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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.

NFI5
number of stems
development stage · main tree species
regional demarcation: protection forest region
unit: n/ha
evaluation area: accessible forest without shrub forest
grid: 1.4 km grid, subgrids 1-5
state 2018/26
		protection forest region
		Jura + Plateau		Northwestern Alps		Northeastern Alps		Southwestern Alps		Southeastern Alps		Southern Alps		Switzerland
development stage	main tree species	n/ha	±%	n/ha	±%	n/ha	±%	n/ha	±%	n/ha	±%	n/ha	±%	n/ha	±%
n/a	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	20	83	42	32	11	70	0	.	74	29	57	48	38	23
	fir	1	97	22	70	0	.	4	89	0	.	0	.	4	64
	pine	11	61	0	.	0	.	4	90	3	65	0	.	4	48
	larch	0	.	0	.	0	.	8	55	17	82	8	89	6	66
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	beech	32	68	10	94	25	61	0	.	0	.	0	.	13	50
	maple	3	97	3	94	56	80	0	.	0	.	0	.	9	74
	ash	1	97	0	.	0	.	0	.	0	.	0	.	0	99
	oak	3	66	0	.	0	.	0	.	0	.	0	.	1	70
	sweet chestnut	0	.	2	91	0	.	0	.	0	.	0	.	0	99
	other broadleaves	1	97	0	.	0	.	0	.	0	.	0	.	0	99
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	73	44	79	25	92	46	16	22	95	30	65	38	76	18
young growth/ thicket	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	25	27	74	17	32	31	10	54	61	21	36	47	41	11
	fir	30	43	10	33	8	41	0	.	0	.	0	.	13	33
	pine	2	43	0	.	0	99	0	.	6	71	7	99	2	42
	larch	4	79	2	85	1	99	12	53	18	45	7	43	6	28
	Arolla pine	0	.	0	.	0	.	1	98	10	99	0	.	1	94
	other conifers	2	60	1	99	2	99	0	.	6	78	0	.	2	44
	beech	20	16	23	32	14	33	0	.	1	99	5	70	14	15
	maple	6	35	9	41	13	45	4	68	8	84	0	.	7	23
	ash	2	66	2	99	5	58	4	98	0	.	0	.	2	39
	oak	3	46	0	.	1	98	0	.	0	.	0	.	1	43
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	1	98	0	100
	other broadleaves	9	37	17	39	12	55	14	52	9	65	34	36	14	18
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	103	17	137	12	89	20	45	25	118	15	89	21	103	8
pole timber	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	160	12	221	17	238	17	64	24	278	16	44	38	155	7
	fir	64	18	63	39	52	41	7	72	1	76	4	45	37	15
	pine	6	40	4	99	9	88	48	49	99	29	0	.	20	22
	larch	15	45	18	40	0	.	79	26	41	35	60	24	33	15
	Arolla pine	0	.	0	.	0	.	2	86	40	35	0	.	5	36
	other conifers	3	38	13	61	3	99	7	61	19	40	0	.	6	26
	beech	122	11	57	32	37	55	23	51	4	70	79	25	73	10
	maple	65	15	71	18	58	28	55	32	1	99	29	38	50	10
	ash	32	16	26	32	47	31	40	37	6	78	27	29	29	12
	oak	17	39	5	84	0	.	30	42	0	.	24	46	15	24
	sweet chestnut	0	.	0	.	0	.	1	99	0	.	98	27	19	28
	other broadleaves	46	16	91	22	76	34	125	18	131	25	196	15	103	9
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	531	4	569	7	519	9	481	8	620	7	561	7	546	3
young timber	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	159	11	353	17	245	18	266	24	287	16	51	35	202	8
	fir	52	17	74	30	70	33	0	99	9	62	12	68	38	14
	pine	12	31	6	69	0	.	118	35	49	48	7	86	26	23
	larch	3	39	4	99	21	71	123	30	80	33	42	42	34	19
	Arolla pine	0	.	0	.	0	.	19	60	42	50	2	99	7	38
	other conifers	12	40	0	.	5	55	1	99	1	99	0	.	5	36
	beech	118	12	67	32	153	28	17	69	11	46	185	22	102	10
	maple	41	14	72	30	78	25	0	.	16	61	13	45	36	13
	ash	18	22	42	43	46	36	8	48	8	67	34	48	24	18
	oak	20	41	5	54	0	.	8	54	0	.	25	34	14	26
	sweet chestnut	0	.	0	.	0	.	4	82	1	99	104	26	19	26
	other broadleaves	42	20	34	34	43	44	42	32	48	60	148	19	61	12
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	478	4	657	9	660	9	608	11	550	9	622	6	568	3
medium timber	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	81	11	247	16	211	14	250	19	280	11	115	27	156	6
	fir	62	12	60	27	47	19	36	48	4	90	12	61	46	10
	pine	12	26	2	99	3	89	39	42	30	38	1	99	12	19
	larch	1	37	0	.	0	.	67	32	28	28	67	29	14	19
	Arolla pine	0	.	0	.	0	.	3	98	8	47	0	.	1	45
	other conifers	4	48	0	.	3	75	0	.	0	.	0	.	2	43
	beech	138	7	107	18	115	14	48	64	11	58	95	30	106	6
	maple	26	13	24	29	33	23	2	98	2	70	7	45	20	11
	ash	21	18	20	42	23	28	8	72	0	.	3	62	16	14
	oak	12	24	5	61	0	100	7	59	0	.	7	48	7	20
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	39	42	4	45
	other broadleaves	23	16	19	28	8	28	17	42	6	47	78	25	24	12
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	378	4	485	8	442	7	477	9	368	8	424	7	409	3
old timber	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	49	8	162	8	168	10	201	12	212	10	125	14	123	4
	fir	66	8	94	11	52	15	22	39	7	43	24	42	56	6
	pine	4	21	2	100	4	78	1	76	8	35	0	.	3	21
	larch	1	39	1	71	2	44	81	21	40	18	28	23	14	13
	Arolla pine	0	.	0	.	0	.	9	47	10	38	0	.	2	30
	other conifers	3	40	0	.	1	57	0	.	0	.	0	.	1	36
	beech	101	6	84	13	73	13	1	99	17	33	46	33	72	5
	maple	21	12	12	19	23	20	12	51	3	60	0	.	15	9
	ash	14	15	6	39	11	29	3	61	1	71	0	.	8	12
	oak	7	18	0	100	0	100	1	99	1	99	2	60	3	17
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	46	31	4	33
	other broadleaves	19	19	10	26	13	36	10	40	7	52	27	33	15	13
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	285	3	371	5	347	5	342	8	306	6	298	7	318	2
mixed	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	87	9	210	8	188	14	163	11	260	10	121	23	164	5
	fir	94	10	80	13	55	21	14	42	4	39	9	43	51	7
	pine	7	26	11	66	12	51	29	30	16	34	2	69	12	19
	larch	1	61	1	61	4	83	78	15	46	17	82	16	30	10
	Arolla pine	0	.	0	100	0	.	31	26	40	32	0	100	10	22
	other conifers	3	34	1	57	4	73	0	.	4	63	1	70	2	27
	beech	82	9	63	15	95	20	25	41	14	49	59	21	58	7
	maple	28	14	31	20	29	28	10	38	7	43	6	40	20	10
	ash	17	18	10	31	14	32	7	53	11	63	11	27	12	14
	oak	13	29	1	57	4	46	6	81	1	100	10	38	7	20
	sweet chestnut	0	.	0	.	0	.	4	95	1	100	52	25	8	25
	other broadleaves	35	14	28	21	48	25	30	20	12	32	78	21	37	9
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	368	4	436	5	454	8	396	6	415	6	431	9	411	2
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	92	5	200	5	178	6	157	8	235	6	85	12	145	3
	fir	65	5	71	8	48	11	12	24	4	26	10	23	44	4
	pine	7	13	5	47	5	36	38	21	31	18	2	53	12	10
	larch	4	32	3	31	3	47	78	11	42	11	55	11	23	6
	Arolla pine	0	.	0	100	0	.	15	21	26	19	0	79	5	15
	other conifers	4	20	2	53	3	34	1	56	5	32	0	70	3	14
	beech	104	4	68	8	80	9	19	27	11	23	82	12	71	3
	maple	32	7	32	11	35	11	16	24	5	29	11	26	24	5
	ash	18	8	14	18	20	15	12	26	5	43	15	22	15	6
	oak	12	15	2	34	1	41	9	32	1	72	14	24	7	11
	sweet chestnut	0	.	0	100	0	.	2	67	0	72	66	13	9	13
	other broadleaves	29	7	30	12	30	16	43	13	32	20	107	10	41	5
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	367	2	428	3	403	4	403	4	396	4	449	4	400	1

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. 1356761. Birmensdorf, Swiss Federal Research Institute WSL

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