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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
volume of deadwood (stemwood)
diameter at breast height (10 classes)
regional demarcation: canton
unit: 1000 m³
evaluation area: accessible forest without shrub forest NFI1-NFI5
grid: 1.4 km grid, subgrids 1-5
state 2018/26
	canton
	AG		AI		AR		BE		BL/BS		FR		GE		GL		GR		JU		LU		NE		NW		OW		SG		SH		SO		SZ		TG		TI		UR		VD		VS		ZG		ZH		Switzerland
diameter at breast height (10 classes)	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	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%
n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
12-20 cm	87	26	26	43	31	35	491	11	65	28	191	22	5	51	79	32	555	11	189	23	218	20	92	23	23	52	85	32	187	18	35	34	91	26	116	27	50	36	801	12	74	32	345	13	573	12	24	49	115	32	4550	4
21-30 cm	108	29	5	100	132	29	878	13	113	37	213	26	12	100	103	36	1063	13	201	27	383	29	30	53	79	40	84	32	307	24	41	55	225	27	249	35	67	47	616	15	166	27	468	21	624	14	27	82	248	29	6442	5
31-40 cm	76	48	14	100	155	44	1484	13	141	32	267	32	0	0	136	37	1133	15	444	39	353	22	148	32	84	45	150	45	394	24	57	41	140	41	152	39	54	82	428	19	124	43	556	20	1011	14	44	77	161	28	7705	5
41-50 cm	194	34	28	71	67	51	1164	15	109	40	292	26	14	100	109	43	1036	16	180	33	366	25	71	45	52	77	183	37	390	23	139	81	141	37	217	38	103	41	402	18	98	46	429	25	700	15	12	100	169	36	6665	6
51-60 cm	217	39	20	100	103	82	1032	17	83	71	314	38	0	0	103	56	1048	16	84	50	150	46	67	58	35	72	66	59	201	35	61	78	40	71	183	44	43	71	307	40	118	41	357	29	667	21	43	100	180	43	5520	7
61-70 cm	182	55	0	0	31	100	349	30	29	100	152	54	0	0	32	100	425	25	71	72	487	39	0	0	0	0	109	51	104	50	39	100	96	58	0	0	34	100	199	50	139	45	154	46	291	29	0	0	68	100	2989	12
71-80 cm	26	100	0	0	0	0	316	40	40	100	170	58	0	0	0	0	52	73	87	71	137	58	0	0	0	0	0	0	135	58	0	0	0	0	47	100	0	0	190	41	0	0	72	71	90	58	0	0	75	71	1437	17
81-90 cm	0	0	0	0	0	.	92	71	0	0	0	0	0	.	0	0	104	58	0	0	0	0	0	0	0	.	0	0	44	100	0	.	0	0	0	0	0	0	58	75	0	0	55	100	37	100	0	.	0	0	389	33
91-100 cm	0	0	0	.	0	.	53	100	0	.	0	.	0	.	49	100	0	0	0	0	0	.	0	0	0	.	0	.	0	0	0	.	0	0	0	0	0	0	23	100	0	.	0	0	26	100	0	.	0	0	152	53
>100 cm	0	.	0	.	0	.	0	0	0	.	0	0	0	.	0	0	0	0	0	0	0	0	106	100	0	.	0	.	0	0	0	.	0	.	0	0	0	0	0	0	0	.	0	0	0	0	0	.	0	.	106	100
total	891	21	94	39	519	35	5858	9	579	26	1599	21	31	64	612	26	5415	10	1256	20	2094	18	514	31	273	35	677	28	1761	15	372	50	733	21	962	22	351	35	3025	10	719	23	2435	14	4020	10	149	49	1016	22	35956	3

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. 1267142. Birmensdorf, Swiss Federal Research Institute WSL

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