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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: 1000 n
evaluation area: accessible forest without shrub forest NFI1-NFI5
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	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%
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	.	69	100	14488	10	1706	27	16263	10
	one visible damage	0	.	0	.	7	100	4593	11	512	34	5112	11
	two or more visible damages	0	.	0	.	66	100	2216	15	384	34	2665	14
	dead or lying tree	0	.	0	.	0	0	450	40	0	0	450	40
	total	0	.	0	.	142	100	21746	10	2602	25	24491	9
1601-1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	0	.	3847	31	15067	11	4120	19	23034	9
	one visible damage	0	.	0	.	693	30	4683	11	989	21	6365	10
	two or more visible damages	0	.	0	.	424	41	2431	13	432	27	3287	12
	dead or lying tree	0	.	0	.	101	75	49	54	0	0	151	53
	total	0	.	0	.	5064	29	22231	10	5540	18	32836	9
1401-1600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	571	39	386	53	6694	18	19914	9	5943	19	33509	7
	one visible damage	183	40	61	61	1997	16	5179	10	1537	21	8956	8
	two or more visible damages	91	55	0	.	825	23	3141	12	590	22	4646	9
	dead or lying tree	0	0	0	0	37	72	286	44	18	100	341	38
	total	845	37	446	53	9552	15	28520	8	8088	18	47452	7
1201-1400 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	5032	16	207	78	9742	12	14103	11	4695	20	33778	7
	one visible damage	1126	19	39	82	2595	13	3776	11	1572	17	9109	7
	two or more visible damages	375	25	27	100	1532	18	2312	15	817	23	5062	10
	dead or lying tree	0	0	0	0	42	62	184	39	108	43	334	27
	total	6533	15	273	75	13911	11	20375	10	7191	17	48282	6
1001-1200 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	12295	10	913	41	12946	10	11366	12	5567	19	43088	6
	one visible damage	2315	12	123	54	3083	12	3506	13	1669	18	10695	7
	two or more visible damages	995	17	89	79	1549	16	2136	16	1002	22	5771	9
	dead or lying tree	0	0	0	0	113	54	158	59	43	71	314	37
	total	15604	9	1125	39	17691	10	17165	11	8282	17	59867	5
801-1000 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	12486	10	5432	19	16902	10	8417	13	5562	26	48799	6
	one visible damage	3001	15	850	24	3313	12	2752	14	2069	23	11984	7
	two or more visible damages	1549	17	397	25	1476	16	1631	18	985	26	6038	9
	dead or lying tree	0	0	0	0	94	55	66	48	188	63	348	38
	total	17035	10	6679	18	21786	9	12866	12	8804	23	67170	6
601-800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	12766	11	22623	8	10558	12	6132	16	4497	20	56576	5
	one visible damage	2525	12	4267	11	2754	15	1853	17	2513	22	13911	7
	two or more visible damages	1162	19	1843	12	1260	18	757	22	1697	22	6719	8
	dead or lying tree	35	100	50	58	96	44	52	58	98	44	330	25
	total	16488	10	28783	8	14668	11	8793	15	8805	17	77536	5
=600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	13193	10	32583	6	1693	32	2790	26	6220	18	56479	5
	one visible damage	2984	12	5461	7	504	43	441	29	2168	16	11558	6
	two or more visible damages	1225	14	2873	10	414	48	214	35	1869	21	6595	8
	dead or lying tree	152	34	97	41	21	74	34	71	323	41	627	24
	total	17552	9	41015	5	2633	34	3479	25	10580	15	75259	4
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	56342	3	62145	3	62452	4	92277	3	38310	6	311526	2
	one visible damage	12133	5	10801	5	14945	5	26781	4	13029	6	77689	2
	two or more visible damages	5395	7	5229	7	7545	7	14837	5	7775	8	40782	3
	dead or lying tree	186	33	147	34	503	24	1279	20	779	24	2895	12
	total	74057	3	78322	3	85446	4	135175	3	59893	5	432892	2

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. 1198801. Birmensdorf, Swiss Federal Research Institute WSL

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