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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)
site quality · main tree species
regional demarcation: economic 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
		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
site quality	main tree species	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	.
	spruce	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	fir	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	larch	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	beech	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	maple	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	ash	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	oak	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other broadleaves	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	indeterminable	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	.
low	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	21	47	2	100	0	21586	1	157	4	82	14	41	67	27	11	52	48	31	13	72	48	38	12	40	82	24	13	43	339	12
	fir	52	23	3	97	0	.	3	59	4	81	0	84	0	395	1	95	17	57	4	86	3	107	2	76	0	.	0	.	90	19
	pine	6	81	1	63	0	.	2	69	2	88	0	.	4	82	0	.	1	100	2	96	0	.	0	79	10	42	0	.	28	28
	larch	0	.	0	100	0	.	0	.	0	.	0	.	0	.	0	.	0	100	0	.	0	.	23	45	42	22	14	47	80	19
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	10	45	9	72	0	.	19	41
	other conifers	0	68	1	100	0	.	0	77	0	100	0	.	0	96	0	.	0	100	0	100	0	100	0	0	0	44	0	.	3	35
	beech	53	24	1	515	6	100	28	41	14	75	-1	533	11	96	0	658	3	177	7	71	6	53	4	72	0	.	0	.	132	19
	maple	6	53	1	54	0	100	0	83	1	64	2	40	1	275	1	61	4	45	0	884	1	69	3	76	0	.	0	.	21	28
	ash	0	965	1	85	0	0	-1	243	1	69	7	100	3	103	0	72	1	73	0	100	0	.	0	77	0	.	0	.	13	60
	oak	4	71	0	100	0	.	-1	158	0	103	0	100	4	101	0	.	0	371	1	100	0	.	1	77	0	.	0	.	8	54
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	1	76	0	.	0	.	1	76
	other broadleaves	1	149	0	208	0	.	1	67	0	515	1	93	3	69	0	78	1	59	0	65	0	100	7	59	0	89	0	100	15	32
	indeterminable	0	0	0	.	0	0	0	.	0	.	0	.	0	.	0	.	0	0	0	0	0	.	0	0	0	0	0	.	0	0
	total	144	17	10	75	6	123	36	35	26	49	23	41	93	25	14	44	77	26	27	45	58	34	64	24	144	16	28	33	748	8
moderate	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	61	24	0	.	2	215	0	100	1	100	109	19	43	31	70	27	153	18	25	50	36	37	269	13	413	11	126	17	1309	6
	fir	88	21	0	.	4	56	1	100	0	.	42	36	26	38	28	34	29	33	6	106	1	89	26	32	11	49	34	34	298	11
	pine	0	100	0	.	0	.	0	.	0	.	0	.	0	.	0	100	1	73	2	100	0	.	20	33	37	31	-2	223	57	24
	larch	0	.	0	.	0	.	0	.	0	.	1	100	0	100	0	.	8	55	0	.	0	135	77	23	57	21	71	23	213	13
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	2	100	0	.	0	.	2	134	20	43	0	100	24	38
	other conifers	0	100	0	.	0	.	0	.	0	.	0	.	0	.	2	100	0	.	0	.	0	.	0	93	0	100	0	.	3	86
	beech	38	26	0	.	1	194	2	100	2	100	9	60	18	45	33	32	13	71	3	75	11	57	1	585	16	41	48	34	194	14
	maple	9	43	0	.	1	62	0	100	0	.	4	84	3	59	4	38	6	147	2	92	9	59	7	57	10	54	4	76	58	24
	ash	1	189	0	.	0	.	0	.	0	.	3	57	3	56	0	367	0	991	5	88	6	65	7	52	3	74	3	56	30	29
	oak	0	.	0	.	0	.	0	.	0	.	0	.	0	100	0	.	0	100	0	.	0	.	4	50	1	100	2	67	7	37
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	100	0	100	13	56	14	54
	other broadleaves	2	37	0	.	0	.	0	100	0	.	2	88	-2	130	0	489	4	37	1	70	1	67	25	27	24	38	19	83	76	26
	indeterminable	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	199	15	0	.	8	77	4	100	2	100	169	18	92	23	137	21	215	17	43	39	64	30	437	11	592	9	320	12	2283	4
good	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	146	17	23	29	52	33	40	35	83	22	64	25	162	15	233	16	35	33	58	32	42	39	10	54	144	20	62	36	1156	6
	fir	190	15	5	45	37	34	69	25	50	27	26	73	262	15	104	18	15	45	20	64	12	42	14	65	15	45	3	93	822	8
	pine	5	64	8	72	2	97	3	65	10	46	0	.	11	64	1	212	0	.	1	68	0	.	0	.	0	.	0	.	40	27
	larch	1	77	1	86	2	107	0	73	3	108	1	100	0	100	0	.	1	90	0	0	1	277	0	.	0	415	11	72	20	46
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	2	71	4	92	2	82	17	48	4	77	0	.	1	92	1	71	0	.	0	0	0	124	0	.	0	.	2	92	33	30
	beech	97	14	45	25	30	29	56	24	89	21	31	37	84	22	59	30	23	42	15	46	28	46	7	60	4	80	83	22	651	7
	maple	28	30	7	58	11	46	12	41	31	28	2	197	11	58	34	26	4	65	3	90	10	62	4	62	4	65	7	53	168	12
	ash	11	34	3	100	21	61	7	93	22	61	8	55	10	38	27	37	3	115	7	55	3	63	1	66	6	87	22	51	150	18
	oak	3	73	5	51	10	50	10	49	9	37	2	88	1	100	0	100	0	100	1	65	0	.	0	0	2	100	14	37	55	18
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	100	0	.	0	.	0	100	0	100	84	24	84	24
	other broadleaves	10	35	5	40	8	54	5	61	7	38	3	59	16	28	11	31	1	285	0	675	5	50	1	94	18	45	94	22	184	13
	indeterminable	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	492	9	107	20	175	21	219	17	307	15	136	23	558	10	471	12	82	24	106	24	100	26	37	39	192	18	383	11	3362	4
very good	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	81	21	39	24	74	28	266	13	339	11	9	51	60	32	31	35	7	55	1	100	4	61	0	.	0	.	0	.	909	7
	fir	125	20	23	39	44	32	197	15	106	21	5	61	73	23	52	39	0	100	0	100	1	198	0	.	0	.	0	.	626	8
	pine	11	60	7	92	3	74	2	210	13	32	0	.	0	0	1	100	0	.	0	.	0	.	0	.	0	.	0	.	37	30
	larch	0	742	2	116	13	52	4	64	11	61	0	.	1	100	5	53	2	90	0	.	0	100	0	.	0	.	0	.	39	28
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	3	93	9	83	5	100	11	52	13	49	0	.	0	.	0	83	0	.	0	.	0	.	0	.	0	.	0	.	41	30
	beech	92	19	76	18	57	31	149	16	175	12	4	79	25	40	35	39	7	59	-2	227	10	54	-4	100	0	.	5	87	631	7
	maple	37	35	11	42	7	51	25	27	38	34	1	100	1	399	18	89	8	50	0	100	0	59	0	100	0	.	0	.	148	18
	ash	18	30	20	42	25	56	24	32	63	20	9	87	7	66	11	38	3	70	0	.	4	74	1	78	0	.	1	75	186	13
	oak	9	43	13	64	20	49	7	38	20	44	0	100	0	.	2	90	0	.	0	.	0	.	0	100	0	.	1	89	73	22
	sweet chestnut	0	.	0	.	0	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	100	0	92
	other broadleaves	4	66	11	34	25	37	37	28	55	24	0	.	3	79	9	46	3	206	0	100	1	126	0	627	0	.	3	93	149	14
	indeterminable	0	0	0	0	0	0	0	.	0	0	0	.	0	.	0	0	0	.	0	.	0	.	0	.	0	.	0	.	0	0
	total	381	12	211	15	273	16	721	9	834	7	27	48	169	18	165	23	31	38	-1	976	22	39	-2	224	0	.	10	61	2839	4
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	310	10	64	18	128	21	308	12	427	10	197	13	331	11	345	12	244	14	97	25	130	21	291	12	638	9	202	15	3711	3
	fir	455	9	32	31	85	22	270	12	160	16	73	33	361	12	185	16	61	25	29	49	17	38	42	30	26	33	38	32	1837	5
	pine	22	41	15	55	5	59	7	62	24	26	0	.	15	51	2	96	2	69	5	54	0	.	20	32	47	26	-2	223	163	14
	larch	1	81	3	82	15	48	4	60	14	53	1	71	1	79	5	53	12	44	0	0	1	267	100	21	99	15	97	20	351	10
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	2	100	0	.	0	.	13	44	29	37	0	100	43	28
	other conifers	6	54	13	60	7	72	28	35	17	41	0	.	2	72	3	70	0	100	0	100	0	144	0	93	1	41	2	92	80	20
	beech	281	9	122	15	94	22	235	12	279	10	42	31	138	18	127	19	46	32	24	42	55	28	8	93	20	36	136	18	1608	4
	maple	81	20	20	32	19	33	37	22	70	22	8	59	15	49	57	32	22	46	5	66	21	40	14	37	14	42	12	43	394	9
	ash	29	23	24	38	46	41	30	33	86	21	26	42	23	30	38	29	7	78	12	47	13	39	9	42	8	64	26	43	378	10
	oak	16	33	19	48	29	36	17	34	30	32	2	78	4	83	2	86	0	725	2	56	0	.	6	41	2	78	17	32	144	14
	sweet chestnut	0	.	0	.	0	100	0	.	0	.	0	.	0	.	0	.	0	100	0	.	0	.	1	64	0	89	97	22	99	21
	other broadleaves	17	28	15	26	33	31	43	25	63	22	5	45	20	30	21	26	10	76	2	175	6	40	33	24	43	29	115	22	425	9
	indeterminable	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	1217	5	328	11	462	13	980	7	1170	6	355	13	911	7	785	9	405	12	176	19	244	16	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. 1393174. Birmensdorf, Swiss Federal Research Institute WSL

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