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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
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	.	92	40	140	26	70	28	302	18
	16-23 cm	0	.	0	.	0	.	285	41	400	18	161	27	846	17
	24-35 cm	0	.	0	.	0	.	495	25	875	19	549	29	1919	13
	36-51 cm	0	.	0	.	0	.	849	27	1355	19	324	28	2528	14
	=52 cm	0	.	0	.	0	.	796	27	1399	23	347	44	2542	16
	total	0	.	0	.	0	.	2517	20	4170	15	1451	22	8138	10
subalpine	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	3	100	0	.	213	18	228	25	289	23	108	26	840	12
	16-23 cm	5	100	0	.	791	18	640	18	1113	16	421	18	2970	9
	24-35 cm	1	100	0	.	2200	17	1422	18	2882	14	1134	19	7638	8
	36-51 cm	22	100	0	.	4259	15	2698	18	5164	12	1816	18	13959	7
	=52 cm	45	100	0	.	3840	15	3987	17	5983	14	2530	18	16385	8
	total	77	100	0	.	11302	13	8975	14	15430	10	6009	15	41793	6
high-montane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	29	82	0	.	530	14	473	15	627	17	194	17	1852	8
	16-23 cm	47	59	0	.	1643	12	1650	15	1810	12	791	17	5941	7
	24-35 cm	48	77	0	.	4048	12	3651	14	3663	12	1980	15	13390	6
	36-51 cm	116	52	0	.	7211	11	4459	13	6962	10	3603	14	22352	6
	=52 cm	456	53	0	.	10505	11	4835	14	8114	12	5384	14	29294	6
	total	696	43	0	.	23937	9	15067	11	21176	9	11953	11	72829	4
lower and upper montane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	1160	9	712	17	1651	8	62	29	120	22	511	18	4217	5
	16-23 cm	4024	7	2143	12	5748	7	279	34	459	23	1520	13	14174	4
	24-35 cm	9938	7	5383	11	16204	6	337	35	1395	21	3506	17	36763	4
	36-51 cm	19005	5	11416	9	28297	5	615	31	2263	18	3180	17	64777	3
	=52 cm	18248	7	16554	9	38114	5	306	46	3088	19	3244	21	79554	3
	total	52375	4	36208	7	90015	4	1599	28	7326	15	11961	14	199485	2
submontane	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	345	25	1689	8	240	31	19	100	28	46	0	.	2321	8
	16-23 cm	1018	14	4834	8	743	22	21	100	104	42	0	.	6721	6
	24-35 cm	2509	15	10327	6	1555	22	20	100	241	42	0	.	14653	6
	36-51 cm	4690	11	17616	6	1969	19	0	.	279	41	0	.	24553	5
	=52 cm	4070	15	24601	6	2154	23	0	.	353	40	0	.	31178	5
	total	12631	10	59068	4	6662	16	60	100	1005	35	0	.	79426	4
hyperinsubric and colline	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	0	.	43	39	0	.	101	27	0	.	642	15	786	13
	16-23 cm	0	.	112	57	0	.	294	27	0	.	2058	11	2465	10
	24-35 cm	0	.	218	39	0	.	287	36	0	.	3610	10	4115	10
	36-51 cm	0	.	385	40	0	.	326	32	0	.	2893	11	3604	10
	=52 cm	0	.	132	87	0	.	185	62	0	.	2329	17	2646	16
	total	0	.	890	35	0	.	1192	26	0	.	11533	8	13615	7
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-15 cm	1537	9	2444	7	2634	6	974	10	1203	11	1525	9	10318	3
	16-23 cm	5095	6	7089	6	8926	5	3169	10	3887	8	4952	6	33117	3
	24-35 cm	12496	6	15929	5	24007	5	6212	10	9056	7	10778	7	78478	2
	36-51 cm	23833	4	29417	4	41736	4	8947	9	16022	6	11816	6	131773	2
	=52 cm	22819	5	41287	4	54613	4	10109	10	18937	7	13834	7	161599	2
	total	65779	3	96167	3	131916	3	29411	7	49106	5	42905	4	415285	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. 1234302. Birmensdorf, Swiss Federal Research Institute WSL

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