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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
diameter at breast height (10 classes)
regional demarcation: canton
unit: 1000 n
evaluation area: accessible forest without shrub forest NFI1-NFI5
grid: 1.4 km grid, subgrids 1-5
state 2018/26
	canton
	AG		AI		AR		BE		BL/BS		FR		GE		GL		GR		JU		LU		NE		NW		OW		SG		SH		SO		SZ		TG		TI		UR		VD		VS		ZG		ZH		Switzerland
diameter at breast height (10 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	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%
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	.
12-20 cm	5532	14	257	37	1099	33	26895	7	3238	21	5560	15	190	61	1706	25	23334	8	4624	14	8712	13	4767	15	1561	37	4079	22	7194	15	1773	27	5176	18	3327	22	3528	17	23683	8	3238	21	15578	10	18513	8	408	38	6537	14	180509	2
21-30 cm	2953	15	367	38	933	29	15109	7	1454	20	4127	14	121	65	1148	24	14240	7	2424	15	4357	12	2887	14	1272	34	2516	21	4950	14	1067	24	2654	15	2051	20	2299	17	14386	7	2429	19	7921	10	10985	9	419	37	3794	14	106866	2
31-40 cm	1415	16	590	29	828	26	9565	7	1010	20	2780	14	110	60	669	23	9141	7	1723	16	2680	13	1455	18	766	33	1560	21	3423	12	848	23	1902	17	1471	18	1325	21	6318	9	1389	21	5115	9	5879	9	293	35	2342	12	64597	2
41-50 cm	1118	14	405	29	445	27	6421	6	506	22	1646	13	57	58	599	22	5900	6	1418	15	1643	12	1164	13	337	32	776	20	2000	12	534	21	1102	15	1040	17	751	18	3094	8	788	23	3446	9	3469	9	184	38	1656	12	40500	2
51-60 cm	699	15	249	33	371	30	4055	7	311	23	1050	14	22	100	390	23	3439	7	721	16	1346	13	722	15	97	39	411	24	1328	12	189	25	564	18	743	16	429	19	1663	14	338	24	1776	10	2027	10	80	36	993	13	24013	2
61-70 cm	259	20	106	36	91	42	1724	9	91	33	305	18	7	100	164	30	1439	9	339	20	511	18	281	23	91	42	119	36	678	17	121	29	148	30	262	25	220	23	576	13	164	27	941	13	835	13	28	71	459	17	9961	3
71-80 cm	185	21	22	58	36	45	699	12	57	43	162	25	7	100	106	41	599	12	101	36	199	23	141	23	19	58	111	38	318	20	51	42	75	39	128	32	60	45	318	19	64	46	291	18	398	19	14	71	177	24	4338	5
81-90 cm	53	39	7	100	0	.	203	21	7	100	62	39	0	.	27	50	272	20	15	71	28	50	60	39	0	.	21	77	133	26	0	.	14	71	35	51	55	43	115	27	32	51	60	36	128	28	0	.	65	34	1393	8
91-100 cm	20	58	0	.	0	.	74	32	0	.	0	.	0	.	35	45	85	31	7	100	0	.	8	100	0	.	0	.	26	60	0	.	7	100	14	71	21	58	59	46	0	.	23	58	73	31	0	.	14	71	465	13
>100 cm	0	.	0	.	0	.	35	45	0	.	7	100	0	.	7	100	44	41	14	71	7	100	8	100	0	.	0	.	14	71	0	.	0	.	7	100	16	100	69	45	0	.	7	100	14	71	0	.	0	.	251	20
total	12234	11	2003	29	3803	24	64780	5	6674	16	15699	11	515	54	4852	19	58492	6	11387	12	19483	10	11493	11	4143	30	9593	17	20065	11	4584	19	11641	13	9080	14	8705	14	50282	6	8442	17	35159	8	42322	7	1426	32	16036	10	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. 1304242. Birmensdorf, Swiss Federal Research Institute WSL

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