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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: economic region
unit: n/ha
evaluation area: accessible forest without shrub forest NFI1-NFI5
grid: 1.4 km grid, subgrids 1-5
state 2018/26
		economic region
		Western Jura		Eastern Jura		Western Plateau		Central Plateau		Eastern Plateau		Western Pre-Alps		Central Pre-Alps		Eastern Pre-Alps		Northwestern Alps		Central Alps		Northeastern Alps		Southwestern Alps		Southeastern 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/ha	±%	n/ha	±%	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	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	one visible damage	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	two or more visible damages	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	dead or lying tree	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
>1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	0	.	0	.	0	.	0	.	0	.	200	0	0	.	345	33	0	.	0	.	248	11	276	9	249	15	265	7
	one visible damage	0	.	0	.	0	.	0	.	0	.	0	.	20	0	0	.	108	29	0	.	0	.	74	13	91	12	75	26	83	8
	two or more visible damages	0	.	0	.	0	.	0	.	0	.	0	.	190	0	0	.	42	37	0	.	0	.	49	21	36	17	56	25	44	12
	dead or lying tree	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	5	69	11	47	0	.	7	40
	total	0	.	0	.	0	.	0	.	0	.	0	.	410	0	0	.	494	26	0	.	0	.	375	9	414	9	379	12	400	6
1601-1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	0	.	0	.	0	.	0	.	320	38	600	27	620	0	222	16	146	16	416	40	319	14	289	10	271	12	309	7
	one visible damage	0	.	0	.	0	.	0	.	0	.	85	48	104	20	0	.	85	22	142	15	41	27	105	14	81	13	65	15	85	7
	two or more visible damages	0	.	0	.	0	.	0	.	0	.	53	50	63	46	0	.	51	36	76	52	6	60	48	15	47	17	28	23	44	10
	dead or lying tree	0	.	0	.	0	.	0	.	0	.	0	.	17	88	50	0	0	.	0	.	0	.	3	52	0	.	0	.	2	53
	total	0	.	0	.	0	.	0	.	0	.	458	40	785	22	670	0	358	13	364	14	463	37	474	12	417	8	364	10	440	6
1401-1600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	171	21	0	.	225	29	0	.	0	.	297	30	261	16	295	23	265	14	399	21	209	20	308	12	301	10	380	13	299	5
	one visible damage	55	23	0	.	35	43	0	.	0	.	89	22	94	12	52	39	68	16	120	21	70	25	81	13	74	11	98	16	80	6
	two or more visible damages	27	43	0	.	0	.	0	.	0	.	51	35	34	21	12	45	50	20	38	30	43	44	49	19	45	16	38	17	41	8
	dead or lying tree	0	.	0	.	0	.	0	.	0	.	5	68	0	.	0	.	1	99	0	.	9	64	10	63	2	57	1	99	3	37
	total	254	18	0	.	261	29	0	.	0	.	442	22	389	11	358	23	384	11	558	21	331	21	448	9	422	8	518	11	424	4
1201-1400 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	262	10	0	.	281	38	0	.	0	.	319	13	279	15	224	13	308	17	274	22	229	23	379	12	273	15	274	14	284	5
	one visible damage	59	14	0	.	53	47	0	.	0	.	63	16	86	15	68	16	81	17	66	19	82	18	67	17	107	13	92	11	77	5
	two or more visible damages	20	22	0	.	37	66	0	.	0	.	65	27	34	26	32	25	40	24	34	40	108	25	39	27	56	26	48	19	43	9
	dead or lying tree	0	.	0	.	0	.	0	.	0	.	0	.	3	68	0	99	0	.	7	97	18	53	4	50	0	.	6	40	3	26
	total	340	8	0	.	371	29	0	.	0	.	447	10	402	11	324	10	428	14	380	20	437	13	489	10	436	11	420	10	406	4
1001-1200 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	318	6	0	.	411	27	293	23	139	35	340	17	309	9	242	13	320	17	377	16	300	26	309	11	261	21	307	13	306	4
	one visible damage	60	9	0	.	38	75	10	69	62	49	65	16	72	15	70	15	92	19	147	24	115	18	73	15	81	27	92	12	76	5
	two or more visible damages	26	15	0	.	54	77	0	.	13	82	27	26	37	19	37	27	35	34	86	26	57	31	42	30	80	26	55	17	41	8
	dead or lying tree	0	.	0	.	0	.	0	.	0	.	2	99	2	99	4	75	2	98	0	.	0	.	12	72	2	98	2	70	2	37
	total	404	5	0	.	503	22	303	20	215	27	433	15	419	8	354	10	449	12	610	13	472	20	436	10	424	16	457	10	425	3
801-1000 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	322	7	329	11	292	18	418	18	429	27	268	24	339	10	354	10	321	12	321	28	148	23	362	15	215	20	415	21	328	4
	one visible damage	80	13	56	30	42	32	72	23	61	48	48	31	69	13	68	14	72	20	136	24	76	19	98	22	80	18	154	16	81	6
	two or more visible damages	42	15	20	35	29	36	16	30	45	25	23	25	32	22	28	20	19	32	75	51	74	25	62	36	44	21	73	20	41	8
	dead or lying tree	0	.	0	.	0	.	0	.	0	.	0	.	4	54	0	.	1	97	0	.	4	74	3	97	2	98	14	61	2	38
	total	444	6	406	12	362	18	507	16	535	21	339	19	444	8	449	9	414	12	533	20	301	14	524	12	341	16	656	16	452	4
601-800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	339	8	245	13	324	15	324	9	258	8	409	20	329	9	300	15	316	13	316	40	245	34	324	36	263	15	289	14	304	4
	one visible damage	64	10	60	21	64	20	55	16	53	14	99	45	82	17	85	17	110	28	121	34	61	42	77	22	81	20	162	17	75	6
	two or more visible damages	26	15	39	45	21	22	25	17	25	17	11	92	43	24	37	19	29	30	58	34	24	51	60	39	29	36	109	17	36	7
	dead or lying tree	0	.	4	98	0	.	0	.	2	57	0	.	2	69	5	54	0	.	0	.	4	96	10	63	0	.	6	42	2	24
	total	429	7	349	10	409	12	404	9	338	7	519	18	457	8	427	12	454	12	496	32	334	35	470	23	372	11	566	10	417	3
=600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	252	10	278	9	279	12	285	7	244	5	0	.	383	34	215	26	463	36	563	23	165	24	288	24	100	0	331	14	272	3
	one visible damage	65	17	57	13	48	19	36	12	47	8	0	.	53	80	88	39	133	20	77	23	85	13	23	38	0	.	115	11	56	5
	two or more visible damages	28	18	22	16	28	19	18	16	25	13	0	.	19	44	82	44	61	39	19	55	0	.	24	39	0	.	99	16	32	8
	dead or lying tree	3	51	3	43	0	.	0	.	1	41	0	.	0	.	5	69	11	90	0	.	0	.	4	96	0	.	17	39	3	24
	total	348	9	361	8	355	11	339	6	318	5	0	.	455	37	390	30	668	23	659	19	250	11	339	22	100	0	562	9	363	3
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	304	3	276	7	301	8	310	6	253	5	316	9	326	5	285	6	293	6	337	10	240	12	311	5	277	5	317	5	297	2
	one visible damage	66	5	58	10	53	13	46	9	50	7	69	10	78	6	71	8	84	8	115	11	79	10	80	6	84	6	108	6	74	2
	two or more visible damages	29	8	26	18	25	14	20	11	25	10	43	16	38	10	34	12	41	11	57	17	58	15	47	9	45	8	64	7	39	3
	dead or lying tree	0	52	3	41	0	.	0	.	1	33	1	58	3	36	2	37	1	51	2	99	6	37	6	29	4	39	6	24	3	12
	total	399	3	362	6	380	7	376	5	329	4	429	7	445	4	393	5	419	5	510	8	383	9	444	4	410	4	496	4	412	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. 1374645. Birmensdorf, Swiss Federal Research Institute WSL

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