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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
altitudinal vegetation belts (NaiS; 6 classes) · tree state (living/dead)
regional demarcation: economic region
unit: 1000 n
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
altitudinal vegetation belts (NaiS; 6 classes)	tree state (living/dead)	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	.
	living	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	dead	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	.
upper subalpine	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	living	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	4309	19	8509	15	4291	21	17110	10
	dead	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	531	25	1378	24	370	33	2279	17
	total	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	4840	19	9887	15	4661	21	19388	10
subalpine	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	living	0	.	0	.	137	100	0	.	0	.	1199	49	5003	27	322	92	4618	20	1984	34	1818	37	11784	13	18562	11	7559	15	52987	6
	dead	0	.	0	.	110	100	0	.	0	.	95	48	912	42	127	100	1253	31	219	48	133	48	2829	19	3167	16	918	27	9764	10
	total	0	.	0	.	247	100	0	.	0	.	1294	47	5915	27	449	94	5871	20	2203	33	1951	36	14613	13	21729	11	8478	15	62751	6
high-montane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	living	648	64	0	.	240	75	0	.	0	.	5342	24	4907	20	2341	30	8632	15	3844	25	1530	34	23828	10	26804	9	12161	12	90278	5
	dead	15	71	0	.	23	100	0	.	0	.	1050	30	966	29	669	51	1709	21	557	33	386	48	4271	15	4215	14	2241	16	16103	7
	total	664	64	0	.	264	70	0	.	0	.	6392	24	5873	20	3010	29	10341	15	4401	24	1916	33	28100	10	31020	9	14402	12	106381	5
lower and upper montane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	living	48599	5	4519	18	4822	19	9707	15	11851	12	12786	13	31108	7	24262	8	10732	13	7093	19	8544	15	5002	21	5680	18	21575	11	206279	3
	dead	5844	9	597	31	459	29	723	25	953	21	2265	18	4648	13	4109	13	1641	19	1093	26	2128	21	883	27	746	23	2460	17	28549	5
	total	54443	5	5115	19	5280	18	10430	15	12804	12	15051	12	35756	7	28371	8	12373	13	8186	19	10672	15	5885	21	6426	18	24035	12	234828	3
submontane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	living	10913	13	10827	12	9486	15	19391	9	23515	7	170	100	3735	24	2365	36	2058	33	1533	42	415	86	1086	43	1233	36	0	.	86728	4
	dead	1595	18	1410	19	908	25	1076	17	1742	16	21	100	238	38	405	42	400	35	82	63	111	71	273	48	78	72	0	.	8338	7
	total	12508	13	12237	12	10394	15	20467	9	25256	7	191	100	3973	24	2770	36	2457	32	1616	42	526	81	1359	43	1312	37	0	.	95066	4
hyperinsubric and colline	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	living	169	73	0	.	866	44	0	.	318	65	0	.	0	.	0	.	0	.	0	.	0	.	3706	24	89	100	25714	8	30862	8
	dead	17	100	0	.	217	46	0	.	14	71	0	.	0	.	0	.	0	.	0	.	0	.	959	29	0	.	6978	11	8185	10
	total	186	75	0	.	1083	42	0	.	332	65	0	.	0	.	0	.	0	.	0	.	0	.	4665	24	89	100	32692	8	39048	7
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	living	60329	4	15346	10	15551	11	29098	7	35684	6	19498	11	44753	6	29290	8	26039	8	14455	13	12307	13	49715	6	60878	5	71300	4	484244	1
	dead	7472	8	2007	16	1717	17	1799	14	2708	12	3431	15	6763	11	5310	13	5002	12	1951	18	2758	18	9747	9	9585	9	12967	7	73219	3
	total	67801	4	17353	10	17269	11	30897	7	38392	6	22929	11	51517	6	34600	8	31042	8	16406	13	15065	12	59462	6	70464	5	84268	4	557462	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. 1194660. Birmensdorf, Swiss Federal Research Institute WSL

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