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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 deadwood stems
deadwood: mechanical strength of wood (3 classes) · deadwood: colonization by shrubs (5 classes)
regional demarcation: economic region
unit: 1000 n
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
deadwood: mechanical strength of wood (3 classes)	deadwood: colonization by shrubs (5 classes)	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%
n/a	n/a	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
	0-1	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	2-10	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	11-20	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	21-50	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	>50	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	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
fresh/firm wood	n/a	3167	11	900	21	751	23	617	20	1035	19	888	22	2324	15	2090	15	1441	19	572	22	713	25	2821	13	2890	12	5852	11	26060	4
	0-1	1347	17	616	25	325	27	269	40	549	18	411	22	1126	18	744	19	1026	20	203	44	728	39	2452	12	2344	17	2710	14	14851	5
	2-10	0	.	0	.	0	.	0	.	7	100	0	.	0	.	18	100	0	.	0	.	0	.	0	.	7	100	0	.	32	64
	11-20	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	7	100	0	.	7	100
	21-50	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	>50	0	.	0	.	0	.	0	.	0	.	0	.	15	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	15	100
	total	4515	9	1517	17	1076	21	886	19	1590	16	1299	19	3466	14	2851	14	2467	16	775	22	1441	25	5273	11	5248	12	8561	9	40966	4
rotten wood	n/a	502	20	62	45	58	56	132	34	187	33	163	40	616	27	622	17	303	25	320	29	174	41	389	22	290	24	646	18	4465	7
	0-1	1246	15	321	25	306	28	345	27	517	24	785	20	1081	16	888	26	1046	22	243	34	437	23	1818	14	1495	16	1122	16	11652	5
	2-10	17	100	0	.	0	.	17	100	0	.	6	100	0	.	0	.	0	.	0	.	0	.	0	.	14	71	0	.	54	50
	11-20	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	21-50	0	.	0	.	0	.	0	.	0	.	0	.	48	73	0	.	0	.	0	.	0	.	0	.	0	.	0	.	48	73
	>50	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	1766	13	383	24	364	26	495	21	704	20	954	19	1745	14	1510	18	1349	19	563	29	611	22	2208	14	1799	15	1768	13	16219	5
mouldering/mull wood	n/a	176	42	7	100	20	74	37	77	7	100	33	52	164	37	116	46	62	45	73	50	39	61	79	45	51	55	215	37	1078	15
	0-1	981	15	101	46	196	34	284	23	375	25	941	24	970	17	630	22	699	29	175	32	200	31	1017	17	1085	15	1083	18	8738	6
	2-10	0	.	0	.	0	.	0	.	17	100	6	100	34	65	9	100	21	100	0	.	7	100	0	.	38	55	0	.	132	32
	11-20	0	.	0	.	0	.	0	.	0	.	0	.	0	.	9	100	7	100	0	.	0	.	0	.	0	.	0	.	16	71
	21-50	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	>50	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	1156	14	108	44	216	33	321	22	399	25	980	23	1167	16	764	21	789	27	248	31	247	31	1097	16	1174	14	1298	16	9964	6
total	n/a	3846	10	969	21	828	22	786	17	1229	17	1085	20	3104	14	2828	13	1805	16	965	20	926	24	3289	13	3231	12	6713	10	31603	4
	0-1	3574	10	1038	19	827	20	899	19	1441	14	2137	18	3178	12	2262	18	2772	16	621	25	1365	24	5288	11	4924	12	4915	10	35241	4
	2-10	17	100	0	.	0	.	17	100	24	77	12	71	34	65	27	75	21	100	0	.	7	100	0	.	59	41	0	.	218	25
	11-20	0	.	0	.	0	.	0	.	0	.	0	.	0	.	9	100	7	100	0	.	0	.	0	.	7	100	0	.	23	58
	21-50	0	.	0	.	0	.	0	.	0	.	0	.	48	73	0	.	0	.	0	.	0	.	0	.	0	.	0	.	48	73
	>50	0	.	0	.	0	.	0	.	0	.	0	.	15	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	15	100
	total	7437	8	2007	16	1656	18	1702	14	2693	12	3234	15	6379	11	5125	13	4605	13	1587	20	2299	19	8577	10	8222	10	11627	8	67148	3

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. 1411553. Birmensdorf, Swiss Federal Research Institute WSL

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