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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: protection forest 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
		protection forest region
		Jura + Plateau		Northwestern Alps		Northeastern Alps		Southwestern Alps		Southeastern 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	.	19	46	0	.	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	47	21	18	40	108	17
	Arolla pine	0	.	0	.	0	.	11	49	30	35	0	100	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	.	19	46	0	.	85	20	162	16	36	30	302	11
1401-1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	13	63	254	14	100	26	198	16	362	11	97	19	1023	7
	fir	6	64	37	37	1	326	7	68	5	53	19	53	75	25
	pine	0	.	6	63	2	100	6	66	9	41	-4	91	19	41
	larch	0	.	8	54	1	94	36	39	38	28	60	25	144	16
	Arolla pine	0	.	2	100	0	.	2	80	-1	109	0	.	3	111
	other conifers	0	.	0	100	0	100	0	100	0	100	0	.	0	63
	beech	1	71	0	.	0	.	0	.	1	100	19	37	21	35
	maple	4	78	0	1066	0	100	1	58	0	177	2	123	7	95
	ash	0	.	0	100	0	.	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	3	55	1	57	12	37	21	47	4	42	41	27
	indeterminable	0	.	0	0	0	0	0	0	0	0	0	0	0	0
	total	24	59	311	14	105	26	261	15	435	11	197	14	1332	6
1001-1400 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	188	14	328	11	279	14	52	24	147	21	56	28	1050	6
	fir	215	13	204	18	98	20	32	37	8	73	18	38	575	9
	pine	0	116	0	0	1	77	10	41	18	56	2	90	31	36
	larch	0	.	1	62	0	.	16	38	7	47	16	61	40	29
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	0	100	0	79	2	96	0	100	0	.	0	.	3	75
	beech	87	15	67	28	91	22	1	593	7	78	80	25	334	11
	maple	30	28	31	29	32	26	4	44	1	90	3	100	101	15
	ash	2	55	6	70	12	48	4	49	0	.	13	76	38	34
	oak	0	.	0	114	0	.	1	48	0	.	1	58	2	35
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	70	0	70
	other broadleaves	3	55	13	31	2	119	6	70	7	54	39	38	71	24
	indeterminable	0	0	0	0	0	0	0	0	0	0	0	.	0	0
	total	527	8	651	9	517	11	126	19	195	18	228	15	2245	5
601-1000 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	506	9	155	16	180	17	12	59	55	24	28	67	937	7
	fir	514	9	248	13	132	20	3	56	13	46	1	100	912	7
	pine	26	31	11	64	4	70	4	59	10	46	0	.	56	22
	larch	14	43	2	92	3	79	4	55	7	55	3	93	34	26
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	38	28	2	77	0	142	0	0	0	.	0	.	39	27
	beech	487	9	155	16	83	24	7	49	13	40	33	37	778	7
	maple	95	16	13	60	47	39	7	59	12	45	3	60	177	15
	ash	77	25	46	29	45	26	4	77	7	74	4	53	183	15
	oak	21	24	6	64	0	100	4	58	2	78	6	46	40	19
	sweet chestnut	0	100	0	100	0	.	1	100	0	89	69	28	69	27
	other broadleaves	43	18	17	37	16	25	11	40	11	51	31	38	129	14
	indeterminable	0	0	0	0	0	0	0	.	0	0	0	0	0	0
	total	1821	5	654	9	511	11	57	26	132	18	179	16	3355	4
=600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	526	9	18	68	13	62	0	.	0	.	3	73	559	8
	fir	267	12	7	100	0	743	0	.	0	.	0	.	274	12
	pine	47	26	0	.	1	100	-2	83	0	.	0	.	46	27
	larch	23	40	3	72	1	100	0	0	0	.	0	100	25	36
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	34	34	0	.	0	133	0	.	0	.	2	92	36	33
	beech	435	8	4	69	33	38	0	1955	0	.	3	57	475	8
	maple	99	18	0	1847	3	118	3	96	0	.	4	78	109	18
	ash	134	17	5	54	7	58	1	49	1	100	9	52	158	15
	oak	88	20	0	.	4	61	0	76	0	.	10	47	102	18
	sweet chestnut	0	.	0	.	0	.	0	67	0	.	29	37	29	36
	other broadleaves	124	15	2	374	9	50	4	66	4	100	41	43	184	15
	indeterminable	0	0	0	0	0	0	0	0	0	.	0	0	0	0
	total	1777	5	38	44	70	31	7	103	5	100	100	23	1997	5
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	1234	5	773	7	572	10	291	12	638	9	202	15	3711	3
	fir	1002	6	496	10	231	14	42	30	26	33	38	32	1837	5
	pine	74	20	17	46	7	47	20	32	47	26	-2	223	163	14
	larch	37	29	14	37	5	56	100	21	99	15	97	20	351	10
	Arolla pine	0	.	2	100	0	.	13	44	29	37	0	100	43	28
	other conifers	72	22	2	63	3	76	0	93	1	41	2	92	80	20
	beech	1010	5	226	14	206	15	8	93	20	36	136	18	1608	4
	maple	227	11	45	30	82	25	14	37	14	42	12	43	394	9
	ash	214	14	57	25	63	21	9	42	8	64	26	43	378	10
	oak	110	17	6	63	4	57	6	41	2	78	17	32	144	14
	sweet chestnut	0	100	0	100	0	.	1	64	0	89	97	22	99	21
	other broadleaves	170	12	35	28	29	23	33	24	43	29	115	22	425	9
	indeterminable	0	0	0	0	0	0	0	0	0	0	0	0	0	0
	total	4149	3	1672	5	1203	7	536	9	927	7	739	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. 1399443. Birmensdorf, Swiss Federal Research Institute WSL

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