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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 NFI4/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	.	344	36	301	57	204	12	266	9	220	11	243	6
	fire	0	.	0	.	0	.	0	.	0	.	0	99	0	100
	rockfall	0	.	0	.	0	.	12	24	4	42	19	51	9	25
	various	0	.	13	45	26	82	9	35	15	24	12	22	13	16
	indeterminable	0	.	108	25	106	41	75	15	105	10	83	13	92	7
	wood harvest	0	.	0	.	0	.	3	52	0	75	0	.	1	45
	other human activity	0	.	6	66	0	.	11	45	1	46	4	67	5	34
	weather	0	.	0	.	16	82	15	24	7	25	34	36	15	20
	lying living trees	0	.	0	.	0	.	5	61	11	37	5	47	7	29
	dead trees	0	.	118	47	17	81	69	18	69	14	49	25	66	10
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
1601-1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	323	16	261	31	283	13	271	9	254	12	280	6
	fire	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	rockfall	0	.	17	35	0	.	7	34	10	35	11	50	10	20
	various	0	.	21	38	29	69	8	28	14	27	18	31	16	17
	indeterminable	0	.	102	16	66	29	101	13	93	10	60	17	89	7
	wood harvest	0	.	3	99	0	.	0	99	1	45	1	99	1	49
	other human activity	0	.	4	52	1	97	10	50	7	39	2	60	6	26
	weather	0	.	11	33	4	73	19	40	10	31	14	21	13	18
	lying living trees	0	.	6	69	4	96	3	46	1	99	1	99	2	39
	dead trees	0	.	99	23	52	39	95	22	45	15	32	22	65	11
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
1401-1600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	174	17	266	10	260	14	285	12	295	10	357	11	285	5
	fire	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	rockfall	2	97	22	37	5	45	19	39	16	43	19	32	17	19
	various	23	41	8	27	15	47	11	28	6	41	24	20	12	13
	indeterminable	40	20	90	9	66	18	82	13	85	11	73	14	80	5
	wood harvest	1	97	3	47	3	84	2	55	4	41	1	99	3	25
	other human activity	0	.	9	35	5	83	8	45	6	36	2	70	6	21
	weather	4	75	9	24	11	49	15	29	9	28	19	22	11	13
	lying living trees	0	.	1	58	10	56	10	58	3	52	4	58	4	28
	dead trees	30	58	85	14	77	28	74	17	73	21	69	17	75	8
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
1201-1400 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	272	11	293	9	246	9	377	12	266	14	255	14	281	5
	fire	0	.	0	.	0	.	0	.	0	.	2	99	0	100
	rockfall	1	99	25	28	42	31	30	37	20	51	35	24	26	15
	various	14	27	14	28	25	24	49	44	8	44	22	26	21	15
	indeterminable	44	14	82	10	66	11	61	17	114	16	73	14	72	5
	wood harvest	5	42	4	41	7	45	0	.	8	43	3	49	5	21
	other human activity	4	39	8	45	5	46	1	99	12	46	1	75	5	24
	weather	12	42	10	24	10	39	7	48	14	44	17	25	11	14
	lying living trees	0	.	1	70	10	54	5	44	0	.	5	41	4	32
	dead trees	39	23	80	14	87	16	87	16	92	18	56	21	73	7
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
1001-1200 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	314	6	325	7	270	10	313	10	241	18	290	12	300	4
	fire	0	.	0	.	0	.	0	.	1	99	3	90	0	84
	rockfall	9	35	30	27	29	32	25	49	37	41	37	25	26	14
	various	11	26	10	26	27	27	17	33	23	45	20	38	16	13
	indeterminable	42	11	56	13	71	11	69	20	106	23	75	15	62	6
	wood harvest	18	18	10	27	15	28	1	99	3	80	0	99	11	13
	other human activity	5	36	5	49	11	37	1	69	5	55	1	99	5	22
	weather	5	36	15	24	8	30	11	31	14	61	17	23	11	13
	lying living trees	0	.	2	62	5	63	11	64	2	99	6	70	3	33
	dead trees	38	16	64	12	76	18	85	20	56	22	56	22	59	7
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
801-1000 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	338	5	331	8	298	9	365	15	210	20	402	18	329	4
	fire	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	rockfall	20	32	11	49	38	27	47	60	9	57	33	27	23	16
	various	9	21	17	19	17	21	11	49	12	40	29	40	15	12
	indeterminable	58	10	48	13	58	13	100	19	85	22	122	18	66	6
	wood harvest	17	20	13	30	16	27	4	98	9	44	0	.	13	14
	other human activity	7	32	8	42	7	34	1	98	5	72	4	45	6	19
	weather	8	23	8	33	10	24	5	68	24	40	35	52	12	19
	lying living trees	0	.	3	50	1	61	2	98	2	98	13	56	2	35
	dead trees	41	12	61	15	71	15	97	22	48	21	119	20	63	7
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
601-800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	302	5	332	7	291	13	262	37	263	15	285	14	301	4
	fire	0	.	0	.	0	.	0	.	0	.	27	68	2	69
	rockfall	6	34	25	42	19	43	32	56	18	68	25	26	12	18
	various	12	17	31	37	26	31	17	76	21	23	78	38	22	15
	indeterminable	43	8	58	13	74	16	66	37	70	24	129	15	57	6
	wood harvest	19	11	17	28	5	39	0	.	4	98	6	99	15	10
	other human activity	4	27	3	43	1	74	0	.	2	68	2	75	4	22
	weather	6	17	5	38	6	43	9	54	5	81	49	40	10	20
	lying living trees	1	53	1	70	4	48	8	65	0	.	6	42	2	24
	dead trees	41	9	54	19	65	19	104	25	51	29	146	17	56	7
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
=600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	259	4	417	25	271	19	256	25	100	0	308	13	267	3
	fire	0	.	0	.	0	.	0	.	0	.	6	99	1	100
	rockfall	2	71	2	94	56	71	10	68	0	.	23	32	6	32
	various	10	13	23	64	17	65	22	53	0	.	39	32	14	13
	indeterminable	39	6	72	50	65	26	40	39	0	.	142	13	50	6
	wood harvest	16	11	22	71	8	54	4	97	0	.	0	.	14	10
	other human activity	4	27	0	.	7	50	15	96	0	.	9	39	5	22
	weather	6	14	14	64	12	53	7	66	0	.	20	25	8	12
	lying living trees	1	26	5	96	3	71	4	97	0	.	15	39	3	24
	dead trees	34	8	66	26	67	22	86	33	0	.	157	13	49	7
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	287	2	312	4	273	5	284	5	267	4	296	5	288	2
	fire	0	.	0	.	0	.	0	.	0	100	4	50	1	49
	rockfall	6	20	21	15	29	16	19	17	13	19	25	11	16	7
	various	11	8	15	13	22	12	16	20	13	13	29	14	16	5
	indeterminable	43	4	71	5	67	6	79	6	96	5	93	6	67	2
	wood harvest	16	7	9	14	10	16	2	33	3	21	1	50	9	5
	other human activity	4	15	7	19	6	20	7	26	5	19	3	22	5	8
	weather	7	9	10	12	9	15	13	16	10	15	25	14	11	6
	lying living trees	1	24	2	27	5	27	6	26	4	30	7	21	3	11
	dead trees	37	5	73	6	73	8	83	8	63	8	84	7	62	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. 1345759. Birmensdorf, Swiss Federal Research Institute WSL

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