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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 NFI4/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	5625	14	310	35	1099	33	28900	7	3332	20	6417	14	307	54	1947	22	29549	7	4624	14	8884	13	4767	15	1685	35	4454	20	7959	14	1773	27	5210	18	4352	19	3528	17	28616	7	3955	20	16723	10	21392	8	453	36	6791	14	202653	2
21-30 cm	2976	15	421	35	933	29	16113	7	1573	20	4530	14	121	65	1219	23	17828	6	2424	15	4446	12	2887	14	1385	32	2643	20	5369	13	1067	24	2672	15	2630	18	2299	17	16613	7	2805	17	8638	10	12530	8	464	35	3883	13	118470	2
31-40 cm	1425	16	623	28	828	26	10010	6	1061	20	3078	14	110	60	697	22	10558	6	1723	16	2745	12	1455	18	773	32	1736	19	3741	12	848	23	1909	17	1564	17	1331	21	7094	8	1492	20	5319	9	6582	8	350	32	2382	12	69435	2
41-50 cm	1129	14	413	28	445	27	6800	6	535	22	1731	13	57	58	657	21	6643	6	1418	15	1725	12	1164	13	358	30	783	20	2228	12	534	21	1123	14	1140	16	758	18	3312	8	833	22	3552	9	3744	9	256	34	1663	12	43001	2
51-60 cm	720	15	279	31	371	30	4247	7	321	22	1063	14	22	100	410	22	3713	7	721	16	1381	13	722	15	97	39	418	24	1454	12	189	25	571	18	794	16	429	19	1780	13	360	23	1865	9	2141	9	135	36	993	13	25195	2
61-70 cm	259	20	121	34	91	42	1819	9	108	30	305	18	7	100	164	30	1561	9	339	20	511	18	289	22	98	39	126	35	776	16	121	29	155	29	268	25	220	23	599	12	180	26	988	13	901	13	28	71	466	16	10501	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	339	19	51	42	82	37	134	31	60	45	332	18	64	46	313	17	438	17	14	71	177	24	4562	5
81-90 cm	53	39	7	100	0	.	203	21	7	100	62	39	0	.	35	45	319	19	15	71	37	45	60	39	0	.	21	77	146	25	0	.	14	71	35	51	55	43	152	24	32	51	67	34	145	26	11	100	65	34	1541	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	.	26	60	0	.	7	100	14	71	21	58	66	42	0	.	37	45	80	30	0	.	14	71	529	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	.	0	.	7	100	30	71	76	42	0	.	14	71	14	71	0	.	0	.	299	18
total	12403	11	2195	28	3803	24	68944	5	7005	16	17365	11	632	48	5283	18	70961	5	11387	12	19942	10	11500	11	4422	28	10298	16	22059	10	4584	19	11742	13	10938	13	8732	14	58641	5	9721	16	37517	7	47968	6	1710	29	16434	10	476187	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. 1304253. Birmensdorf, Swiss Federal Research Institute WSL

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