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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 NFI4/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	.	27	41	4	92	35	25	110	22	29	32	205	14
	fir	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	pine	0	.	0	71	0	.	1	79	10	41	0	282	11	37
	larch	0	.	2	100	0	100	50	28	74	20	55	23	181	13
	Arolla pine	0	.	0	.	0	.	14	40	38	29	0	87	52	24
	other conifers	0	.	0	.	0	.	0	0	0	43	0	.	1	43
	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	95	0	74	0	54	1	44
	indeterminable	0	.	0	.	0	.	0	0	0	0	0	0	0	0
	total	0	.	29	39	3	97	100	19	233	14	85	22	451	10
1401-1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	17	50	308	13	111	24	216	15	428	11	110	17	1189	6
	fir	6	64	38	36	1	326	6	72	5	53	22	47	78	24
	pine	0	.	6	63	2	76	6	62	11	37	-4	91	22	36
	larch	0	.	8	54	1	94	49	30	46	25	65	24	170	15
	Arolla pine	0	.	2	100	0	.	2	74	0	321	0	.	4	83
	other conifers	0	.	0	69	0	100	0	100	0	99	0	.	0	49
	beech	1	71	0	.	0	.	0	100	1	100	22	33	24	31
	maple	4	78	2	345	2	84	2	43	0	177	4	68	14	51
	ash	0	.	0	100	0	100	0	.	0	.	0	.	0	81
	oak	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other broadleaves	1	73	5	38	1	57	13	35	26	40	16	54	61	23
	indeterminable	0	.	0	0	0	0	0	0	0	0	0	0	0	0
	total	27	51	369	13	119	23	295	14	517	10	235	13	1562	6
1001-1400 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	191	14	357	11	326	13	65	22	166	20	69	25	1176	6
	fir	217	13	205	18	100	20	32	37	8	73	18	38	579	9
	pine	0	116	0	0	-1	258	10	40	19	55	2	74	30	36
	larch	0	.	1	62	0	100	22	36	21	46	16	59	60	26
	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	70	27	92	22	1	593	7	71	82	25	341	11
	maple	34	26	35	28	36	25	8	45	3	70	6	69	123	14
	ash	2	55	6	73	15	41	10	51	3	71	15	68	51	27
	oak	0	.	1	82	0	100	1	46	0	.	3	66	5	40
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	70	0	70
	other broadleaves	6	58	19	26	10	57	15	47	19	48	48	35	117	19
	indeterminable	0	0	0	0	0	0	0	0	0	0	0	0	0	0
	total	538	8	694	9	581	11	166	17	246	16	258	14	2485	4
601-1000 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	510	9	159	16	196	16	12	57	55	24	28	67	961	7
	fir	523	9	249	13	139	19	3	56	13	46	1	100	929	7
	pine	26	31	11	64	4	70	4	59	10	46	0	.	56	22
	larch	14	43	2	92	3	79	4	52	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	510	9	169	17	87	23	7	49	13	40	38	35	823	7
	maple	102	15	12	63	51	37	7	65	12	45	4	51	188	14
	ash	83	23	49	28	45	25	4	77	7	74	3	68	191	14
	oak	22	24	6	64	0	76	6	50	2	78	7	45	43	18
	sweet chestnut	0	100	0	100	0	.	1	100	0	89	70	27	71	27
	other broadleaves	45	18	19	33	17	24	11	38	14	45	36	34	142	13
	indeterminable	0	0	0	0	0	0	0	0	0	0	0	0	0	0
	total	1873	5	678	9	542	11	60	25	134	17	190	16	3478	4
=600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	526	9	18	68	13	59	0	.	0	.	3	73	560	8
	fir	267	12	7	100	2	123	0	.	0	.	0	.	277	12
	pine	47	26	0	.	1	97	-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	34	37	0	1079	0	.	3	57	477	7
	maple	97	19	0	1847	4	87	3	96	0	.	7	58	111	18
	ash	135	17	5	54	7	58	1	45	1	100	10	49	159	15
	oak	93	19	0	.	4	59	1	61	0	.	10	47	107	17
	sweet chestnut	0	.	0	.	0	.	1	68	0	.	33	33	34	32
	other broadleaves	124	16	2	374	10	46	5	59	4	100	52	37	197	15
	indeterminable	0	0	0	0	0	0	0	0	0	.	0	0	0	0
	total	1781	5	38	44	76	29	9	84	5	100	118	21	2028	5
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	1244	5	869	7	650	9	328	11	758	8	239	13	4090	3
	fir	1014	6	499	10	241	14	41	30	26	33	41	30	1864	5
	pine	74	20	17	46	7	55	21	31	50	25	-2	253	166	14
	larch	37	29	16	35	5	58	125	18	148	14	139	16	469	8
	Arolla pine	0	.	2	100	0	.	16	36	38	30	0	87	56	23
	other conifers	72	22	2	57	3	76	0	93	1	39	2	92	80	20
	beech	1034	5	243	14	212	14	8	88	21	35	145	17	1665	4
	maple	237	11	49	28	94	22	20	32	15	39	21	32	435	9
	ash	220	13	59	24	66	20	16	40	11	50	28	41	401	9
	oak	115	16	7	59	5	50	8	38	2	78	19	30	155	13
	sweet chestnut	0	100	0	100	0	.	2	56	0	89	103	21	105	20
	other broadleaves	176	12	45	23	39	22	44	22	62	25	153	19	518	8
	indeterminable	0	0	0	0	0	0	0	0	0	0	0	0	0	0
	total	4221	3	1807	5	1322	7	629	9	1133	6	887	6	10005	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. 1305296. Birmensdorf, Swiss Federal Research Institute WSL

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