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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 wood volume (stemwood)
tree condition · diameter at breast height (≤ or >30 cm)
regional demarcation: economic region
unit: 1000 m³
evaluation area: accessible forest without shrub forest
grid: 1.4 km grid, subgrids 1-5
state 2018/26
		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
tree condition	diameter at breast height (≤ or >30 cm)	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	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	=30 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	>30 cm	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	.
standing dead	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	=30 cm	640	15	205	27	125	26	133	24	229	23	220	33	623	18	530	18	239	20	211	22	156	27	541	15	548	13	1074	11	5474	5
	>30 cm	2058	16	555	33	381	29	597	25	791	24	517	27	1648	16	1280	18	960	20	462	26	439	28	1124	15	993	20	1238	16	13041	5
	total	2698	13	759	27	506	26	730	21	1019	20	737	23	2271	13	1810	14	1198	17	673	21	595	23	1665	12	1541	14	2312	10	18514	4
standing living	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	=30 cm	10803	6	2753	11	3132	14	5770	10	7021	8	3482	15	8079	8	5369	10	3857	10	2464	15	1960	19	8175	8	9735	7	12137	5	84737	2
	>30 cm	43621	4	10903	11	12460	12	23425	8	30871	6	14808	10	33141	6	30011	7	18481	9	9572	15	9622	13	25235	7	38004	6	29209	6	329360	1
	total	54424	4	13656	10	15592	11	29195	7	37892	5	18289	10	41220	6	35380	7	22338	9	12036	13	11581	13	33409	7	47738	5	41346	4	414097	1
lying dead	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	=30 cm	720	13	182	23	144	27	199	25	288	18	367	21	562	14	468	21	443	20	129	26	254	21	854	11	870	13	877	11	6358	4
	>30 cm	899	17	540	28	260	35	460	25	614	23	1005	27	1840	17	651	22	1187	17	194	36	439	23	1858	13	2287	12	1384	16	13618	5
	total	1619	12	722	23	404	26	660	20	902	18	1372	22	2402	14	1120	17	1631	15	323	25	693	18	2713	10	3156	11	2261	12	19977	4
lying living	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	=30 cm	17	71	33	50	0	.	0	.	21	40	11	63	75	36	26	61	15	57	46	51	36	46	98	29	61	26	172	27	612	12
	>30 cm	26	74	67	62	0	.	0	.	76	100	0	.	41	74	172	45	4	100	0	.	17	72	41	51	24	72	109	36	576	23
	total	42	53	99	47	0	.	0	.	97	79	11	63	116	40	198	42	19	50	46	51	53	39	139	25	86	27	281	26	1188	14
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	=30 cm	12180	5	3173	11	3401	14	6103	10	7559	8	4080	14	9339	7	6394	10	4554	10	2851	14	2405	17	9668	8	11214	7	14261	5	97181	2
	>30 cm	46604	4	12064	10	13100	11	24482	8	32352	6	16329	10	36670	6	32114	7	20632	9	10227	14	10516	13	28258	7	41307	6	31940	5	356595	1
	total	58784	4	15236	9	16501	11	30585	7	39911	5	20409	10	46009	6	38508	7	25186	8	13078	13	12921	12	37926	6	52521	5	46201	4	453776	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. 1329421. Birmensdorf, Swiss Federal Research Institute WSL

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