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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.

NFI2
total wood volume (stemwood)
tree condition · diameter at breast height (≤ or >30 cm)
regional demarcation: economic region
unit: 1000 m³
evaluation area: accessible forest without shrub forest
grid: 1.4-km grid
state 1993/95
		economic region
		Western Jura		Eastern Jura		Western Plateau		Central Plateau		Eastern Plateau		Western Pre-Alps		Central Pre-Alps		Eastern Pre-Alps		Northwestern Alps		Central Alps		Northeastern Alps		Southwestern Alps		Southeastern Alps		Southern Alps		Switzerland
tree condition	diameter at breast height (≤ or >30 cm)	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	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	=30 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	>30 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
standing dead	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	=30 cm	456	12	128	22	134	19	115	33	180	18	173	21	276	14	306	14	186	19	90	24	166	21	424	13	385	12	604	10	3621	4
	>30 cm	360	19	92	34	127	46	103	41	164	30	290	34	318	23	397	22	313	25	138	26	338	28	533	16	436	21	483	17	4092	7
	total	816	12	220	20	261	25	219	28	343	18	463	25	594	15	703	14	499	19	228	20	504	22	957	11	820	13	1086	10	7713	4
standing living	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	=30 cm	13997	4	3778	9	4738	9	6665	8	9498	6	4667	10	8483	6	7015	7	3851	9	2130	13	2491	14	7029	6	8220	6	9799	4	92361	2
	>30 cm	41374	3	12437	8	15663	8	26192	6	35214	5	14176	9	35846	5	26542	6	14557	8	6257	13	7943	10	19036	6	31226	5	18409	5	304874	1
	total	55371	3	16215	7	20401	7	32857	5	44713	4	18842	8	44329	5	33557	6	18408	8	8387	12	10434	10	26065	5	39446	4	28208	3	397234	1
lying dead	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	=30 cm	127	20	22	39	44	28	16	42	72	31	45	33	95	21	60	25	101	28	55	35	94	26	409	14	278	15	183	17	1600	6
	>30 cm	71	38	29	52	26	100	10	74	43	55	58	53	206	24	251	30	223	32	107	41	299	38	770	14	555	19	291	19	2940	8
	total	197	21	50	36	70	41	26	38	115	28	103	33	301	19	311	25	324	25	163	36	393	33	1179	12	833	16	474	14	4540	6
lying living	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	=30 cm	12	58	6	100	7	62	2	73	14	70	6	100	30	52	10	52	8	50	14	47	4	49	42	28	46	33	34	29	235	14
	>30 cm	21	71	38	72	21	73	11	100	6	100	5	100	27	58	9	100	8	100	0	.	0	.	45	38	46	57	80	42	315	20
	total	33	50	44	64	27	67	14	83	20	78	11	100	57	49	19	55	15	55	14	47	4	49	87	24	92	33	114	32	550	14
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	=30 cm	14591	4	3933	8	4923	9	6798	7	9764	6	4890	10	8884	6	7391	7	4146	9	2288	13	2755	14	7904	6	8929	6	10620	4	97817	1
	>30 cm	41825	3	12596	8	15837	8	26316	6	35427	5	14529	9	36397	5	27199	6	15101	8	6503	13	8580	10	20384	6	32263	5	19263	4	312221	1
	total	56417	3	16529	7	20760	7	33114	5	45191	4	19419	8	45282	5	34590	6	19247	7	8791	12	11335	10	28288	5	41192	4	29883	3	410038	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. 1329353. Birmensdorf, Swiss Federal Research Institute WSL

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