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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
growing stock (stemwood)
altitudinal vegetation belts (NaiS; 6 classes) · diameter at breast height (10 classes)
regional demarcation: biogeographical region
unit: 1000 m³
evaluation area: accessible forest without shrub forest
grid: 1.4 km grid, subgrids 1-5
state 2018/26
		biogeographical region
		Jura		Plateau		Northern Alps		Western Central-Alps		Eastern Central-Alps		Southern Alps		Switzerland
altitudinal vegetation belts (NaiS; 6 classes)	diameter at breast height (10 classes)	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%
n/a	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	21-30 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	31-40 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	41-50 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	51-60 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	61-70 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	71-80 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	81-90 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	91-100 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	>100 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	.	0	.	0	.	0	.	0	.	0	.	0	.
upper subalpine	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	0	.	0	.	0	.	266	43	349	19	156	26	771	18
	21-30 cm	0	.	0	.	0	.	329	29	649	21	344	29	1322	14
	31-40 cm	0	.	0	.	0	.	553	28	801	19	375	29	1729	14
	41-50 cm	0	.	0	.	0	.	543	27	920	21	209	32	1672	15
	51-60 cm	0	.	0	.	0	.	290	32	660	23	163	31	1113	16
	61-70 cm	0	.	0	.	0	.	205	37	269	33	38	73	512	23
	71-80 cm	0	.	0	.	0	.	167	38	241	39	0	.	408	28
	81-90 cm	0	.	0	.	0	.	69	75	198	61	75	71	341	41
	91-100 cm	0	.	0	.	0	.	57	71	48	100	38	100	143	51
	>100 cm	0	.	0	.	0	.	39	100	36	100	52	100	128	58
	total	0	.	0	.	0	.	2517	20	4170	15	1451	22	8138	10
subalpine	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	3	100	0	.	711	18	586	20	886	17	368	20	2554	9
	21-30 cm	14	100	0	.	1399	17	1075	18	1792	15	876	21	5156	8
	31-40 cm	0	100	0	.	2477	17	1389	19	2999	13	1025	19	7891	8
	41-50 cm	14	100	0	.	2735	16	1862	20	3443	13	1125	20	9178	8
	51-60 cm	33	100	0	.	1587	18	1706	18	2785	13	1214	20	7325	8
	61-70 cm	12	100	0	.	1110	20	1329	21	1852	19	514	24	4817	11
	71-80 cm	0	.	0	.	912	22	631	41	782	25	383	32	2709	15
	81-90 cm	0	.	0	.	203	42	301	49	485	42	456	38	1444	22
	91-100 cm	0	.	0	.	95	72	95	71	170	58	48	100	408	36
	>100 cm	0	.	0	.	74	71	0	.	237	58	0	.	311	47
	total	77	100	0	.	11302	13	8975	14	15430	10	6009	15	41793	6
high-montane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	62	65	0	.	1429	12	1299	14	1617	12	663	17	5070	6
	21-30 cm	46	77	0	.	2791	12	2691	15	3025	12	1318	14	9870	7
	31-40 cm	89	54	0	.	3963	11	3115	14	3409	12	2114	16	12689	6
	41-50 cm	43	71	0	.	4909	12	2868	14	4611	11	2268	14	14698	6
	51-60 cm	80	54	0	.	4549	12	2767	15	4121	13	2142	15	13659	7
	61-70 cm	100	80	0	.	3203	16	1030	22	2298	17	1420	19	8051	9
	71-80 cm	81	74	0	.	2007	18	770	29	1171	21	1165	26	5195	11
	81-90 cm	122	100	0	.	525	35	276	43	575	31	456	47	1953	19
	91-100 cm	71	100	0	.	461	36	188	50	226	51	206	58	1153	23
	>100 cm	0	.	0	.	100	71	64	100	123	71	203	73	491	40
	total	696	43	0	.	23937	9	15067	11	21176	9	11953	11	72829	4
lower and upper montane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	3325	7	1918	13	4827	7	196	30	411	21	1401	13	12079	4
	21-30 cm	6948	7	3842	11	11001	6	375	34	1004	23	2638	14	25808	4
	31-40 cm	10450	6	5398	10	15858	5	358	33	1246	20	2447	21	35757	4
	41-50 cm	12254	5	7582	9	18377	5	365	34	1439	19	2068	19	42087	3
	51-60 cm	10287	7	8117	10	18665	5	142	50	1384	20	1540	28	40135	4
	61-70 cm	5419	10	4351	13	11783	8	142	48	1039	21	831	22	23566	5
	71-80 cm	2494	15	2791	16	6670	10	0	.	560	34	410	33	12925	7
	81-90 cm	674	31	1791	20	1866	19	0	0	241	47	303	40	4875	11
	91-100 cm	269	50	346	47	597	32	21	100	0	.	212	58	1446	22
	>100 cm	255	59	72	100	370	48	0	.	0	.	111	100	808	33
	total	52375	4	36208	7	90015	4	1599	28	7326	15	11961	14	199485	2
submontane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	878	16	4513	7	691	26	36	100	94	36	0	.	6211	6
	21-30 cm	1764	14	7658	7	1065	23	25	100	186	39	0	.	10699	6
	31-40 cm	2743	13	9576	6	1338	20	0	.	169	45	0	.	13825	5
	41-50 cm	3004	12	11553	6	1306	22	0	.	203	40	0	.	16066	5
	51-60 cm	2160	16	11731	6	1242	22	0	.	244	42	0	.	15376	6
	61-70 cm	1432	20	7336	8	603	35	0	.	24	100	0	.	9395	7
	71-80 cm	485	31	3843	12	267	45	0	.	33	100	0	.	4629	11
	81-90 cm	53	100	1681	20	151	60	0	.	0	.	0	.	1885	19
	91-100 cm	0	.	605	33	0	.	0	.	52	100	0	.	657	31
	>100 cm	112	100	571	45	0	.	0	.	0	.	0	.	683	41
	total	12631	10	59068	4	6662	16	60	100	1005	35	0	.	79426	4
hyperinsubric and colline	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	0	.	76	42	0	.	238	27	0	.	1842	11	2156	10
	21-30 cm	0	.	212	44	0	.	328	28	0	.	3112	11	3652	10
	31-40 cm	0	.	234	42	0	.	271	31	0	.	2291	11	2796	10
	41-50 cm	0	.	195	41	0	.	170	38	0	.	1815	13	2181	12
	51-60 cm	0	.	90	65	0	.	155	71	0	.	983	19	1229	18
	61-70 cm	0	.	37	100	0	.	0	.	0	.	525	24	561	23
	71-80 cm	0	.	45	100	0	.	0	.	0	.	255	32	301	31
	81-90 cm	0	.	0	.	0	.	0	.	0	.	153	46	153	46
	91-100 cm	0	.	0	.	0	.	29	100	0	.	145	59	174	52
	>100 cm	0	.	0	.	0	.	0	.	0	.	411	55	411	55
	total	0	.	890	35	0	.	1192	26	0	.	11533	8	13615	7
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	4268	6	6507	6	7658	5	2620	10	3358	8	4430	6	28841	3
	21-30 cm	8773	6	11713	6	16256	5	4822	10	6656	8	8288	6	56508	2
	31-40 cm	13282	5	15208	5	23636	4	5686	10	8624	7	8252	8	74688	2
	41-50 cm	15316	4	19331	5	27327	4	5808	10	10616	7	7485	7	85882	2
	51-60 cm	12560	6	19939	5	26042	4	5061	10	9193	8	6042	9	78837	2
	61-70 cm	6964	9	11723	7	16698	6	2706	14	5482	10	3328	10	46901	3
	71-80 cm	3061	13	6680	9	9856	8	1568	22	2788	13	2214	16	26166	5
	81-90 cm	849	29	3473	14	2744	15	645	30	1499	21	1442	21	10652	8
	91-100 cm	340	45	951	27	1154	23	391	33	495	34	648	31	3980	12
	>100 cm	367	51	643	42	544	36	103	73	396	42	777	38	2830	18
	total	65779	3	96167	3	131916	3	29411	7	49106	5	42905	4	415285	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. 1321342. Birmensdorf, Swiss Federal Research Institute WSL

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