Selection from the list of topics

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.

NFI1
growing stock (stemwood)
diameter at breast height (10 classes) · main tree species
regional demarcation: protection forest region
unit: 1000 m³
evaluation area: accessible forest without shrub forest
grid: 1.4-km grid
state 1983/85
		protection forest region
		Jura + Plateau		Northwestern Alps		Northeastern Alps		Southwestern Alps		Southeastern Alps		Southern Alps		Switzerland
diameter at breast height (10 classes)	main tree species	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	.
	spruce	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	fir	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	larch	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	beech	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	maple	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	ash	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	oak	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other broadleaves	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	.	0	.	0	.	0	.	0	.	0	.	0	.
12-20 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	3309	7	2412	7	1439	10	932	10	1454	8	379	15	9925	3
	fir	1876	7	870	9	445	14	132	27	59	28	51	31	3435	5
	pine	142	21	49	40	43	33	397	18	308	18	13	51	951	10
	larch	71	35	10	48	12	56	300	16	131	17	171	22	695	10
	Arolla pine	0	.	5	100	1	100	57	29	75	22	0	.	138	17
	other conifers	93	24	5	57	13	34	2	100	21	54	0	.	134	19
	beech	3958	5	1022	10	833	12	150	29	110	22	774	13	6848	4
	maple	782	9	354	12	289	15	49	28	18	36	48	28	1539	6
	ash	919	10	313	18	332	17	46	30	42	51	134	21	1786	7
	oak	515	16	35	37	11	48	37	29	8	65	155	24	761	12
	sweet chestnut	9	87	0	.	2	100	8	73	0	.	953	11	972	11
	other broadleaves	1011	8	445	13	381	17	334	15	163	19	1044	9	3378	5
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	12684	3	5520	5	3801	6	2446	7	2388	6	3722	5	30562	2
21-30 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	7842	5	5969	6	4274	9	2396	10	3984	8	955	14	25421	3
	fir	4568	6	1987	10	1178	12	143	30	92	30	83	38	8051	5
	pine	676	15	101	31	185	28	619	17	592	17	100	46	2272	8
	larch	209	29	11	77	26	64	750	14	434	15	466	18	1896	8
	Arolla pine	0	.	11	100	8	71	190	28	201	23	1	100	411	17
	other conifers	79	33	0	.	-3	77	0	.	5	73	0	.	80	33
	beech	8760	4	1913	9	1925	11	140	31	188	32	801	13	13727	4
	maple	1602	8	492	14	619	12	32	40	39	43	57	35	2841	6
	ash	1685	9	350	19	526	18	65	43	45	55	72	40	2744	7
	oak	1103	12	78	42	29	67	27	44	11	100	211	27	1457	10
	sweet chestnut	28	88	0	.	0	.	6	73	2	100	792	13	828	13
	other broadleaves	1456	9	227	18	354	17	189	27	99	30	879	12	3205	6
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	28008	2	11138	4	9121	6	4558	7	5691	6	4418	5	62933	2
31-40 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	15515	5	11424	6	6330	8	2816	9	6092	7	1531	13	43708	3
	fir	7373	6	3025	9	1928	11	223	24	191	25	234	35	12974	4
	pine	2455	9	111	34	203	31	466	18	799	16	161	53	4196	7
	larch	356	21	57	42	173	54	1271	11	1091	13	771	15	3719	7
	Arolla pine	0	.	9	71	4	100	158	23	323	21	4	100	498	15
	other conifers	92	47	0	.	0	.	6	100	0	.	0	.	98	45
	beech	10855	4	2483	10	2402	10	39	56	183	35	647	13	16610	4
	maple	1057	11	344	20	409	17	20	73	13	58	16	66	1859	8
	ash	1896	9	308	21	392	23	23	71	10	100	33	64	2662	8
	oak	1277	11	41	53	14	61	0	.	49	66	172	33	1552	10
	sweet chestnut	0	.	0	.	0	.	18	59	2	100	385	17	405	16
	other broadleaves	913	12	212	30	164	26	72	34	61	55	383	19	1805	9
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	41788	2	18015	4	12018	6	5114	7	8814	6	4336	6	90085	2
41-50 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	16264	4	11556	5	7197	7	2539	10	6118	7	1680	11	45353	2
	fir	6980	6	3672	8	1883	12	231	29	316	30	306	25	13388	4
	pine	2455	10	234	43	157	35	306	26	598	17	42	68	3790	8
	larch	336	23	96	38	128	41	1530	11	1190	13	776	12	4057	6
	Arolla pine	0	.	0	.	0	.	110	28	275	25	-1	100	384	20
	other conifers	159	55	0	.	0	.	0	.	0	.	0	.	159	55
	beech	8684	5	2114	12	1677	11	38	59	224	34	371	16	13108	4
	maple	522	14	165	23	149	25	0	.	16	59	5	100	858	11
	ash	974	12	92	35	211	24	0	.	6	100	22	75	1305	10
	oak	1191	12	26	50	6	100	10	115	39	51	50	39	1323	11
	sweet chestnut	4	100	0	.	0	.	4	100	4	100	415	18	427	18
	other broadleaves	461	17	105	36	88	35	52	51	5	100	93	37	803	13
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	38030	2	18059	4	11496	6	4821	7	8790	6	3758	7	84955	2
51-60 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	10419	5	7939	6	4979	9	2040	12	4612	8	1243	14	31232	3
	fir	3768	8	2717	11	1192	15	186	36	253	33	187	33	8304	6
	pine	1236	14	55	74	39	73	181	56	298	27	38	50	1847	12
	larch	242	23	189	40	145	44	1355	12	942	15	641	16	3514	8
	Arolla pine	0	.	0	.	7	100	30	54	203	27	0	.	240	24
	other conifers	87	50	0	.	0	.	0	.	0	.	0	.	87	50
	beech	4132	8	1377	15	783	17	20	111	119	51	288	28	6719	6
	maple	207	31	41	46	60	47	0	.	8	100	0	.	316	23
	ash	545	19	37	58	52	52	0	.	15	100	0	.	649	17
	oak	891	16	21	71	33	73	0	.	11	100	22	101	979	15
	sweet chestnut	0	.	0	.	0	.	6	100	0	.	196	22	202	22
	other broadleaves	268	24	72	48	14	100	27	84	0	.	42	42	424	19
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	21796	3	12448	5	7304	7	3845	9	6462	7	2657	8	54512	2
61-70 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	3656	9	3304	9	2438	12	634	22	2121	12	709	22	12862	5
	fir	1440	12	1353	15	397	26	47	58	75	67	142	39	3453	9
	pine	241	30	48	61	18	100	7	100	104	50	0	.	417	23
	larch	105	47	21	100	64	58	620	18	475	21	276	27	1562	11
	Arolla pine	0	.	0	.	0	.	24	58	76	42	0	.	99	35
	other conifers	58	58	25	100	0	.	0	.	0	.	0	.	82	51
	beech	1929	12	383	27	160	39	14	73	93	51	119	29	2699	10
	maple	108	45	0	.	6	100	0	.	0	.	0	.	114	43
	ash	130	41	0	.	25	100	0	.	0	.	0	.	155	38
	oak	350	28	15	100	62	61	0	.	0	.	12	100	439	24
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	110	32	110	32
	other broadleaves	52	58	19	100	19	100	16	100	0	.	13	73	118	38
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	8069	6	5168	8	3188	11	1362	14	2943	10	1381	14	22110	4
71-80 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	1392	15	1190	16	1194	20	398	28	1028	17	468	26	5671	8
	fir	831	19	702	22	171	43	12	100	98	58	105	60	1919	13
	pine	20	100	0	.	0	.	0	.	20	100	0	.	40	71
	larch	40	71	0	.	0	.	405	24	213	31	146	37	804	16
	Arolla pine	0	.	0	.	0	.	53	46	66	44	0	.	118	32
	other conifers	30	100	0	.	0	.	0	.	0	.	0	.	30	100
	beech	506	23	92	53	74	58	19	100	0	.	110	46	802	18
	maple	34	100	8	100	30	58	0	.	0	.	9	100	82	49
	ash	94	53	0	.	0	.	0	.	0	.	0	.	94	53
	oak	259	30	0	.	11	100	0	.	0	.	0	.	271	29
	sweet chestnut	0	.	0	.	0	.	11	100	0	.	211	35	222	34
	other broadleaves	18	100	0	.	0	.	0	.	0	.	0	.	18	100
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	3224	10	1993	13	1480	17	897	17	1426	14	1051	17	10071	6
81-90 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	310	30	159	39	420	27	129	41	220	34	134	40	1372	14
	fir	125	50	408	30	28	100	30	100	30	100	67	73	688	22
	pine	39	100	0	.	0	.	0	.	0	.	0	.	39	100
	larch	28	100	0	.	0	.	143	39	139	44	29	75	339	26
	Arolla pine	0	.	0	.	0	.	13	100	16	100	0	.	28	71
	other conifers	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	beech	398	29	14	100	19	100	0	.	28	78	0	0	459	26
	maple	0	.	22	71	0	.	0	.	0	.	0	.	22	71
	ash	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	oak	203	39	0	.	0	.	0	.	0	.	0	.	203	39
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	85	49	85	49
	other broadleaves	27	100	0	.	0	.	0	.	0	.	0	.	27	100
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	1130	18	602	23	467	25	314	26	432	24	315	27	3261	10
91-100 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	134	51	134	54	113	47	0	.	173	49	43	75	596	24
	fir	108	58	84	71	79	72	0	.	49	100	0	.	320	36
	pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	larch	0	.	0	.	0	.	75	59	0	.	31	100	106	51
	Arolla pine	0	.	0	.	0	.	18	100	0	.	0	.	18	100
	other conifers	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	beech	58	74	0	.	0	.	0	.	0	.	0	.	58	74
	maple	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	ash	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	oak	52	72	0	.	0	.	0	.	0	.	0	.	52	72
	sweet chestnut	0	.	0	.	0	.	0	.	16	100	129	41	145	38
	other broadleaves	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	352	31	217	43	193	41	94	51	238	42	203	34	1296	16
>100 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	0	.	122	65	71	77	0	0	28	100	105	72	326	39
	fir	37	100	0	0	0	.	0	.	0	.	118	61	155	52
	pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	larch	0	.	0	.	0	.	31	100	45	72	64	71	140	46
	Arolla pine	0	.	0	.	0	.	16	100	17	100	0	.	34	71
	other conifers	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	beech	0	.	0	.	0	.	0	.	0	.	48	100	48	100
	maple	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	ash	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	oak	36	100	0	.	0	.	0	.	0	.	0	.	36	100
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	487	40	487	40
	other broadleaves	54	100	0	.	0	.	0	.	0	.	13	100	67	83
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	126	59	122	65	71	77	47	74	90	51	835	28	1292	21
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	58840	3	44208	4	28455	6	11884	7	25830	5	7248	9	176466	2
	fir	27107	4	14818	6	7301	9	1005	21	1164	19	1293	20	52687	3
	pine	7264	7	598	32	644	23	1977	15	2718	13	352	37	13553	6
	larch	1386	15	383	30	549	31	6482	8	4660	10	3373	10	16833	5
	Arolla pine	0	.	26	86	19	71	670	17	1251	16	4	135	1969	12
	other conifers	597	27	29	85	10	43	9	77	26	47	0	.	670	24
	beech	39281	3	9398	8	7874	8	420	24	946	27	3158	9	61077	3
	maple	4312	6	1426	10	1563	10	101	27	93	31	136	28	7630	4
	ash	6243	6	1100	13	1537	14	134	29	118	43	261	20	9394	5
	oak	5876	7	216	28	166	33	74	31	118	56	623	22	7073	6
	sweet chestnut	41	89	0	.	2	100	52	46	24	74	3763	10	3883	10
	other broadleaves	4259	7	1080	13	1021	13	691	19	327	21	2466	9	9843	5
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	155207	1	73281	3	49140	4	23499	5	37275	4	22677	4	361078	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. 1217874. Birmensdorf, Swiss Federal Research Institute WSL

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