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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
total number of stems
altitudinal vegetation belts (NaiS, 3 classes) · diameter at breast height (10 classes)
regional demarcation: economic region
unit: 1000 n
evaluation area: accessible forest without shrub forest
grid: 1.4 km grid, subgrids 1-5
state 2018/26
		economic region
		Western Jura		Eastern Jura		Western Plateau		Central Plateau		Eastern Plateau		Western Pre-Alps		Central Pre-Alps		Eastern Pre-Alps		Northwestern Alps		Central Alps		Northeastern Alps		Southwestern Alps		Southeastern Alps		Southern Alps		Switzerland
altitudinal vegetation belts (NaiS, 3 classes)	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	±%
n/a	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	21-30 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	31-40 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	41-50 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	51-60 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	61-70 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	71-80 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	81-90 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	91-100 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	>100 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
subalpine	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	0	.	0	.	50	100	0	.	0	.	510	58	2484	33	197	100	2260	24	1095	41	734	44	8497	12	13863	11	5927	15	35616	7
	21-30 cm	0	.	0	.	67	100	0	.	0	.	282	66	1523	30	175	100	1440	23	511	38	334	48	4390	13	7651	11	3497	15	19871	7
	31-40 cm	0	.	0	.	64	100	0	.	0	.	175	48	1052	33	39	100	1063	24	280	42	393	46	2846	14	4640	10	1780	15	12332	6
	41-50 cm	0	.	0	.	33	100	0	.	0	.	194	43	579	28	9	100	644	23	152	47	295	39	1847	14	2867	10	951	17	7572	6
	51-60 cm	0	.	0	.	27	100	0	.	0	.	81	53	137	33	14	100	248	28	73	51	98	42	993	14	1580	11	635	17	3885	7
	61-70 cm	0	.	0	.	7	100	0	.	0	.	18	74	103	39	7	100	107	34	72	49	28	61	510	18	582	16	172	23	1604	9
	71-80 cm	0	.	0	.	0	.	0	.	0	.	16	71	39	47	7	100	109	30	7	100	28	62	220	26	234	20	78	30	739	12
	81-90 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	14	71	29	50	100	35	129	30	91	37	362	18
	91-100 cm	0	.	0	.	0	.	0	.	0	.	9	100	0	.	0	.	0	.	0	.	7	100	44	41	35	53	7	100	102	28
	>100 cm	0	.	0	.	0	.	0	.	0	.	7	100	0	.	0	.	0	.	0	.	7	100	7	100	36	45	0	.	57	35
	total	0	.	0	.	247	100	0	.	0	.	1294	47	5915	27	449	94	5871	20	2203	33	1951	36	19453	11	31617	8	13139	12	82139	5
montane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	22843	6	2023	25	2001	24	5063	20	5091	17	8625	13	17737	9	10480	11	10807	12	5380	18	5589	16	15900	10	16568	10	17994	9	146102	3
	21-30 cm	12983	6	1241	23	1270	25	2187	21	2878	15	5556	14	10477	9	7680	10	4532	12	3248	17	3144	17	9041	11	9786	9	9926	9	83950	3
	31-40 cm	9075	7	824	21	752	25	1225	19	1835	16	3432	13	5708	8	5790	9	3232	12	1864	17	1569	16	4640	11	4820	9	5188	10	49954	3
	41-50 cm	5694	5	565	22	679	22	875	19	1404	13	1862	12	3668	8	3482	9	2049	12	1051	20	1137	15	2268	11	3155	9	2646	9	30535	2
	51-60 cm	2841	7	337	27	494	23	599	18	952	15	1213	13	2399	9	2364	9	1169	13	587	18	639	18	1333	12	1871	10	1501	16	18299	3
	61-70 cm	1085	11	87	35	225	24	281	23	368	21	510	17	1053	12	1020	13	545	16	251	25	256	24	468	18	787	13	637	13	7572	4
	71-80 cm	416	15	38	52	80	35	127	31	198	25	178	25	411	14	389	18	276	19	182	29	161	31	231	23	308	18	312	19	3308	6
	81-90 cm	98	31	0	.	44	47	62	36	45	47	41	46	142	25	142	25	58	35	17	71	35	45	60	36	104	26	143	27	990	9
	91-100 cm	44	41	0	.	0	.	10	100	33	52	18	71	12	71	14	71	38	45	7	100	50	38	37	45	31	51	58	38	350	15
	>100 cm	28	50	0	.	0	.	0	.	0	.	9	100	21	57	21	58	7	100	0	.	7	100	7	100	16	71	32	59	150	23
	total	55107	5	5115	19	5544	18	10430	15	12804	12	21444	11	41629	7	31381	8	22714	10	12587	15	12588	13	33985	9	37446	8	38437	8	341209	2
hyperinsubric, colline, submontane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	6213	16	6069	16	5671	18	9518	12	11113	10	104	100	1680	29	1071	44	1271	36	613	66	277	95	3737	23	652	39	17897	10	65884	5
	21-30 cm	2914	16	2628	15	2627	16	4237	12	6619	10	42	100	1050	26	880	42	547	37	452	48	108	71	1470	23	396	38	9108	9	33077	4
	31-40 cm	1650	15	1519	17	1458	17	2819	11	3251	10	29	100	529	29	448	32	291	41	274	51	74	92	535	26	143	42	3341	11	16362	5
	41-50 cm	1069	15	1125	15	948	17	1714	11	2178	10	8	100	385	33	226	33	189	35	163	44	37	70	159	31	106	39	1376	12	9684	4
	51-60 cm	559	17	502	16	503	18	1331	12	1353	10	0	.	208	30	97	38	117	40	54	58	31	100	92	49	78	41	518	17	5442	5
	61-70 cm	221	25	268	19	180	23	549	15	617	13	0	.	58	42	21	57	37	74	36	71	0	.	16	71	12	70	185	20	2200	7
	71-80 cm	42	41	112	28	55	35	220	21	257	19	8	100	62	42	8	100	6	100	6	100	0	.	8	100	6	100	127	29	918	10
	81-90 cm	15	71	14	70	14	71	33	45	137	25	0	.	0	.	18	71	0	.	17	72	0	.	0	.	0	.	53	47	302	17
	91-100 cm	0	.	0	.	7	100	33	52	33	45	0	.	0	.	0	.	0	.	0	.	0	.	7	100	7	100	38	60	125	27
	>100 cm	11	100	0	.	14	71	14	71	30	71	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	50	51	120	32
	total	12694	12	12237	12	11477	14	20467	9	25588	7	191	100	3973	24	2770	36	2457	32	1616	42	526	81	6024	21	1401	35	32692	8	134114	3
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	29055	5	8092	13	7722	15	14581	10	16204	8	9240	12	21900	8	11748	11	14338	10	7088	16	6600	15	28134	7	31083	7	41817	6	247602	2
	21-30 cm	15897	5	3869	12	3964	13	6424	11	9497	8	5880	13	13050	8	8735	10	6519	10	4210	14	3586	15	14901	8	17834	7	22531	5	136898	2
	31-40 cm	10725	6	2343	13	2273	14	4044	10	5085	8	3636	13	7289	8	6278	9	4586	10	2419	15	2036	15	8021	8	9603	6	10309	6	78647	2
	41-50 cm	6764	5	1690	12	1661	13	2589	9	3582	7	2065	11	4632	8	3717	9	2882	10	1366	17	1468	14	4274	8	6129	6	4974	6	47791	2
	51-60 cm	3400	6	839	14	1024	14	1930	9	2305	8	1293	13	2744	8	2475	9	1534	11	714	16	768	16	2417	9	3529	7	2654	10	27626	2
	61-70 cm	1306	9	355	17	411	16	829	12	985	11	528	17	1214	11	1048	13	689	14	358	21	284	23	993	12	1381	10	994	9	11375	3
	71-80 cm	458	14	150	25	135	25	348	17	455	15	202	23	512	13	404	17	392	16	195	27	189	28	460	17	548	13	517	14	4965	4
	81-90 cm	113	29	14	70	58	39	95	28	182	22	41	46	142	25	160	24	58	35	48	41	64	33	160	26	233	20	286	20	1654	7
	91-100 cm	44	41	0	.	7	100	42	46	66	34	27	58	12	71	14	71	38	45	7	100	57	35	87	29	73	35	103	32	577	12
	>100 cm	40	46	0	.	14	71	14	71	30	71	16	71	21	57	21	58	7	100	0	.	14	71	14	71	51	38	83	39	327	17
	total	67801	4	17353	10	17269	11	30897	7	38392	6	22929	11	51517	6	34600	8	31042	8	16406	13	15065	12	59462	6	70464	5	84268	4	557462	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. 1318939. Birmensdorf, Swiss Federal Research Institute WSL

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