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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
conifers and broadleaves · diameter at breast height (10 classes)
regional demarcation: biogeographical region
unit: 1000 n
evaluation area: accessible forest without shrub forest
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
conifers and broadleaves	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	.
conifers	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	13354	8	17838	8	31182	6	13352	9	21495	8	9723	11	106944	3
	21-30 cm	7859	7	10415	8	19978	6	9080	10	13499	8	6607	10	67439	3
	31-40 cm	5438	8	6016	8	14383	5	5674	10	8044	7	4019	10	43574	3
	41-50 cm	3905	6	4527	7	9939	5	3254	9	5346	7	2545	9	29516	2
	51-60 cm	2428	7	2941	7	6403	5	1891	10	2990	7	1684	11	18337	3
	61-70 cm	1136	11	1380	9	3146	7	742	14	1222	10	655	12	8280	4
	71-80 cm	435	14	682	12	1486	8	333	21	502	13	348	18	3786	5
	81-90 cm	111	29	327	16	357	15	118	29	225	21	198	25	1336	8
	91-100 cm	37	45	34	45	135	24	66	33	73	35	65	36	409	14
	>100 cm	33	51	21	58	64	33	14	71	44	41	40	52	217	19
	total	34736	5	44181	5	87073	4	34522	8	53440	6	25885	8	279837	2
broadleaves	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	16805	7	21858	6	23917	6	7146	13	4897	15	25066	7	99690	3
	21-30 cm	9246	7	10753	6	13836	7	2682	15	2384	18	14035	7	52937	3
	31-40 cm	6186	7	6450	6	7347	7	596	22	904	17	5392	9	26876	3
	41-50 cm	3744	7	4204	6	3569	7	208	32	412	22	2025	9	14163	3
	51-60 cm	1548	9	2814	6	1758	9	30	50	224	24	772	14	7146	4
	61-70 cm	413	15	979	10	555	16	15	71	65	34	265	19	2292	7
	71-80 cm	90	31	387	15	202	21	0	.	32	52	124	27	834	10
	81-90 cm	0	.	95	28	50	41	0	0	8	100	82	32	235	18
	91-100 cm	0	.	82	32	13	71	7	100	0	.	38	60	140	26
	>100 cm	0	.	44	53	0	.	0	.	0	.	50	51	94	37
	total	38034	5	47665	4	51248	5	10685	13	8926	14	47849	6	204406	2
indeterminable	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	0	0	0	.	0	0	0	.	0	.	0	.	0	0
	21-30 cm	0	0	0	.	0	.	0	0	0	.	0	.	0	0
	31-40 cm	0	0	0	0	0	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	0	0	0	0	.	0	0
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	30159	5	39695	5	55099	5	20498	8	26393	7	34789	6	206634	2
	21-30 cm	17106	5	21168	5	33814	4	11762	9	15883	7	20643	5	120376	2
	31-40 cm	11625	5	12466	5	21730	4	6270	9	8948	7	9411	7	70450	2
	41-50 cm	7649	4	8732	4	13508	4	3462	9	5758	6	4570	6	43678	2
	51-60 cm	3976	5	5755	5	8160	4	1921	10	3214	7	2457	10	25483	2
	61-70 cm	1549	9	2359	6	3701	6	756	14	1287	10	920	10	10572	3
	71-80 cm	525	13	1069	9	1688	8	333	21	533	13	472	14	4620	5
	81-90 cm	111	29	422	14	407	14	118	29	233	20	280	20	1571	8
	91-100 cm	37	45	116	26	148	22	73	32	73	35	102	32	549	12
	>100 cm	33	51	65	40	64	33	14	71	44	41	90	37	311	17
	total	72770	3	91846	3	138321	3	45207	7	62366	5	73733	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. 1348733. Birmensdorf, Swiss Federal Research Institute WSL

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