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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.

NFI3
growing stock (stemwood)
forest type (17 classes)
regional demarcation: economic region
unit: 1000 m³
evaluation area: accessible forest without shrub forest
grid: 1.4-km grid
state 2004/06
	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
forest type (17 classes)	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	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
inaccessible forest	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
shrub forest	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
permanently unstocked forest area	1131	30	621	47	1187	42	1095	42	952	29	430	41	1504	30	1454	30	221	48	160	68	143	53	397	36	305	57	874	53	10475	11
temporarily unstocked forest area	85	89	6	100	108	75	159	52	252	43	350	45	241	35	208	43	290	49	100	81	82	95	99	59	795	31	166	70	2941	14
aisle, embankment	179	48	115	100	222	99	12	178	0	.	200	67	7	88	3	100	2	100	52	100	109	83	71	71	100	54	189	53	1262	27
permanently open stand	2133	24	5	100	148	64	11	100	28	71	394	37	996	22	481	35	1124	29	183	50	580	39	1278	22	2970	13	1604	16	11934	8
(nut) orchard, plantation	0	.	0	.	40	100	0	.	0	.	0	.	0	.	0	.	149	100	0	.	0	.	52	81	0	.	435	44	675	37
coppice forest	80	64	119	100	42	100	0	.	279	68	59	52	24	72	0	.	432	39	5	62	33	81	164	53	252	49	3333	13	4821	11
coppice with standards	199	57	91	100	438	44	0	.	403	43	0	.	0	.	0	.	22	100	71	89	0	.	0	.	55	75	1412	21	2691	16
selection type high forest	5664	12	69	100	320	48	976	32	363	42	2898	27	6199	12	853	33	2368	18	667	33	533	37	2875	14	5916	10	2843	14	32544	5
non-uniform high forest	2532	18	905	49	491	43	1140	32	3034	18	1372	30	2793	21	1021	37	1924	24	200	59	559	42	3446	17	2676	18	3843	13	25935	6
young growth/ thicket	699	32	634	30	360	37	524	31	930	23	88	68	458	35	187	53	365	48	128	60	254	46	339	31	795	23	225	29	5986	9
poletimber	1942	18	592	26	1150	23	2176	15	4576	12	1179	30	880	27	1777	20	803	27	406	35	195	38	2312	15	2614	14	3370	11	23971	5
young timber	8348	10	2446	19	1653	25	3230	17	4628	14	1944	23	1878	22	3037	19	841	30	594	37	2383	32	4459	13	2640	17	4100	12	42179	5
medium timber	20159	6	5960	12	4800	15	6195	14	9470	11	5104	16	7418	13	8629	12	5028	16	1888	25	2566	20	6391	12	9085	10	4862	13	97556	3
old timber	14201	9	4622	16	8056	13	14377	10	16901	8	4529	19	19796	8	17192	9	6114	15	4395	18	4053	19	8310	12	14773	9	6968	11	144288	3
total	57353	3	16185	7	19013	8	29895	6	41814	4	18547	8	42193	5	34843	5	19683	7	8850	11	11491	11	30193	5	42974	4	34225	3	407258	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. 1232825. Birmensdorf, Swiss Federal Research Institute WSL

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