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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
growing stock (stemwood)
altitudinal vegetation belts (NaiS; 6 classes) · diameter at breast height (main diameter classes)
regional demarcation: biogeographical region
unit: 1000 m³
evaluation area: accessible forest without shrub forest NFI4/NFI5
grid: 1.4 km grid, subgrids 1-5
state 2018/26
		biogeographical region
		Jura		Plateau		Northern Alps		Western Central-Alps		Eastern Central-Alps		Southern Alps		Switzerland
altitudinal vegetation belts (NaiS; 6 classes)	diameter at breast height (main diameter classes)	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	.
	12-15 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	16-23 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	24-35 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	36-51 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	=52 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	.	0	.	0	.	0	.	0	.	0	.	0	.
upper subalpine	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	0	.	0	.	0	.	79	44	140	26	70	28	289	19
	16-23 cm	0	.	0	.	0	.	250	45	374	19	161	27	785	18
	24-35 cm	0	.	0	.	0	.	483	25	814	19	549	29	1846	14
	36-51 cm	0	.	0	.	0	.	835	28	1336	19	324	28	2495	14
	=52 cm	0	.	0	.	0	.	765	27	1380	23	347	44	2491	17
	total	0	.	0	.	0	.	2411	20	4044	15	1451	22	7906	11
subalpine	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	3	100	0	.	200	19	228	25	277	23	100	28	808	12
	16-23 cm	5	100	0	.	764	19	624	19	1073	16	406	19	2873	9
	24-35 cm	1	100	0	.	2188	17	1400	19	2780	14	1106	20	7476	9
	36-51 cm	22	100	0	.	3856	15	2691	18	5125	12	1773	19	13468	7
	=52 cm	45	100	0	.	3758	16	3987	17	5983	14	2502	18	16274	8
	total	77	100	0	.	10766	13	8930	14	15239	10	5887	15	40899	6
high-montane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	29	82	0	.	517	14	463	15	623	17	193	17	1825	8
	16-23 cm	47	59	0	.	1611	12	1614	15	1806	12	791	17	5869	7
	24-35 cm	48	77	0	.	3977	12	3429	14	3630	12	1980	15	13064	6
	36-51 cm	116	52	0	.	7109	11	4358	13	6938	10	3603	14	22124	6
	=52 cm	456	53	0	.	10368	11	4808	14	8114	12	5333	14	29079	6
	total	696	43	0	.	23582	9	14672	11	21111	9	11900	11	71961	5
lower and upper montane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	1160	9	698	17	1605	8	62	29	104	23	494	19	4123	5
	16-23 cm	4024	7	2137	12	5661	7	279	34	447	23	1466	13	14014	4
	24-35 cm	9938	7	5383	11	16069	6	337	35	1312	21	3453	18	36491	4
	36-51 cm	18897	5	11222	9	27632	5	615	31	2208	18	3021	17	63596	3
	=52 cm	18121	7	16554	9	37535	5	306	46	3050	19	3186	21	78751	3
	total	52140	4	35995	7	88502	4	1599	28	7120	15	11620	14	196975	2
submontane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	341	25	1676	8	240	31	19	100	28	46	0	.	2304	8
	16-23 cm	1018	14	4834	8	743	22	21	100	104	42	0	.	6721	6
	24-35 cm	2509	15	10341	6	1555	22	20	100	241	42	0	.	14667	6
	36-51 cm	4610	12	17580	6	1969	19	0	.	279	41	0	.	24438	5
	=52 cm	3958	15	24161	6	2154	23	0	.	353	40	0	.	30625	5
	total	12436	10	58591	4	6662	16	60	100	1005	35	0	.	78755	4
hyperinsubric and colline	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	0	.	43	39	0	.	93	29	0	.	642	15	778	13
	16-23 cm	0	.	112	57	0	.	258	28	0	.	2058	11	2428	10
	24-35 cm	0	.	218	39	0	.	282	37	0	.	3610	10	4110	10
	36-51 cm	0	.	385	40	0	.	314	33	0	.	2893	11	3593	10
	=52 cm	0	.	132	87	0	.	185	62	0	.	2329	17	2646	16
	total	0	.	890	35	0	.	1132	27	0	.	11533	8	13555	7
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	1533	9	2417	7	2562	6	943	11	1171	11	1500	9	10126	3
	16-23 cm	5095	6	7084	6	8780	5	3046	10	3804	8	4882	6	32690	3
	24-35 cm	12496	6	15942	5	23790	5	5951	9	8777	8	10697	7	77653	2
	36-51 cm	23646	4	29187	4	40566	4	8814	9	15886	6	11615	6	129714	2
	=52 cm	22580	5	40847	4	53814	4	10050	10	18879	7	13696	7	159867	2
	total	65350	3	95477	3	129511	3	28805	7	48517	5	42390	4	410050	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. 1234297. Birmensdorf, Swiss Federal Research Institute WSL

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