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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: protection forest region
unit: 1000 m³
evaluation area: accessible forest without shrub forest
grid: 1.4 km grid, subgrids 1-5
state 2018/26
		protection forest region
		Jura + Plateau		Northwestern Alps		Northeastern Alps		Southwestern Alps		Southeastern 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	350	19	155	26	771	18
	21-30 cm	0	.	0	.	0	.	329	29	663	20	330	30	1322	14
	31-40 cm	0	.	0	.	0	.	553	28	815	19	361	30	1729	14
	41-50 cm	0	.	0	.	0	.	543	27	920	21	209	32	1672	15
	51-60 cm	0	.	0	.	0	.	290	32	676	23	147	32	1113	16
	61-70 cm	0	.	0	.	0	.	205	37	293	31	14	100	512	23
	71-80 cm	0	.	0	.	0	.	167	38	241	39	0	.	408	28
	81-90 cm	0	.	0	.	0	.	69	75	232	54	40	100	341	41
	91-100 cm	0	.	0	.	0	.	57	71	48	100	38	100	143	51
	>100 cm	0	.	0	.	0	.	39	100	88	72	0	.	128	58
	total	0	.	0	.	0	.	2517	20	4327	15	1294	22	8138	10
subalpine	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	3	100	493	21	190	32	657	19	894	17	318	21	2554	9
	21-30 cm	14	100	1076	19	316	37	1164	17	1784	15	802	22	5156	8
	31-40 cm	0	100	1770	18	738	36	1487	18	2913	13	984	20	7891	8
	41-50 cm	14	100	2052	18	656	34	2007	19	3385	13	1065	21	9178	8
	51-60 cm	33	100	1077	21	377	33	1884	17	2785	13	1169	20	7325	8
	61-70 cm	12	100	746	25	312	40	1409	21	1852	19	486	25	4817	11
	71-80 cm	0	.	595	26	217	46	797	35	782	25	318	32	2709	15
	81-90 cm	0	.	0	.	203	42	418	41	485	42	339	43	1444	22
	91-100 cm	0	.	57	100	38	100	143	58	170	58	0	.	408	36
	>100 cm	0	.	36	100	38	100	0	.	237	58	0	.	311	47
	total	77	100	7901	15	3085	24	9965	13	15285	10	5480	15	41793	6
high-montane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	62	65	1043	15	335	22	1365	13	1700	12	566	17	5070	6
	21-30 cm	46	77	1790	15	884	20	2871	14	3119	12	1160	15	9870	7
	31-40 cm	89	54	2800	13	1130	21	3180	14	3432	12	2058	17	12689	6
	41-50 cm	43	71	3380	14	1431	26	2980	13	4652	11	2213	14	14698	6
	51-60 cm	80	54	3469	14	1038	23	2809	15	4146	13	2117	16	13659	7
	61-70 cm	100	80	2100	19	761	29	1372	22	2351	17	1367	19	8051	9
	71-80 cm	81	74	1275	21	490	43	1047	25	1171	21	1129	27	5195	11
	81-90 cm	122	100	411	41	78	71	312	40	575	31	456	47	1953	19
	91-100 cm	71	100	290	45	172	58	188	50	226	51	206	58	1153	23
	>100 cm	0	.	49	100	51	100	64	100	123	71	203	73	491	40
	total	696	43	16606	11	6370	18	16188	10	21496	9	11473	11	72829	4
lower and upper montane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	4887	7	3173	9	2038	11	293	25	286	24	1401	13	12079	4
	21-30 cm	9862	6	6765	8	5213	10	583	25	748	24	2638	14	25808	4
	31-40 cm	14497	6	9145	7	8041	8	721	27	908	23	2447	21	35757	4
	41-50 cm	18096	5	10593	7	9483	8	680	28	1166	22	2068	19	42087	3
	51-60 cm	16275	6	10838	7	9879	8	539	38	1063	23	1540	28	40135	4
	61-70 cm	8864	8	6745	10	5876	12	306	36	944	22	831	22	23566	5
	71-80 cm	4716	12	3352	13	3845	15	90	58	513	36	410	33	12925	7
	81-90 cm	1783	20	1370	22	1273	23	0	0	146	58	303	40	4875	11
	91-100 cm	615	34	238	50	359	43	21	100	0	.	212	58	1446	22
	>100 cm	255	59	263	61	179	58	0	.	0	.	111	100	808	33
	total	79849	4	52481	5	46185	6	3234	23	5775	17	11961	14	199485	2
submontane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	5280	7	485	30	279	38	89	54	78	39	0	.	6211	6
	21-30 cm	9107	6	694	25	647	32	90	64	160	42	0	.	10699	6
	31-40 cm	11892	6	872	25	809	27	129	58	123	49	0	.	13825	5
	41-50 cm	13943	6	1118	26	819	27	26	72	160	43	0	.	16066	5
	51-60 cm	13561	6	980	25	553	32	84	71	198	46	0	.	15376	6
	61-70 cm	8658	8	430	43	267	47	16	100	24	100	0	.	9395	7
	71-80 cm	4068	11	427	37	83	71	18	100	33	100	0	.	4629	11
	81-90 cm	1689	20	0	.	196	52	0	.	0	.	0	.	1885	19
	91-100 cm	605	33	0	.	0	.	0	.	52	100	0	.	657	31
	>100 cm	683	41	0	.	0	.	0	.	0	.	0	.	683	41
	total	69485	4	5005	19	3654	24	452	43	829	37	0	.	79426	4
hyperinsubric and colline	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	76	42	0	.	0	.	238	27	3	100	1839	11	2156	10
	21-30 cm	212	44	0	.	0	.	328	28	11	100	3101	11	3652	10
	31-40 cm	234	42	0	.	0	.	271	31	9	100	2282	11	2796	10
	41-50 cm	195	41	0	.	0	.	170	38	27	100	1788	13	2181	12
	51-60 cm	90	65	0	.	0	.	155	71	30	100	953	20	1229	18
	61-70 cm	37	100	0	.	0	.	0	.	32	100	493	24	561	23
	71-80 cm	45	100	0	.	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	890	35	0	.	0	.	1192	26	113	100	11420	8	13615	7
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	10309	4	5194	7	2841	9	2907	9	3312	8	4278	6	28841	3
	21-30 cm	19242	4	10325	6	7060	8	5365	9	6485	8	8031	6	56508	2
	31-40 cm	26712	4	14585	5	10718	7	6342	9	8200	7	8131	8	74688	2
	41-50 cm	32292	3	17142	6	12389	7	6405	9	10311	7	7343	7	85882	2
	51-60 cm	30039	3	16364	6	11848	7	5762	10	8898	8	5926	9	78837	2
	61-70 cm	17672	5	10021	8	7215	10	3307	13	5496	10	3191	10	46901	3
	71-80 cm	8910	8	5650	10	4635	13	2118	18	2741	14	2112	16	26166	5
	81-90 cm	3594	14	1780	19	1750	18	798	27	1438	21	1291	23	10652	8
	91-100 cm	1291	23	585	32	569	33	439	31	495	34	601	32	3980	12
	>100 cm	938	34	347	50	269	45	103	73	448	39	725	40	2830	18
	total	150998	2	81993	4	59294	6	33548	6	47824	5	41627	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. 1321330. Birmensdorf, Swiss Federal Research Institute WSL

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