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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
number of stems
conifers and broadleaves · diameter at breast height (10 classes)
regional demarcation: economic region
unit: 1000 n
evaluation area: accessible forest without shrub forest NFI1-NFI5
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
conifers and broadleaves	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	.
conifers	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	11286	9	1751	24	2477	25	7721	13	5686	14	3567	18	11512	11	4283	17	5061	14	2749	20	2073	22	12174	10	16287	9	5656	14	92282	3
	21-30 cm	6604	8	1020	20	1424	24	3773	15	3871	13	2608	18	6778	10	3436	14	2886	14	1820	20	1389	22	8537	10	9887	9	4540	12	58571	3
	31-40 cm	4624	9	670	22	821	21	1914	14	2229	14	2089	16	4231	10	3128	12	2226	14	1251	19	773	22	5221	10	6709	8	3244	11	39130	3
	41-50 cm	3390	7	438	21	668	18	1346	13	1797	10	1419	14	2737	9	1835	11	1710	13	924	21	603	20	3243	9	4653	7	2199	11	26962	3
	51-60 cm	2064	8	247	24	468	21	946	13	971	12	925	14	1896	9	1584	11	975	14	474	20	430	19	1963	10	2725	8	1508	13	17176	3
	61-70 cm	954	12	125	27	203	24	535	16	478	15	434	18	822	13	807	15	529	16	241	23	178	28	801	14	1143	11	568	13	7819	4
	71-80 cm	371	15	56	46	80	35	200	21	254	21	133	29	362	16	330	18	299	18	165	30	160	31	391	19	471	14	297	20	3569	5
	81-90 cm	97	31	7	100	50	42	82	31	124	27	41	46	126	27	88	31	44	41	23	58	41	41	128	28	199	22	106	36	1158	9
	91-100 cm	37	45	0	.	0	.	14	71	20	58	9	100	12	71	6	100	31	50	7	100	36	45	66	33	63	37	44	45	344	15
	>100 cm	22	58	0	.	7	100	7	100	0	.	7	100	21	57	14	71	7	100	0	.	14	71	14	71	37	45	32	59	184	21
	total	29449	5	4313	16	6198	16	16537	10	15430	9	11232	13	28498	8	15513	10	13768	10	7654	16	5697	17	32539	8	42173	6	18194	10	247194	2
broadleaves	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	13217	8	5208	14	3967	19	5701	13	8518	9	2196	20	5949	12	3862	14	4611	15	1557	24	2029	23	6339	13	3721	19	21352	8	88227	3
	21-30 cm	7323	8	2260	14	2156	16	2171	13	4711	10	1702	19	3803	13	3225	15	2029	17	1023	27	1243	22	2448	16	1862	21	12337	8	48294	3
	31-40 cm	4837	8	1461	15	1278	17	1790	13	2610	10	785	24	2026	13	2286	13	1004	20	629	29	597	22	658	21	635	19	4872	9	25467	3
	41-50 cm	2833	8	1069	14	842	17	1061	13	1511	10	258	26	1032	14	1324	14	543	20	259	26	438	19	225	28	256	27	1886	9	13538	3
	51-60 cm	1035	10	499	19	479	18	862	14	1165	10	149	29	589	18	508	17	247	23	128	36	242	27	64	44	149	29	720	15	6837	4
	61-70 cm	256	20	162	25	174	22	266	18	430	15	14	71	148	30	156	26	91	38	42	57	65	44	34	51	54	35	250	20	2142	7
	71-80 cm	43	47	77	32	55	35	97	37	159	22	36	45	70	37	36	66	25	49	6	100	9	100	6	100	32	52	118	27	769	11
	81-90 cm	8	100	7	100	8	100	0	.	57	35	0	.	7	100	33	50	0	.	25	58	8	100	0	0	0	.	82	32	235	18
	91-100 cm	0	.	0	.	0	.	17	72	47	42	0	.	0	.	7	100	0	.	0	.	6	100	7	100	0	.	38	60	121	28
	>100 cm	0	.	0	.	0	.	7	100	16	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	44	57	68	46
	total	29552	6	10744	11	8959	13	11973	9	19225	7	5141	17	13625	10	11437	11	8549	13	3668	21	4636	18	9782	12	6708	17	41699	6	185698	2
indeterminable	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	.	0	.	0	0
	21-30 cm	0	0	0	.	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	.	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	.	0	0	0	0	0	.	0	0
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	24502	6	6958	13	6444	16	13422	10	14204	8	5763	14	17461	9	8145	12	9672	11	4306	19	4102	18	18513	8	20008	8	27009	7	180509	2
	21-30 cm	13927	6	3280	12	3580	14	5944	11	8582	8	4310	14	10581	8	6661	11	4915	12	2842	17	2631	18	10985	9	11749	8	16877	6	106866	2
	31-40 cm	9461	6	2131	13	2099	14	3704	10	4838	9	2874	14	6257	8	5414	9	3230	11	1880	17	1370	16	5879	9	7343	7	8116	7	64597	2
	41-50 cm	6223	5	1507	12	1510	13	2407	10	3308	7	1677	13	3769	8	3159	9	2253	12	1183	18	1042	16	3469	9	4909	7	4085	7	40500	2
	51-60 cm	3099	6	746	15	948	15	1808	10	2136	8	1074	13	2486	8	2092	10	1222	12	602	18	671	17	2027	10	2873	8	2228	10	24013	2
	61-70 cm	1210	10	288	18	377	17	801	13	908	11	448	18	970	12	963	14	621	15	282	22	242	24	835	13	1198	10	818	10	9961	3
	71-80 cm	415	15	133	26	135	25	297	18	413	15	169	25	432	14	366	18	324	17	171	29	169	31	398	19	502	13	414	16	4338	5
	81-90 cm	105	30	14	70	58	39	82	31	182	22	41	46	133	26	122	26	44	41	48	41	49	38	128	28	199	22	188	24	1393	8
	91-100 cm	37	45	0	.	0	.	30	50	66	34	9	100	12	71	14	71	31	50	7	100	42	41	73	31	63	37	81	37	465	13
	>100 cm	22	58	0	.	7	100	14	71	16	100	7	100	21	57	14	71	7	100	0	.	14	71	14	71	37	45	76	41	251	20
	total	59000	4	15057	10	15157	11	28510	8	34655	6	16373	11	42123	6	26950	8	22317	9	11322	15	10333	14	42322	7	48881	6	59893	5	432892	2

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. 1198423. Birmensdorf, Swiss Federal Research Institute WSL

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