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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)
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	.	29	100	174	61	0	.	0	0	0	.	42	71	535	39	0	0	44	100	0	.	0	.	0	.	72	100	0	.	20	100	0	0	73	100	97	64	0	.	92	100	80	89	0	.	11	100	1270	23
young growth/ thicket	130	48	20	100	102	75	924	30	69	100	169	76	3	71	18	82	550	31	38	100	280	48	0	0	0	.	44	100	118	44	0	0	23	100	106	100	0	0	19	67	7	100	54	58	249	55	92	74	83	91	3100	14
pole timber	217	45	0	.	27	69	481	28	136	57	308	43	0	.	12	77	367	25	138	68	312	45	69	40	15	100	14	72	19	56	7	75	9	92	150	36	53	53	474	19	61	56	182	28	316	24	6	77	109	44	3482	10
young timber	30	49	8	100	0	0	532	33	20	71	82	46	0	.	72	75	265	25	212	56	94	62	21	100	16	100	220	63	142	44	9	100	129	47	0	0	26	100	720	19	68	48	209	29	607	23	5	100	125	49	3612	10
medium timber	165	42	45	56	18	68	986	24	86	42	107	44	15	100	134	56	1226	26	211	42	96	43	47	46	69	69	23	59	338	31	225	75	238	37	161	45	1	100	396	31	117	68	405	30	423	33	1	100	266	38	5799	9
old timber	321	40	22	75	206	47	1537	17	143	51	469	35	12	100	210	51	1496	17	266	35	977	31	195	70	140	54	194	41	587	30	91	85	146	58	498	32	177	51	624	31	296	42	868	27	1034	21	15	81	298	50	10822	7
mixed	28	75	0	0	136	95	1941	15	125	62	478	48	5	100	147	47	1521	15	391	42	365	31	182	37	39	71	184	49	663	25	40	71	168	39	134	39	21	88	980	21	262	38	718	26	1668	14	31	76	176	48	10406	6
total	891	21	95	39	519	35	6575	9	579	26	1613	21	36	57	635	25	5960	9	1256	20	2169	18	514	31	279	34	679	28	1940	15	372	50	733	21	1050	21	351	35	3310	10	811	23	2528	14	4377	9	149	49	1067	21	38491	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. 1346074. Birmensdorf, Swiss Federal Research Institute WSL

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