleaves	13796	5	3193	13	2682	13	204	43	414	28	1536	15	21824	4
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	30039	3	16364	6	11848	7	5762	10	8898	8	5926	9	78837	2
61-70 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	11012	7	8771	9	5966	11	3199	13	5223	11	2378	13	36548	4
	broadleaves	6660	8	1250	23	1249	22	108	53	273	35	813	21	10353	7
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	17672	5	10021	8	7215	10	3307	13	5496	10	3191	10	46901	3
71-80 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	6141	10	4875	11	4237	14	2071	19	2580	14	1717	19	21622	5
	broadleaves	2768	14	775	26	398	46	47	73	161	56	395	26	4544	11
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	8910	8	5650	10	4635	13	2118	18	2741	14	2112	16	26166	5
81-90 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	2951	15	1736	20	1339	21	798	27	1438	21	966	29	9228	8
	broadleaves	644	31	44	100	411	37	0	0	0	.	325	32	1423	19
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	3594	14	1780	19	1750	18	798	27	1438	21	1291	23	10652	8
91-100 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	634	32	585	32	489	36	409	32	495	34	456	39	3069	14
	broadleaves	657	34	0	.	80	76	29	100	0	.	145	59	911	27
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	1291	23	585	32	569	33	439	31	495	34	601	32	3980	12
>100 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	522	41	347	50	269	45	103	73	448	39	314	59	2003	20
	broadleaves	416	56	0	.	0	.	0	.	0	.	411	55	827	39
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	938	34	347	50	269	45	103	73	448	39	725	40	2830	18
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	81269	3	62554	5	41590	7	30010	7	44527	5	21949	8	281899	2
	broadleaves	69729	3	19439	7	17704	8	3538	14	3297	15	19678	5	133386	2
	indeterminable	0	0	0	0	0	.	0	0	0	0	0	.	0	0
	total	150998	2	81993	4	59294	6	33548	6	47824	5	41627	4	415285	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. 1353913. Birmensdorf, Swiss Federal Research Institute WSL

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