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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
total number of stems with two most important forms of damages
altitude (in 200 m classes) · cause of damage to trees (10 classes)
regional demarcation: protection forest region
unit: n/ha
evaluation area: accessible forest without shrub forest NFI1-NFI5
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
altitude (in 200 m classes)	cause of damage to trees (10 classes)	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	.
	no visible damage	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	fire	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	rockfall	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	various	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	wood harvest	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other human activity	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	weather	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	lying living trees	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	dead trees	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
>1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	324	31	0	.	248	11	276	9	249	15	265	7
	fire	0	.	0	.	0	.	0	.	0	.	1	97	0	100
	rockfall	0	.	0	.	0	.	14	25	2	44	32	63	10	28
	various	0	.	17	47	0	.	7	32	14	23	15	28	12	16
	indeterminable	0	.	145	23	0	.	80	17	109	12	76	20	97	9
	wood harvest	0	.	0	.	0	.	4	52	1	75	0	.	2	45
	other human activity	0	.	9	62	0	.	14	45	1	46	7	83	7	35
	weather	0	.	0	.	0	.	14	27	6	31	17	63	10	21
	lying living trees	0	.	0	.	0	.	5	69	11	47	0	.	7	40
	dead trees	0	.	172	46	0	.	81	18	74	16	80	34	81	11
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
1601-1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	358	18	331	29	318	14	289	10	271	12	309	7
	fire	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	rockfall	0	.	21	34	0	.	8	36	13	37	7	41	11	20
	various	0	.	23	43	34	76	10	28	13	28	20	34	17	19
	indeterminable	0	.	106	17	72	33	118	13	98	12	60	19	95	7
	wood harvest	0	.	4	99	0	.	0	99	2	45	2	99	2	49
	other human activity	0	.	2	61	0	.	6	40	6	49	2	75	4	28
	weather	0	.	8	42	5	72	22	45	9	41	15	22	13	22
	lying living trees	0	.	5	90	5	94	3	52	0	.	0	.	2	53
	dead trees	0	.	118	24	67	36	105	25	52	16	35	24	75	12
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
1401-1600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	190	18	271	11	300	14	308	12	301	10	380	13	299	5
	fire	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	rockfall	3	96	15	39	6	44	21	41	12	52	23	33	15	20
	various	22	49	9	27	18	49	12	30	7	41	26	21	13	14
	indeterminable	45	21	93	10	64	21	88	14	92	12	77	16	84	6
	wood harvest	2	96	3	47	3	84	2	54	5	41	1	99	3	25
	other human activity	0	.	7	40	7	83	7	57	5	35	3	70	6	24
	weather	4	96	10	23	13	49	15	29	8	32	21	23	12	13
	lying living trees	0	.	2	58	3	69	10	63	2	57	1	99	3	37
	dead trees	35	60	93	14	81	31	83	17	79	22	70	18	81	9
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
1201-1400 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	263	10	301	9	237	10	378	12	273	15	274	14	284	5
	fire	0	.	0	.	0	.	0	.	0	.	2	99	0	100
	rockfall	1	99	25	30	30	33	34	37	21	51	31	28	23	15
	various	15	28	10	28	19	29	24	47	8	48	26	26	16	14
	indeterminable	47	14	80	10	68	12	53	17	118	17	79	14	73	6
	wood harvest	6	42	5	41	8	45	0	.	9	42	3	48	5	21
	other human activity	4	39	7	50	6	48	0	.	10	53	1	75	5	26
	weather	13	42	11	24	7	36	8	48	13	50	18	26	11	15
	lying living trees	0	.	1	70	6	47	4	50	0	.	6	40	3	26
	dead trees	41	23	86	14	91	17	79	17	93	18	65	21	77	8
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
1001-1200 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	317	6	318	7	283	10	309	11	261	21	307	13	306	4
	fire	0	.	0	.	0	.	0	.	1	98	4	90	1	84
	rockfall	10	35	33	27	31	34	30	51	50	42	45	25	28	14
	various	11	26	10	27	27	28	14	35	24	53	20	43	16	14
	indeterminable	42	10	47	11	74	12	72	21	92	26	76	16	59	6
	wood harvest	18	18	10	28	15	30	1	98	3	98	0	99	11	14
	other human activity	5	36	3	55	11	41	1	98	4	68	1	99	5	24
	weather	5	36	13	24	4	33	11	35	17	69	17	26	10	14
	lying living trees	0	.	2	62	2	75	12	72	2	98	2	70	2	37
	dead trees	38	16	65	13	84	18	92	19	66	25	61	24	62	8
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
801-1000 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	336	6	323	8	306	9	362	15	215	20	415	21	328	4
	fire	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	rockfall	21	32	11	49	34	31	50	60	10	57	34	28	23	17
	various	8	22	16	18	15	22	11	49	13	39	34	40	14	12
	indeterminable	58	10	46	14	54	14	103	18	85	23	136	18	65	6
	wood harvest	17	21	14	30	14	25	5	97	6	49	0	.	13	14
	other human activity	5	35	8	42	8	35	0	.	6	72	5	45	6	20
	weather	8	23	7	35	9	27	6	67	25	40	40	54	12	20
	lying living trees	0	.	3	50	1	76	3	97	2	98	14	61	2	38
	dead trees	42	12	57	14	67	16	99	23	50	20	130	21	62	7
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
601-800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	305	5	334	7	291	13	324	36	263	15	289	14	304	4
	fire	0	.	0	.	0	.	0	.	0	.	27	68	2	69
	rockfall	6	34	25	42	19	43	42	54	18	68	24	28	12	18
	various	12	17	32	37	26	31	22	74	21	23	80	38	22	15
	indeterminable	43	8	59	13	74	16	85	34	70	24	132	15	58	6
	wood harvest	19	11	18	28	5	39	0	.	4	98	6	99	15	10
	other human activity	4	28	3	43	1	74	0	.	2	68	2	75	3	22
	weather	6	17	5	38	6	43	7	69	5	81	50	40	10	20
	lying living trees	1	53	1	70	4	48	10	63	0	.	6	42	2	24
	dead trees	41	9	55	19	65	19	114	24	51	29	149	16	56	7
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
=600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	263	4	417	25	282	21	288	24	100	0	331	14	272	3
	fire	0	.	0	.	0	.	0	.	0	.	7	99	1	100
	rockfall	2	71	2	94	63	70	7	96	0	.	23	35	6	34
	various	10	13	23	64	19	64	13	59	0	.	41	34	14	13
	indeterminable	39	6	72	50	65	28	30	39	0	.	149	14	50	6
	wood harvest	16	11	22	71	9	53	4	96	0	.	0	.	15	10
	other human activity	4	29	0	.	5	61	0	.	0	.	10	39	4	23
	weather	6	14	14	64	13	52	8	65	0	.	22	26	8	12
	lying living trees	1	26	5	96	3	70	4	96	0	.	17	39	3	24
	dead trees	34	8	66	26	68	23	92	35	0	.	169	13	49	7
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	289	2	315	4	284	5	311	5	277	5	317	5	297	2
	fire	0	.	0	.	0	.	0	.	0	100	5	49	1	49
	rockfall	6	20	21	15	28	17	22	18	13	21	27	12	16	7
	various	11	8	15	14	21	14	13	16	13	14	34	15	16	6
	indeterminable	44	4	69	5	66	6	84	7	98	6	100	6	67	2
	wood harvest	17	7	9	15	10	16	2	33	4	22	2	50	10	5
	other human activity	4	15	6	21	7	22	6	30	5	21	4	23	5	9
	weather	7	9	9	12	8	16	13	18	10	17	25	16	10	6
	lying living trees	1	24	2	28	3	26	6	29	4	39	6	24	3	12
	dead trees	38	5	76	6	77	8	90	8	69	9	96	7	64	3
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.

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. 1345756. Birmensdorf, Swiss Federal Research Institute WSL

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