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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
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	.	316	37	301	57	198	12	259	8	216	11	236	6
	fire	0	.	0	.	0	.	0	.	0	.	0	99	0	100
	rockfall	0	.	0	.	0	.	11	24	3	42	19	51	8	25
	various	0	.	12	45	26	82	8	35	14	23	12	22	12	15
	indeterminable	0	.	99	26	106	41	72	14	103	10	81	13	90	7
	wood harvest	0	.	0	.	0	.	3	52	0	76	0	.	1	45
	other human activity	0	.	5	66	0	.	10	45	2	53	3	67	5	32
	weather	0	.	0	.	16	82	14	24	6	25	34	36	14	19
	lying living trees	0	.	0	.	0	.	5	55	10	38	5	47	7	28
	dead trees	0	.	109	48	17	81	62	18	67	14	48	25	63	10
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
1601-1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	295	16	222	32	277	13	274	9	240	12	269	6
	fire	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	rockfall	0	.	16	33	0	.	7	34	10	33	10	51	10	19
	various	0	.	18	38	34	53	8	28	13	27	17	30	15	16
	indeterminable	0	.	93	15	81	33	99	13	88	11	56	17	85	7
	wood harvest	0	.	3	99	0	.	0	99	1	45	1	99	1	49
	other human activity	0	.	4	53	13	90	9	50	7	39	2	60	6	26
	weather	0	.	11	31	3	74	19	40	10	30	14	20	13	17
	lying living trees	0	.	6	60	3	96	3	46	2	73	1	99	3	34
	dead trees	0	.	90	22	44	40	93	22	45	15	32	20	63	11
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
1401-1600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	174	17	262	10	258	13	284	11	295	10	342	12	281	5
	fire	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	rockfall	2	97	21	37	5	45	18	39	16	43	19	32	16	19
	various	23	41	8	28	15	45	11	29	6	41	23	20	12	13
	indeterminable	40	20	90	9	65	18	85	13	85	11	72	14	80	5
	wood harvest	1	97	3	47	3	84	2	55	4	41	1	99	2	25
	other human activity	0	.	9	35	5	83	32	74	6	36	2	70	10	39
	weather	4	75	9	24	10	49	16	27	9	28	19	22	11	12
	lying living trees	0	.	1	58	9	56	9	58	3	52	5	51	4	28
	dead trees	30	58	84	13	73	28	73	16	73	21	68	16	74	8
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
1201-1400 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	270	11	295	9	241	9	363	12	272	14	247	14	279	5
	fire	0	.	0	.	0	.	0	.	0	.	2	99	0	100
	rockfall	7	86	25	27	41	31	29	37	19	51	34	24	26	15
	various	14	27	13	27	24	23	47	44	8	44	21	26	20	15
	indeterminable	46	14	80	10	64	11	58	17	112	16	71	14	71	5
	wood harvest	5	42	4	41	7	45	0	.	8	43	3	49	5	21
	other human activity	4	39	8	43	5	46	1	99	11	46	1	75	5	23
	weather	12	42	10	24	10	39	6	48	13	44	16	25	11	14
	lying living trees	0	.	1	70	9	54	5	44	0	.	6	37	4	31
	dead trees	39	22	81	14	85	16	83	17	87	18	54	21	72	7
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
1001-1200 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	309	6	321	7	270	10	304	11	236	18	289	12	296	4
	fire	0	.	0	.	0	.	0	.	0	99	3	90	0	84
	rockfall	9	35	30	27	29	32	25	49	36	41	38	25	25	14
	various	11	25	10	26	27	27	16	33	23	45	19	38	16	13
	indeterminable	41	11	57	12	71	11	67	20	103	23	74	15	62	6
	wood harvest	18	18	10	27	15	28	1	99	3	80	0	99	10	13
	other human activity	4	36	5	49	11	37	1	69	4	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	10	64	1	99	7	59	3	31
	dead trees	37	16	63	12	76	18	83	21	56	22	54	22	58	7
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
801-1000 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	337	5	331	8	296	9	338	15	210	19	383	18	325	4
	fire	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	rockfall	20	32	11	49	42	27	41	61	9	57	34	26	24	16
	various	9	21	17	19	17	20	10	50	12	40	29	37	15	12
	indeterminable	57	10	48	13	58	13	96	19	86	21	112	19	65	6
	wood harvest	17	20	13	30	15	28	4	98	9	45	0	.	13	14
	other human activity	6	32	8	42	7	34	1	98	5	72	5	41	6	19
	weather	8	23	8	33	10	24	5	68	23	41	32	53	11	19
	lying living trees	0	.	3	50	1	61	2	98	2	98	12	57	2	35
	dead trees	41	12	61	15	71	14	87	23	46	21	113	19	62	7
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
601-800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	300	5	326	7	291	13	242	37	263	15	285	14	298	4
	fire	0	.	0	.	0	.	0	.	0	.	27	68	2	69
	rockfall	6	34	24	42	19	43	30	57	18	68	25	26	12	18
	various	12	17	31	37	26	31	16	76	21	23	78	38	22	15
	indeterminable	43	8	58	13	74	16	61	38	70	24	129	15	56	6
	wood harvest	18	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	55	5	81	49	40	9	20
	lying living trees	1	53	1	70	4	48	7	65	0	.	6	42	2	24
	dead trees	40	9	52	19	65	19	97	26	51	29	146	17	55	7
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
=600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	258	4	417	25	269	19	256	25	100	0	303	14	265	3
	fire	0	.	0	.	0	.	0	.	0	.	6	99	1	100
	rockfall	2	71	2	94	54	71	10	68	0	.	22	32	6	32
	various	10	13	23	64	16	65	22	53	0	.	38	32	14	13
	indeterminable	39	6	72	50	62	26	40	39	0	.	140	14	50	6
	wood harvest	16	11	22	71	8	54	4	97	0	.	0	.	14	10
	other human activity	4	25	0	.	7	50	15	96	0	.	9	39	5	20
	weather	6	14	14	64	12	53	7	66	0	.	20	26	8	12
	lying living trees	1	26	5	96	3	71	4	97	0	.	15	39	3	24
	dead trees	33	8	66	26	64	23	86	33	0	.	154	13	48	7
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	285	2	307	4	269	5	275	5	266	4	288	5	284	2
	fire	0	.	0	.	0	.	0	.	0	100	4	50	1	49
	rockfall	6	19	21	14	30	16	18	17	13	19	25	11	16	6
	various	11	8	15	13	22	12	15	20	13	13	28	14	16	5
	indeterminable	43	4	70	5	67	6	77	6	94	5	90	6	67	2
	wood harvest	16	7	8	15	9	16	1	33	3	21	1	50	9	5
	other human activity	5	14	6	18	7	21	11	41	5	19	3	22	6	10
	weather	6	9	10	12	9	15	13	15	10	15	24	14	11	6
	lying living trees	1	24	2	26	5	27	6	25	4	29	7	20	3	10
	dead trees	37	5	72	6	72	8	79	8	62	8	82	7	60	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. 1345764. Birmensdorf, Swiss Federal Research Institute WSL

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