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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
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	5625	14	310	35	1099	33	29559	7	3332	20	6506	14	307	54	1947	22	30481	7	4624	14	9110	13	4767	15	1685	35	4454	20	8351	13	1773	27	5242	18	4352	19	3632	17	29015	7	4086	19	16777	10	22355	7	453	36	6791	14	206634	2
21-30 cm	2976	15	421	35	933	29	16419	7	1573	20	4530	14	121	65	1219	23	18648	6	2424	15	4479	12	2887	14	1385	32	2643	20	5387	13	1067	24	2672	15	2703	18	2299	17	16715	6	2919	17	8667	10	12941	8	464	35	3883	13	120376	2
31-40 cm	1425	16	623	28	828	26	10218	6	1061	20	3078	14	110	60	828	24	10650	6	1723	16	2788	12	1472	17	773	32	1736	19	3788	12	848	23	1909	17	1604	17	1331	21	7148	8	1541	20	5354	9	6882	8	350	32	2382	12	70450	2
41-50 cm	1129	14	413	28	445	27	6875	6	535	22	1800	13	57	58	745	22	6720	6	1418	15	1771	12	1203	13	358	30	783	20	2305	12	534	21	1180	14	1155	16	758	18	3336	8	840	22	3607	8	3792	9	256	34	1663	12	43678	2
51-60 cm	720	15	279	31	371	30	4346	6	321	22	1091	13	22	100	410	22	3734	7	721	16	1394	13	746	15	97	39	418	24	1478	12	189	25	595	18	808	16	429	19	1795	13	360	23	1865	9	2166	9	135	36	993	13	25483	2
61-70 cm	259	20	121	34	91	42	1842	8	108	30	305	18	7	100	164	30	1574	9	339	20	511	18	289	22	98	39	126	35	791	16	121	29	167	28	268	25	220	23	606	12	180	26	988	13	901	13	28	71	466	16	10572	3
71-80 cm	195	21	22	58	36	45	732	11	68	39	162	25	7	100	112	39	631	12	101	36	206	22	141	23	26	50	118	36	346	19	51	42	94	35	134	31	60	45	347	18	81	42	320	17	438	17	14	71	177	24	4620	5
81-90 cm	53	39	7	100	0	.	211	20	7	100	62	39	0	.	35	45	319	19	15	71	37	45	60	39	0	.	21	77	162	24	0	.	14	71	35	51	55	43	159	24	32	51	67	34	145	26	11	100	65	34	1571	8
91-100 cm	20	58	0	.	0	.	83	30	0	.	9	100	0	.	35	45	102	29	7	100	0	.	8	100	0	.	0	.	33	52	0	.	19	73	14	71	21	58	66	42	0	.	37	45	80	30	0	.	14	71	549	12
>100 cm	0	.	0	.	0	.	35	45	0	.	7	100	0	.	7	100	59	35	14	71	7	100	8	100	0	.	0	.	21	58	0	.	11	100	7	100	30	71	76	42	0	.	14	71	14	71	0	.	0	.	311	17
total	12403	11	2195	28	3803	24	70319	5	7005	16	17550	11	632	48	5501	18	72916	5	11387	12	20305	10	11580	11	4422	28	10298	16	22663	10	4584	19	11903	13	11081	13	8836	14	59262	5	10041	16	37697	7	49715	6	1710	29	16434	10	484244	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. 1304263. Birmensdorf, Swiss Federal Research Institute WSL

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