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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.

NFI1
growing stock (stemwood)
diameter at breast height (10 classes) · conifers and broadleaves
regional demarcation: economic region
unit: 1000 m³
evaluation area: accessible forest without shrub forest
grid: 1.4-km grid
state 1983/85
		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
diameter at breast height (10 classes)	conifers and broadleaves	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	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	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	broadleaves	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	indeterminable	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	.
12-20 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	1956	7	335	21	593	16	1248	13	1359	10	1023	13	1715	7	1070	11	613	11	423	16	460	18	1822	8	2048	7	614	11	15278	3
	broadleaves	2462	6	983	11	1026	13	915	10	1807	8	414	17	1138	10	1163	11	617	14	291	21	395	19	624	13	340	15	3108	6	15284	3
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	4419	5	1318	10	1619	10	2163	9	3166	6	1437	11	2854	6	2233	8	1230	10	714	14	854	15	2446	7	2388	6	3722	5	30562	2
21-30 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	4771	6	810	19	1737	14	2750	10	3306	9	2204	11	4216	7	3450	10	1658	12	1097	15	1120	17	4099	7	5308	7	1606	10	38132	2
	broadleaves	5579	6	2053	10	1643	11	1884	10	3475	7	663	18	1613	10	2310	10	783	14	400	26	744	17	459	18	383	21	2812	7	24801	2
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	10350	4	2863	9	3381	9	4634	8	6780	6	2868	10	5829	6	5760	8	2441	10	1497	14	1864	13	4558	7	5691	6	4418	5	62933	2
31-40 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	7701	6	1700	15	3400	12	5143	9	7847	7	3485	11	7751	7	5303	8	3391	11	1527	16	1808	15	4941	7	8496	6	2700	10	65193	2
	broadleaves	5620	6	2259	10	1909	12	2592	10	3617	7	694	20	1948	12	2297	11	746	16	332	26	752	17	172	24	318	26	1636	8	24892	3
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	13321	4	3959	9	5308	9	7736	7	11464	5	4178	10	9699	6	7600	7	4137	9	1858	14	2560	12	5114	7	8814	6	4336	6	90085	2
41-50 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	8192	5	1450	16	2742	12	5860	8	7949	7	3564	11	8483	7	6071	8	3511	10	1268	16	2026	15	4717	7	8496	6	2803	8	67132	2
	broadleaves	3337	8	1791	11	1229	13	2352	11	3127	8	472	23	1523	14	1363	13	508	23	268	29	500	21	104	35	294	27	955	11	17824	3
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	11529	4	3242	10	3971	9	8212	7	11076	6	4035	10	10006	6	7434	7	4018	9	1536	14	2526	13	4821	7	8790	6	3758	7	84955	2
51-60 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	5218	7	571	19	1571	14	3865	10	4528	9	2209	13	6058	8	4150	10	2633	12	987	19	1226	19	3792	9	6309	7	2108	10	45224	2
	broadleaves	1236	16	1197	15	536	24	1131	16	1944	11	200	31	927	20	667	18	421	22	77	43	197	40	53	61	153	44	549	17	9289	5
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	6454	6	1768	12	2106	12	4996	9	6472	7	2408	13	6985	7	4817	9	3055	11	1064	19	1423	17	3845	9	6462	7	2657	8	54512	2
61-70 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	2112	11	249	30	667	21	1247	15	1224	14	1049	18	2689	11	1642	14	1012	18	566	28	709	25	1332	14	2850	10	1128	16	18476	4
	broadleaves	351	24	518	24	398	35	493	24	809	19	88	45	154	44	192	34	175	42	17	100	63	66	30	64	93	51	253	20	3635	9
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	2463	10	768	19	1065	19	1740	14	2033	11	1137	18	2843	10	1833	14	1187	16	583	27	772	23	1362	14	2943	10	1381	14	22110	4
71-80 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	1004	20	47	71	245	37	449	25	568	26	131	41	1228	18	875	24	533	24	235	42	254	33	868	17	1426	14	719	21	8582	6
	broadleaves	72	58	106	51	116	45	320	30	297	31	31	78	55	75	86	52	15	100	11	100	19	71	30	74	0	.	331	27	1488	13
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	1076	19	153	41	362	29	769	20	865	20	161	42	1283	17	961	22	548	24	247	40	273	31	897	17	1426	14	1051	17	10071	6
81-90 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	162	41	33	100	60	71	190	49	58	71	16	100	456	28	165	45	94	51	84	60	200	38	314	26	404	25	230	33	2466	11
	broadleaves	0	.	107	60	64	71	224	38	233	36	0	.	24	71	0	.	11	100	19	100	0	.	0	.	28	78	85	49	795	19
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	162	41	140	51	124	50	414	33	290	32	16	100	481	26	165	45	105	47	102	53	200	38	314	26	432	24	315	27	3261	10
91-100 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	125	51	0	.	37	100	39	100	40	100	105	60	94	71	21	100	18	100	50	72	121	55	94	51	222	44	74	60	1041	19
	broadleaves	0	.	0	.	20	100	0	.	89	59	0	.	0	.	0	.	0	.	0	.	0	.	0	.	16	100	129	41	255	31
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	125	51	0	.	58	74	39	100	130	51	105	60	94	71	21	100	18	100	50	72	121	55	94	51	238	42	203	34	1296	16
>100 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	37	100	0	.	0	.	0	.	0	.	32	100	0	0	20	100	90	81	0	.	52	100	47	74	90	51	288	39	655	25
	broadleaves	0	.	54	100	0	.	0	.	36	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	548	37	637	33
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	37	100	54	100	0	.	0	.	36	100	32	100	0	0	20	100	90	81	0	.	52	100	47	74	90	51	835	28	1292	21
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	31278	4	5195	11	11053	9	20791	7	26878	5	13817	9	32691	5	22766	7	13553	8	6237	13	7974	11	22026	5	35648	5	12271	6	262178	1
	broadleaves	18658	4	9068	8	6942	10	9911	8	15434	6	2561	15	7384	9	8079	8	3275	13	1414	18	2669	15	1472	13	1627	18	10406	5	98900	2
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	49936	3	14262	7	17994	7	30702	5	42312	4	16378	8	40075	5	30845	6	16828	7	7652	11	10644	10	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. 1353804. Birmensdorf, Swiss Federal Research Institute WSL

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