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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
altitude (in 200 m classes) · number of cases of damage
regional demarcation: production region
unit: n/ha
evaluation area: accessible forest without shrub forest
grid: 1.4 km grid, subgrids 1-5
state 2018/26
		production region
		Jura		Plateau		Pre-Alps		Alps		Southern Alps		Switzerland
altitude (in 200 m classes)	number of cases of damage	n/ha	±%	n/ha	±%	n/ha	±%	n/ha	±%	n/ha	±%	n/ha	±%
n/a	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	0	.	0	.	0	.	0	.	0	.
	one visible damage	0	.	0	.	0	.	0	.	0	.	0	.
	two or more visible damages	0	.	0	.	0	.	0	.	0	.	0	.
	dead or lying tree	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	.	0	.	0	.	0	.	0	.	0	.
>1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	0	.	803	52	235	7	216	11	236	6
	one visible damage	0	.	0	.	31	25	80	7	87	21	81	7
	two or more visible damages	0	.	0	.	94	72	37	11	45	19	39	10
	dead or lying tree	0	.	0	.	0	.	7	32	5	47	7	28
	total	0	.	0	.	927	39	359	6	353	10	362	5
1601-1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	0	.	385	23	260	7	240	12	269	6
	one visible damage	0	.	0	.	71	21	82	8	59	16	76	7
	two or more visible damages	0	.	0	.	48	31	44	10	30	20	41	9
	dead or lying tree	0	.	0	.	11	62	2	39	1	99	3	34
	total	0	.	0	.	515	19	388	6	329	11	390	5
1401-1600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	154	19	225	29	265	13	278	6	342	12	281	5
	one visible damage	51	21	35	43	79	11	77	9	88	15	78	6
	two or more visible damages	22	43	0	.	34	19	49	9	34	15	42	7
	dead or lying tree	0	.	0	.	1	71	6	34	5	51	4	28
	total	226	17	261	29	380	10	410	5	468	9	405	4
1201-1400 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	275	12	201	32	268	8	302	7	247	14	279	5
	one visible damage	56	14	102	62	76	9	85	8	85	10	78	5
	two or more visible damages	18	22	55	57	43	15	57	14	44	17	45	9
	dead or lying tree	0	.	0	.	1	61	6	43	6	37	4	31
	total	349	10	358	28	388	6	450	6	382	10	406	4
1001-1200 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	309	6	296	23	302	7	282	7	289	12	296	4
	one visible damage	59	9	40	44	74	9	94	10	87	12	77	5
	two or more visible damages	25	15	29	72	42	14	52	13	50	16	41	7
	dead or lying tree	0	.	0	.	2	53	5	47	7	59	3	31
	total	394	5	365	20	420	6	434	6	433	9	418	3
801-1000 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	321	6	379	11	338	7	260	8	383	18	325	4
	one visible damage	75	12	62	18	65	9	92	10	130	16	80	6
	two or more visible damages	40	14	29	20	33	14	55	14	64	19	42	7
	dead or lying tree	0	.	0	.	2	54	2	42	12	57	2	35
	total	436	6	470	10	437	5	409	7	588	15	450	3
601-800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	306	7	297	6	322	8	265	11	285	14	298	4
	one visible damage	62	9	56	9	83	12	81	13	158	17	73	6
	two or more visible damages	28	17	24	10	38	16	32	19	108	16	35	7
	dead or lying tree	1	100	1	57	3	43	2	57	6	42	2	24
	total	397	6	377	5	446	7	381	9	558	10	409	3
=600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	260	7	257	4	262	22	310	17	303	14	265	3
	one visible damage	59	10	44	6	78	36	56	20	103	11	55	5
	two or more visible damages	25	12	23	9	64	42	32	31	95	16	32	8
	dead or lying tree	3	33	1	41	3	70	3	69	15	39	3	24
	total	347	6	325	4	408	24	401	14	516	9	355	3
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	291	3	279	3	307	4	269	3	288	5	284	2
	one visible damage	63	5	49	5	74	4	83	3	97	5	73	2
	two or more visible damages	28	7	24	7	39	7	46	5	57	7	39	3
	dead or lying tree	1	33	1	33	2	24	5	16	7	20	3	10
	total	383	3	353	3	423	3	402	2	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. 1374679. Birmensdorf, Swiss Federal Research Institute WSL

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