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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
increment (gross increment)
altitude (in 400 m classes) · main tree species
regional demarcation: biogeographical region
unit: 1000 m³/yr
evaluation area: accessible forest without shrub forest NFI1-NFI5
grid: 1.4 km grid, subgrids 1-5
change 2009/17–2018/26
		biogeographical region
		Jura		Plateau		Northern Alps		Western Central-Alps		Eastern Central-Alps		Southern Alps		Switzerland
altitude (in 400 m classes)	main tree species	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	.
	spruce	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	fir	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	larch	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	beech	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	maple	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	ash	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	oak	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other broadleaves	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	.	0	.	0	.	0	.	0	.	0	.	0	.
>1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	0	.	0	.	19	46	30	26	75	26	17	43	142	17
	fir	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	pine	0	.	0	.	0	.	1	79	10	42	0	100	11	37
	larch	0	.	0	.	0	.	43	32	46	22	19	38	108	17
	Arolla pine	0	.	0	.	0	.	11	49	27	38	3	90	41	29
	other conifers	0	.	0	.	0	.	0	0	0	44	0	.	0	44
	beech	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	maple	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	ash	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	oak	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other broadleaves	0	.	0	.	0	.	0	100	0	100	0	100	0	74
	indeterminable	0	.	0	.	0	.	0	0	0	0	0	.	0	0
	total	0	.	0	.	19	46	85	20	158	16	40	29	302	11
1401-1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	13	63	0	.	365	12	179	18	356	12	110	18	1023	7
	fir	6	64	0	.	38	36	6	71	4	61	20	51	75	25
	pine	0	.	0	.	8	54	5	79	9	41	-3	144	19	41
	larch	0	.	0	.	8	54	36	38	36	29	63	25	144	16
	Arolla pine	0	.	0	.	2	100	2	80	-1	109	0	.	3	111
	other conifers	0	.	0	.	0	100	0	0	0	71	0	100	0	63
	beech	1	71	0	.	0	.	0	.	1	100	19	37	21	35
	maple	4	78	0	.	1	495	0	100	0	224	2	102	7	95
	ash	0	.	0	.	0	100	0	.	0	.	0	.	0	100
	oak	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other broadleaves	1	73	0	.	5	39	11	39	16	51	10	62	41	27
	indeterminable	0	.	0	.	0	0	0	0	0	0	0	0	0	0
	total	24	59	0	.	428	12	240	16	420	11	221	14	1332	6
1001-1400 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	186	14	34	37	580	9	44	27	151	21	56	27	1050	6
	fir	206	13	11	56	310	13	16	41	12	56	18	38	575	9
	pine	0	116	0	100	1	81	10	41	18	56	2	90	31	36
	larch	0	.	1	100	1	79	16	38	7	47	16	61	40	29
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	0	100	2	100	1	65	0	100	0	.	0	.	3	75
	beech	83	15	4	50	150	17	-3	136	18	53	80	25	334	11
	maple	30	28	2	64	61	20	3	46	2	82	3	100	101	15
	ash	2	61	1	80	18	41	4	51	0	.	13	76	38	34
	oak	0	.	0	.	0	100	1	48	0	.	1	58	2	35
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	70	0	70
	other broadleaves	3	55	1	100	12	36	6	70	9	48	39	38	71	24
	indeterminable	0	0	0	.	0	0	0	0	0	0	0	.	0	0
	total	511	8	56	30	1132	7	99	21	217	18	228	15	2245	5
601-1000 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	119	17	458	10	264	12	12	59	58	23	28	67	937	7
	fir	243	12	395	11	253	13	2	73	18	38	1	100	912	7
	pine	13	46	19	35	9	71	4	59	10	46	0	.	56	22
	larch	1	123	16	41	4	70	4	55	6	60	3	88	34	26
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	14	38	24	38	2	82	0	0	0	.	0	.	39	27
	beech	218	11	326	11	165	16	4	67	33	38	33	37	778	7
	maple	59	21	37	24	60	33	4	92	14	41	3	60	177	15
	ash	23	27	67	29	81	21	0	68	7	68	4	53	183	15
	oak	8	45	19	29	1	57	4	58	1	100	8	42	40	19
	sweet chestnut	0	100	0	0	0	100	1	100	0	100	69	28	69	27
	other broadleaves	18	25	30	23	28	25	11	40	11	48	31	38	129	14
	indeterminable	0	0	0	0	0	0	0	.	0	0	0	0	0	0
	total	714	8	1391	7	868	8	46	28	160	17	181	16	3355	4
=600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	37	25	503	9	18	64	0	.	0	.	3	73	559	8
	fir	39	38	227	13	8	92	0	.	0	.	0	.	274	12
	pine	20	40	27	35	1	100	-2	83	0	.	0	.	46	27
	larch	1	64	23	40	2	72	0	0	0	.	0	100	25	36
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	1	83	33	35	0	100	0	.	0	.	2	92	36	33
	beech	79	17	357	9	35	36	0	82	0	.	3	57	475	8
	maple	6	130	87	19	9	43	2	100	0	.	4	78	109	18
	ash	12	64	125	17	11	43	0	71	1	100	9	52	158	15
	oak	9	44	82	21	2	52	0	100	0	.	10	47	102	18
	sweet chestnut	0	.	0	.	0	100	0	76	0	.	29	37	29	36
	other broadleaves	7	40	119	16	10	74	3	62	4	100	41	43	184	15
	indeterminable	0	0	0	0	0	0	0	0	0	.	0	0	0	0
	total	211	15	1584	5	97	26	5	79	5	100	100	23	1997	5
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	353	10	995	6	1247	6	265	13	639	9	215	14	3711	3
	fir	494	8	633	8	610	9	25	33	34	29	38	32	1837	5
	pine	33	30	46	25	18	42	19	34	47	26	0	869	163	14
	larch	1	65	39	28	16	36	100	20	95	16	101	20	351	10
	Arolla pine	0	.	0	.	2	100	13	44	26	40	3	90	43	28
	other conifers	15	34	59	25	3	70	0	100	1	38	2	92	80	20
	beech	382	8	687	7	351	11	2	292	51	31	136	18	1608	4
	maple	98	17	126	15	131	18	10	46	16	38	12	42	394	9
	ash	37	27	193	15	109	17	4	43	9	59	26	43	378	10
	oak	17	31	101	18	3	37	5	44	1	100	18	30	144	14
	sweet chestnut	0	100	0	0	0	166	1	67	0	100	97	22	99	21
	other broadleaves	28	19	151	13	55	20	31	25	40	28	121	22	425	9
	indeterminable	0	0	0	0	0	0	0	0	0	0	0	0	0	0
	total	1460	5	3030	3	2544	4	474	10	959	7	770	7	9232	2

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. 1399445. Birmensdorf, Swiss Federal Research Institute WSL

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