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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
diameter at breast height (10 classes) · main tree species
regional demarcation: production region
unit: 1000 n
evaluation area: accessible forest without shrub forest
grid: 1.4 km grid, subgrids 1-5
state 2018/26
		production region
		Jura		Plateau		Pre-Alps		Alps		Southern Alps		Switzerland
diameter at breast height (10 classes)	main tree species	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%
n/a	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	0	.	0	.	0	.	0	.	0	.	0	.
	fir	0	.	0	.	0	.	0	.	0	.	0	.
	pine	0	.	0	.	0	.	0	.	0	.	0	.
	larch	0	.	0	.	0	.	0	.	0	.	0	.
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	0	.	0	.	0	.	0	.	0	.	0	.
	beech	0	.	0	.	0	.	0	.	0	.	0	.
	maple	0	.	0	.	0	.	0	.	0	.	0	.
	ash	0	.	0	.	0	.	0	.	0	.	0	.
	oak	0	.	0	.	0	.	0	.	0	.	0	.
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.
	other broadleaves	0	.	0	.	0	.	0	.	0	.	0	.
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	.	0	.	0	.	0	.	0	.	0	.
12-20 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	7155	11	10668	10	18120	8	38151	5	5787	15	79881	4
	fir	7498	10	4914	12	7264	11	2917	13	698	27	23291	6
	pine	277	31	255	41	383	57	6474	17	181	60	7569	15
	larch	74	80	791	54	341	50	6767	11	3522	16	11495	9
	Arolla pine	0	.	0	.	0	.	2539	20	49	74	2588	20
	other conifers	490	38	572	39	184	38	1651	25	20	100	2917	18
	beech	10570	8	9229	10	7094	10	5976	12	6630	13	39500	5
	maple	4026	13	3286	14	2813	16	4570	13	1371	28	16065	7
	ash	1984	17	2263	16	1653	17	2949	16	1660	22	10509	8
	oak	1321	38	847	28	54	58	997	31	1184	37	4403	17
	sweet chestnut	0	.	0	.	0	.	149	69	7956	15	8105	15
	other broadleaves	3612	11	5633	11	4773	13	13671	9	12649	11	40339	5
	indeterminable	141	44	50	58	208	29	431	26	110	41	940	16
	total	37147	4	38507	5	42887	5	87242	3	41817	6	247602	2
21-30 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	3714	11	6342	10	12294	8	23039	5	3623	13	49013	4
	fir	4389	10	2671	14	4218	10	1644	14	338	32	13259	6
	pine	598	28	348	37	278	79	3860	14	52	58	5135	12
	larch	17	100	344	39	67	78	4536	12	2848	15	7812	9
	Arolla pine	0	.	0	.	0	.	1898	17	16	100	1914	17
	other conifers	137	43	178	31	53	58	174	47	0	.	542	22
	beech	6041	9	4466	8	5025	10	3519	13	4075	16	23126	5
	maple	2095	11	1936	16	2277	13	2151	14	306	31	8765	7
	ash	863	19	982	16	1523	18	1372	21	710	31	5449	9
	oak	750	30	712	24	184	44	404	29	872	22	2923	13
	sweet chestnut	0	.	0	.	0	.	53	58	4496	14	4549	14
	other broadleaves	1107	19	1890	13	1658	20	4273	12	5178	12	14106	6
	indeterminable	54	58	17	100	89	45	126	44	18	100	305	26
	total	19766	4	19885	5	27665	5	47050	3	22531	5	136898	2
31-40 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	3115	11	3310	10	8618	7	14648	5	2284	14	31976	3
	fir	2181	11	1582	13	2681	11	1229	15	283	31	7956	6
	pine	819	22	329	27	201	53	1833	14	147	51	3329	11
	larch	14	71	97	44	9	100	3347	11	1622	15	5089	9
	Arolla pine	0	.	0	.	0	.	1007	19	0	.	1007	19
	other conifers	31	81	107	44	0	.	40	61	0	.	177	33
	beech	4623	8	2980	9	3344	9	1975	12	1780	15	14703	4
	maple	951	16	796	14	1207	14	897	18	204	40	4055	8
	ash	533	25	1135	16	787	25	747	20	169	32	3372	10
	oak	390	23	381	25	45	55	166	35	313	27	1295	13
	sweet chestnut	0	.	0	.	0	.	87	62	1646	18	1733	17
	other broadleaves	376	24	669	18	270	28	576	16	1841	16	3732	10
	indeterminable	34	71	17	100	42	41	112	36	19	100	224	25
	total	13068	5	11402	5	17203	4	26664	3	10309	6	78647	2
41-50 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	2245	8	2371	9	5615	6	9479	5	1592	13	21301	3
	fir	1667	10	1264	10	1735	8	900	15	184	29	5751	5
	pine	366	19	367	18	134	58	804	16	41	52	1713	10
	larch	21	58	97	36	7	100	2359	10	918	14	3402	8
	Arolla pine	0	.	0	.	0	.	422	18	0	.	422	18
	other conifers	28	61	54	47	0	.	0	.	8	100	90	35
	beech	2790	7	2088	8	2153	10	1145	12	703	15	8879	4
	maple	438	14	209	21	343	17	381	17	44	47	1414	8
	ash	324	20	692	15	315	21	178	26	66	44	1574	9
	oak	304	24	381	18	61	48	66	42	173	29	985	12
	sweet chestnut	0	.	0	.	0	.	29	50	721	18	750	18
	other broadleaves	255	32	310	19	51	38	253	24	524	18	1393	11
	indeterminable	15	71	0	.	0	.	103	32	0	.	117	29
	total	8454	4	7832	4	10414	4	16118	3	4974	6	47791	2
51-60 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	1331	10	1249	10	3508	6	5245	5	1033	20	12365	4
	fir	1016	11	973	12	1581	10	638	15	197	28	4404	6
	pine	136	25	249	22	66	50	334	22	21	74	808	13
	larch	14	70	84	31	14	100	1555	10	580	14	2247	8
	Arolla pine	0	.	0	.	0	.	219	23	0	.	219	23
	other conifers	42	62	74	49	0	.	0	.	8	100	124	36
	beech	1331	10	1566	8	1006	12	542	17	324	19	4769	5
	maple	150	22	116	27	190	23	122	27	0	.	578	12
	ash	74	35	456	16	83	38	98	28	40	63	751	12
	oak	93	31	327	18	0	.	41	59	57	41	518	14
	sweet chestnut	0	.	0	.	0	.	15	72	337	24	352	23
	other broadleaves	51	47	165	29	45	47	138	32	57	42	456	17
	indeterminable	0	.	0	.	19	58	14	71	0	.	34	45
	total	4239	5	5259	4	6512	4	8962	4	2654	10	27626	2
61-70 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	671	13	597	13	1665	9	2173	7	430	16	5535	5
	fir	480	15	543	14	746	12	255	20	37	45	2061	7
	pine	15	71	61	37	24	58	72	34	7	100	179	21
	larch	0	.	34	45	0	.	822	13	222	21	1078	11
	Arolla pine	0	.	0	.	0	.	36	45	0	.	36	45
	other conifers	14	100	47	51	0	.	0	.	8	100	69	42
	beech	374	16	618	12	264	23	176	24	151	28	1582	8
	maple	15	71	48	43	34	65	43	46	0	.	140	27
	ash	53	43	119	25	35	53	29	59	10	100	247	19
	oak	26	60	116	31	7	100	6	100	15	71	170	25
	sweet chestnut	0	.	0	.	0	.	16	71	98	27	114	25
	other broadleaves	14	100	43	41	16	71	70	44	15	71	158	26
	indeterminable	0	.	0	.	0	.	7	100	0	.	7	100
	total	1661	8	2226	6	2790	7	3705	5	994	9	11375	3
71-80 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	239	20	249	19	617	12	1070	10	233	24	2407	6
	fir	211	19	286	17	327	16	226	24	30	49	1080	9
	pine	7	100	27	50	0	.	14	71	0	.	48	38
	larch	7	100	0	.	15	71	319	18	93	27	433	15
	Arolla pine	0	.	0	.	0	.	50	38	0	.	50	38
	other conifers	0	.	41	58	0	.	0	.	0	.	41	58
	beech	80	33	234	20	138	28	64	39	44	41	560	13
	maple	16	71	7	100	6	100	7	100	0	.	36	45
	ash	15	71	16	72	15	71	12	70	6	100	65	34
	oak	18	70	51	38	0	.	7	100	0	.	76	32
	sweet chestnut	0	.	0	.	0	.	8	100	104	33	112	31
	other broadleaves	16	71	27	50	0	.	6	100	7	100	56	35
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.
	total	608	12	938	10	1118	9	1784	7	517	14	4965	4
81-90 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	47	47	104	27	175	22	293	17	88	33	707	11
	fir	58	39	132	26	120	29	42	41	7	100	360	16
	pine	0	.	7	100	0	.	0	.	0	.	7	100
	larch	0	.	0	.	0	.	144	27	101	35	245	22
	Arolla pine	0	.	0	.	0	.	43	52	0	.	43	52
	other conifers	7	100	27	62	7	100	0	.	0	.	41	47
	beech	8	100	20	58	16	71	22	57	37	45	102	27
	maple	0	.	0	.	0	.	8	100	0	.	8	100
	ash	7	100	9	100	17	72	0	.	0	.	33	51
	oak	0	.	29	50	8	100	10	100	0	.	47	41
	sweet chestnut	0	.	0	.	0	.	0	.	53	47	53	47
	other broadleaves	0	.	8	100	0	.	0	.	0	.	8	100
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.
	total	127	27	335	15	343	16	563	12	286	20	1654	7
91-100 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	15	71	20	58	33	51	145	23	25	59	238	18
	fir	29	50	14	71	12	71	22	58	25	58	102	27
	pine	0	.	0	.	0	.	7	100	0	.	7	100
	larch	0	.	0	.	0	.	54	38	7	100	61	36
	Arolla pine	0	.	0	.	0	.	22	58	0	.	22	58
	other conifers	0	.	0	.	0	.	0	.	0	.	0	.
	beech	0	.	44	46	7	100	0	.	0	.	51	42
	maple	0	.	0	.	0	.	6	100	0	.	6	100
	ash	0	.	17	71	0	.	0	.	0	.	17	71
	oak	0	.	14	71	0	.	0	.	0	.	14	71
	sweet chestnut	0	.	0	.	0	.	7	100	45	53	53	48
	other broadleaves	0	.	7	100	0	.	0	.	0	.	7	100
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.
	total	44	41	116	26	53	38	263	17	103	32	577	12
>100 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	14	71	14	71	51	38	59	35	18	72	156	22
	fir	26	59	0	.	7	100	0	.	0	.	33	51
	pine	0	.	0	.	0	.	0	.	0	.	0	.
	larch	0	.	0	.	0	.	15	71	14	100	29	61
	Arolla pine	0	.	0	.	0	.	14	71	0	.	14	71
	other conifers	0	.	0	.	0	.	0	.	0	.	0	.
	beech	0	.	0	.	0	.	0	.	0	.	0	.
	maple	0	.	0	.	0	.	0	.	0	.	0	.
	ash	0	.	0	.	0	.	0	.	0	.	0	.
	oak	0	.	16	100	0	.	0	.	0	.	16	100
	sweet chestnut	0	.	0	.	0	.	0	.	50	51	50	51
	other broadleaves	0	.	27	61	0	.	0	.	0	.	27	61
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.
	total	40	46	58	44	59	35	87	29	83	39	327	17
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	18545	7	24923	7	50698	5	94301	4	15113	11	203580	3
	fir	17556	7	12379	8	18690	7	7873	10	1800	23	58298	4
	pine	2218	18	1642	16	1086	50	13398	12	450	46	18794	10
	larch	148	44	1447	35	452	47	19917	8	9928	11	31892	6
	Arolla pine	0	.	0	.	0	.	6248	15	65	79	6313	15
	other conifers	749	30	1100	25	245	31	1865	25	44	70	4002	15
	beech	25817	5	21245	6	19047	7	13420	9	13744	12	93274	3
	maple	7691	10	6396	10	6869	11	8186	10	1925	25	31067	5
	ash	3853	13	5690	10	4429	14	5386	14	2661	22	22019	6
	oak	2902	24	2873	16	359	30	1698	25	2614	24	10446	11
	sweet chestnut	0	.	0	.	0	.	364	58	15506	12	15870	12
	other broadleaves	5431	11	8778	9	6813	12	18988	9	20271	9	60281	5
	indeterminable	244	32	84	44	358	21	794	18	146	40	1627	12
	total	85153	3	86557	3	109045	3	192439	2	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. 1296804. Birmensdorf, Swiss Federal Research Institute WSL

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