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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 number of stems
degree of damage · conifers and broadleaves
regional demarcation: economic region
unit: 1000 n
evaluation area: accessible forest without shrub forest NFI1-NFI5
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
degree of damage	conifers and broadleaves	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	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	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	broadleaves	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	indeterminable	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	.
no damage	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	23342	6	3419	18	4996	17	13946	10	11930	10	8106	14	22475	9	11919	10	9825	11	5215	17	3843	19	23367	8	28970	7	13060	11	184413	2
	broadleaves	21812	6	8212	11	7081	14	9594	10	14817	7	4011	17	8771	11	7740	12	5947	14	2349	23	2680	21	6570	14	4225	18	26197	8	130005	3
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	45154	4	11632	11	12076	12	23540	8	26746	6	12117	12	31246	7	19659	9	15771	10	7564	16	6524	16	29937	7	33196	7	39257	6	314419	2
slight damage	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	2295	11	482	24	612	26	1520	19	1952	15	1722	18	2659	12	1395	15	2095	13	1266	20	838	23	5022	11	7662	9	2378	13	31899	4
	broadleaves	2166	13	473	19	479	25	601	21	984	14	356	35	1092	16	945	17	870	20	193	42	369	24	737	25	609	24	3269	13	13141	5
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	4461	8	955	16	1090	20	2121	15	2936	11	2079	17	3751	10	2340	11	2965	12	1459	19	1207	18	5759	10	8270	8	5647	9	45040	3
moderate damage	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	1835	12	300	27	305	24	476	20	930	15	754	19	1573	13	1221	16	897	20	586	23	495	22	1785	12	2499	10	1394	16	15049	4
	broadleaves	2557	11	832	21	450	23	885	17	1102	13	257	47	1657	16	1180	19	901	22	631	27	676	23	847	21	709	21	4111	9	16796	4
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	4392	8	1132	19	755	18	1361	13	2032	10	1011	19	3230	10	2401	13	1797	15	1218	20	1171	17	2632	11	3208	9	5505	8	31845	3
severe damage	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	1491	12	62	45	224	28	436	18	442	17	482	20	1395	15	690	16	663	17	406	31	311	24	1448	13	2002	11	1108	18	11160	4
	broadleaves	2088	13	767	17	802	25	586	19	1443	13	320	33	1379	23	961	16	570	20	338	40	394	26	941	24	746	22	5199	11	16534	5
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	3579	9	829	17	1026	20	1022	15	1885	11	802	19	2774	14	1651	12	1232	14	743	26	705	19	2389	12	2748	10	6307	9	27693	3
very severe damage	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	486	18	49	54	61	45	159	28	176	26	168	33	396	32	288	24	290	27	181	51	210	32	917	20	1040	21	254	23	4674	8
	broadleaves	928	15	460	24	148	33	306	22	880	16	196	41	726	22	610	20	262	28	157	41	516	26	688	25	420	26	2924	11	9222	6
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	1414	12	509	23	209	27	466	19	1056	14	364	27	1122	18	899	16	552	19	339	33	726	21	1605	17	1459	17	3177	11	13896	5
dead	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	4095	10	696	25	577	26	1083	16	1248	16	2507	17	4559	14	3347	17	3385	16	1143	22	1046	23	6916	11	6954	11	2426	14	39981	4
	broadleaves	3288	12	1311	19	1079	23	619	21	1429	18	727	26	1802	16	1778	18	1204	21	444	39	1253	27	1642	18	1252	22	9202	9	27030	5
	indeterminable	54	74	0	.	0	.	0	.	17	100	0	.	17	100	0	.	15	100	0	.	0	.	18	100	15	100	0	.	137	40
	total	7437	8	2007	16	1656	18	1702	14	2693	12	3234	15	6379	11	5125	13	4605	13	1587	20	2299	19	8577	10	8222	10	11627	8	67148	3
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	33544	5	5009	15	6775	16	17620	10	16678	9	13739	13	33058	8	18860	9	17154	10	8797	16	6743	17	39455	8	49127	6	20619	9	287176	2
	broadleaves	32840	6	12055	11	10038	13	12592	9	20654	7	5867	16	15427	9	13215	11	9753	13	4112	21	5889	17	11425	12	7961	16	50901	6	212728	2
	indeterminable	54	74	0	.	0	.	0	.	17	100	0	.	17	100	0	.	15	100	0	.	0	.	18	100	15	100	0	.	137	40
	total	66437	4	17064	10	16813	11	30212	7	37348	6	19606	11	48502	6	32075	8	26922	9	12909	14	12631	14	50898	7	57103	6	71520	5	500040	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. 1258746. Birmensdorf, Swiss Federal Research Institute WSL

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