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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 NFI1-NFI5
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	4752	7	2890	9	1288	13	1731	13	2182	10	714	15	13556	4
	broadleaves	5388	5	1750	10	1167	13	756	14	515	19	2983	8	12559	4
	indeterminable	0	0	0	0	0	.	0	.	0	.	0	.	0	0
	total	10140	4	4640	7	2455	10	2487	10	2697	9	3697	7	26115	3
21-30 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	9337	6	5725	8	3509	11	3682	11	4404	9	1903	13	28561	3
	broadleaves	9588	5	3604	10	2840	12	903	17	673	22	5033	9	22642	4
	indeterminable	0	0	0	.	0	.	0	0	0	.	0	.	0	0
	total	18926	4	9329	6	6349	9	4586	10	5077	9	6937	7	51203	2
31-40 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	12541	6	9363	7	5913	10	4997	10	6825	8	3483	14	43123	3
	broadleaves	13841	5	4042	10	3800	11	537	23	443	19	3846	9	26509	3
	indeterminable	0	0	0	0	0	.	0	.	0	0	0	.	0	0
	total	26382	4	13406	6	9713	8	5534	9	7268	8	7329	8	69632	2
41-50 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	16510	5	12073	7	7090	9	5626	10	8850	8	3945	12	54094	3
	broadleaves	15095	5	3715	11	4126	11	311	33	442	30	2801	10	26491	4
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	31604	3	15788	6	11216	8	5937	10	9293	7	6746	7	80585	2
51-60 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	15829	5	12386	7	8454	9	5299	11	7868	8	4072	12	53908	3
	broadleaves	13364	5	3079	13	2521	14	163	48	375	30	1474	15	20975	4
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	29193	3	15465	6	10974	8	5462	10	8243	8	5545	10	74883	2
61-70 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	10864	7	8293	9	5612	12	2971	14	4884	11	2214	13	34838	4
	broadleaves	6242	8	1177	24	1186	22	108	53	219	36	788	21	9721	7
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	17106	5	9470	8	6799	11	3079	14	5103	11	3002	11	44559	3
71-80 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	5902	10	4588	11	4087	14	1904	20	2456	15	1583	21	20521	5
	broadleaves	2615	14	748	26	316	55	30	100	161	56	365	27	4235	11
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	8517	8	5336	10	4403	14	1934	19	2617	14	1948	17	24755	5
81-90 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	2887	15	1634	20	1058	23	723	29	1287	23	654	38	8243	9
	broadleaves	644	31	44	100	411	37	0	0	0	.	325	32	1423	19
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	3531	14	1678	20	1469	20	723	29	1287	23	978	27	9667	8
91-100 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	634	32	399	38	414	38	382	34	422	35	357	45	2608	15
	broadleaves	489	37	0	.	80	76	29	100	0	.	145	59	744	28
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	1124	24	399	38	494	34	412	32	422	35	502	36	3352	13
>100 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	410	45	347	50	218	51	103	73	312	46	314	59	1705	22
	broadleaves	260	79	0	.	0	.	0	.	0	.	374	60	633	48
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	670	41	347	50	218	51	103	73	312	46	687	42	2338	20
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	79666	3	57698	5	37643	7	27418	7	39492	6	19239	9	261157	2
	broadleaves	67526	3	18159	8	16448	8	2838	15	2828	17	18132	6	125932	2
	indeterminable	0	0	0	0	0	.	0	0	0	0	0	.	0	0
	total	147193	2	75857	4	54090	6	30257	7	42320	6	37372	5	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. 1353900. Birmensdorf, Swiss Federal Research Institute WSL

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