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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–NFI3
bolewood harvested
type of last silvicultural treatment
regional demarcation: canton
unit: 1000 m³/yr
evaluation area: accessible forest without shrub forest NFI2/NFI3
grid: 1.4-km grid
change 1993/95–2004/06
	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
type of last silvicultural treatment	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%
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	.
no treatment	12	43	1	95	3	59	45	23	8	61	10	41	0	0	10	93	37	26	21	47	22	40	5	48	0	0	4	71	7	66	3	71	6	40	5	45	4	74	13	53	2	100	31	32	7	42	0	0	7	44	254	10
tending	107	30	0	0	2	100	117	23	22	55	39	55	0	.	2	85	29	47	11	71	32	54	12	56	0	.	11	90	45	45	2	48	56	42	5	74	46	48	0	100	1	71	53	31	4	75	6	80	50	37	643	11
thinning	99	17	0	0	12	60	156	14	30	31	45	24	3	72	14	51	29	29	43	34	69	28	29	27	2	58	11	52	41	35	20	38	69	20	8	59	47	29	8	47	8	64	81	19	12	45	1	100	98	22	928	6
secondary felling	16	51	0	.	2	100	82	28	17	62	36	45	2	100	0	0	35	35	22	39	30	38	13	73	6	77	8	100	25	57	5	100	15	55	25	46	22	70	0	0	8	52	53	31	32	45	0	0	32	41	485	11
final felling	26	38	2	100	14	88	86	29	37	58	10	61	0	.	1	100	55	32	25	46	16	87	10	73	0	.	5	100	12	69	4	100	31	46	19	80	3	100	15	61	13	73	51	40	19	62	0	.	10	72	459	12
selection felling	0	.	0	.	0	.	81	32	0	.	0	.	0	.	0	.	1	72	0	0	2	100	44	24	0	.	0	.	0	.	0	.	0	.	0	.	0	.	1	100	0	.	22	36	0	100	0	.	0	.	154	20
thinning of mountain forest	0	.	0	.	0	.	19	50	0	.	3	73	0	.	0	.	49	27	0	.	0	.	0	.	0	.	4	81	3	100	0	.	0	.	0	0	0	.	0	0	0	.	1	73	37	36	0	.	0	.	118	19
coppice cut	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	1	80	0	.	2	100	0	.	0	.	0	.	3	64
conversion	0	0	0	.	0	.	6	88	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	1	100	0	.	10	74	0	.	0	.	0	.	0	.	0	100	0	.	5	85	10	64	33	38
transformation	0	.	0	.	0	.	0	.	0	.	0	.	0	.	1	100	0	.	0	.	2	100	0	.	0	.	0	.	0	0	0	.	0	.	0	.	0	.	1	100	0	.	0	.	1	100	0	.	0	.	4	53
sanitary felling	213	21	0	100	16	43	611	10	25	64	229	19	0	.	6	57	54	25	105	24	180	22	41	27	19	66	60	35	140	26	10	46	42	35	65	35	99	33	5	71	10	75	99	23	18	31	33	42	197	19	2244	5
thinning of continuous cover forest	16	40	0	.	0	.	9	69	0	.	0	.	0	.	0	.	0	.	0	.	2	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	7	59	0	100	0	.	4	100	0	.	0	.	34	38	72	23
tending of forest edge	8	78	0	.	13	100	8	66	0	.	1	100	1	100	0	.	0	0	0	0	5	100	16	100	0	.	0	.	21	100	5	79	0	.	0	.	5	96	0	0	0	.	0	100	7	64	0	.	1	100	88	34
planting	6	100	0	100	0	.	59	43	0	.	14	91	0	.	0	0	2	100	0	.	4	88	2	100	2	100	0	.	0	.	5	100	20	100	0	.	12	100	0	.	0	.	75	42	0	0	6	100	37	50	243	21
agrosilvicultural treatments	1	93	3	71	2	72	30	46	0	.	3	100	0	0	0	0	2	97	4	100	3	72	3	73	0	.	0	0	18	76	0	.	0	100	0	100	1	100	8	44	0	0	6	66	3	49	0	.	0	0	84	24
total	504	12	7	47	63	33	1301	7	137	23	388	14	6	52	32	38	293	12	231	15	368	14	175	16	30	46	103	25	309	17	54	23	251	16	127	24	246	19	54	25	41	33	467	11	139	18	52	32	474	11	5688	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. 1299583. Birmensdorf, Swiss Federal Research Institute WSL

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