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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.

NFI4–NFI5
fellings and mortality
tree species (5 classes) · higher/lower altitude zone
regional demarcation: economic region
unit: 1000 m³/yr
evaluation area: accessible forest without shrub forest NFI4/NFI5
grid: 1.4 km grid, subgrids 1-5
change 2009/17–2018/26
		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
tree species (5 classes)	higher/lower altitude zone	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%
n/a	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	lower altitude zone	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	higher altitude zone	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	.
spruce	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	lower altitude zone	275	19	128	29	178	25	491	18	657	15	65	70	351	30	75	37	9	65	1	100	85	50	0	72	4	71	23	87	2339	8
	higher altitude zone	231	16	0	.	34	50	2	100	0	0	117	27	266	17	346	21	147	29	112	43	106	42	188	21	506	16	230	27	2289	7
	total	505	12	128	29	212	22	493	18	657	15	182	30	617	18	421	18	156	27	113	43	191	32	189	21	509	16	252	25	4628	5
fir	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	lower altitude zone	267	33	60	36	56	45	260	18	181	24	13	69	153	28	50	43	26	63	1	100	6	89	0	0	1	100	6	68	1079	12
	higher altitude zone	129	30	0	.	15	100	0	0	0	0	29	54	93	28	99	30	3	72	21	57	8	60	5	59	21	41	5	87	430	14
	total	396	24	60	36	71	41	260	18	181	24	43	43	246	20	149	25	29	56	22	55	14	51	5	59	22	40	11	54	1509	9
other conifers	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	lower altitude zone	33	33	26	40	58	50	22	58	60	25	0	.	9	60	4	80	2	82	2	72	2	100	12	43	2	82	0	100	232	17
	higher altitude zone	0	0	0	.	0	.	0	.	0	.	1	100	0	100	1	100	1	100	0	0	0	0	73	24	96	26	43	38	214	16
	total	33	33	26	40	58	50	22	58	60	25	1	100	9	60	6	65	3	64	2	72	2	100	85	22	98	26	43	38	446	12
beech	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	lower altitude zone	263	15	246	22	83	27	245	19	258	15	8	47	120	44	86	36	30	60	5	91	32	45	12	53	0	100	18	34	1406	8
	higher altitude zone	96	24	0	0	0	0	3	100	12	100	0	63	33	39	36	34	0	0	3	69	7	64	0	100	19	45	1	74	210	16
	total	359	13	246	22	83	27	248	19	269	15	8	44	152	36	122	27	30	60	8	61	39	39	12	53	19	44	19	32	1615	7
other broadleaves	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	lower altitude zone	117	19	80	21	172	28	82	22	287	14	11	59	60	29	112	30	69	46	6	49	25	42	12	67	9	62	222	14	1260	7
	higher altitude zone	12	36	0	0	1	100	0	0	0	0	9	48	16	29	26	48	7	30	15	42	15	35	40	38	49	27	19	48	207	13
	total	129	17	80	21	172	27	82	22	287	14	20	39	75	23	137	26	76	42	21	33	39	29	52	33	59	25	241	13	1467	6
indeterminable	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	lower altitude zone	0	0	0	0	0	0	0	0	0	0	0	.	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
	higher altitude zone	0	0	0	.	0	.	0	.	0	.	0	0	0	0	0	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	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	lower altitude zone	955	12	540	15	547	17	1101	11	1443	9	97	59	693	21	327	21	136	34	15	46	148	36	36	34	17	41	268	14	6316	5
	higher altitude zone	467	14	0	0	50	61	5	72	12	100	157	24	408	16	507	18	158	27	151	34	136	35	306	16	691	13	298	23	3351	6
	total	1423	9	540	15	596	16	1105	11	1454	9	253	27	1100	14	834	13	295	21	166	31	285	25	343	15	707	13	566	13	9665	3

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. 1381214. Birmensdorf, Swiss Federal Research Institute WSL

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