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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
deadwood volume (merchantable wood), lying
development stage
regional demarcation: canton
unit: 1000 m³
evaluation area: accessible forest without shrub forest
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
development stage	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	.	12	100	198	53	0	.	88	100	0	.	28	100	511	43	14	100	81	100	0	.	0	.	0	.	23	100	11	100	28	88	5	100	21	79	62	89	0	.	33	59	93	56	0	.	2	100	1211	24
young growth/ thicket	109	52	0	0	37	100	1293	40	77	81	242	53	16	100	45	75	816	32	27	57	209	59	14	100	0	.	16	92	140	45	2	100	77	57	140	89	0	.	16	67	87	79	232	55	201	46	3	100	101	66	3900	17
pole timber	169	37	0	.	18	71	839	28	111	58	428	43	0	.	16	66	347	27	18	54	417	68	84	44	64	75	38	57	32	48	10	63	19	52	113	46	31	43	444	33	77	56	264	34	395	30	10	100	201	33	4143	12
young timber	47	49	11	100	0	.	240	30	26	89	124	42	0	.	245	63	337	31	188	41	61	61	22	65	0	.	165	67	105	51	79	60	124	44	5	100	10	70	352	20	25	49	316	31	535	28	4	100	144	48	3164	10
medium timber	120	41	23	68	14	82	523	36	81	42	129	34	0	.	241	53	923	26	211	40	91	40	74	40	62	84	35	71	423	33	45	46	181	37	94	47	13	59	430	32	33	82	315	26	365	39	17	81	431	43	4873	10
old timber	479	36	83	87	140	44	1241	18	33	61	378	37	3	72	144	58	1478	23	203	35	440	37	75	38	140	51	97	47	482	35	69	50	178	36	340	38	267	39	294	36	219	65	899	24	788	21	23	59	160	32	8654	7
mixed	47	50	1	100	5	100	1355	19	116	58	590	60	0	.	295	58	982	19	310	42	219	31	147	39	10	86	156	71	436	39	1	100	153	48	115	64	61	63	667	24	27	55	633	33	1391	18	8	100	136	44	7863	9
total	970	21	119	63	224	33	5689	12	444	27	1980	23	19	86	1013	27	5394	11	972	19	1520	24	415	19	276	36	508	33	1640	17	217	29	761	18	813	25	402	28	2265	12	467	36	2694	13	3767	10	65	36	1174	20	33808	4

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. 1200882. Birmensdorf, Swiss Federal Research Institute WSL

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