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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.

NFI3–NFI4
bolewood harvested
type of last silvicultural treatment
regional demarcation: canton
unit: 1000 m³/yr
evaluation area: accessible forest without shrub forest NFI3/NFI4
grid: 1.4-km grid
change 2004/06–2009/17
	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	9	39	1	71	3	71	29	36	3	58	11	44	0	0	3	100	24	47	0	100	9	56	7	60	0	0	7	71	23	56	7	80	16	61	3	83	14	40	3	57	0	100	15	49	14	62	1	100	55	34	260	13
tending	73	32	0	.	2	100	146	30	15	64	32	50	5	74	1	88	30	40	22	62	2	100	17	38	0	0	1	100	27	69	0	.	20	45	0	76	57	41	0	0	0	0	153	26	3	100	1	100	51	42	665	12
thinning	110	19	14	78	1	74	195	16	19	39	50	41	2	79	0	.	26	46	62	25	132	20	8	53	4	73	3	76	67	33	27	40	76	25	6	65	63	27	10	45	7	62	89	21	0	100	7	62	125	23	1102	7
secondary felling	54	30	0	.	1	100	227	19	1	100	16	69	0	.	0	0	98	25	59	37	46	36	9	84	0	.	6	83	58	38	3	100	15	54	10	73	26	48	11	73	0	0	134	25	12	57	0	.	21	43	816	9
final felling	58	46	11	88	51	60	216	25	14	100	75	43	2	100	21	72	45	39	17	58	129	34	0	.	8	100	38	50	47	52	0	.	14	62	22	70	31	55	0	100	0	0	4	96	9	76	0	.	61	45	882	12
selection felling	0	.	0	.	0	.	142	22	0	.	10	71	0	.	0	.	17	56	0	.	11	55	85	19	1	100	0	.	7	82	0	.	2	100	7	100	0	.	0	.	0	.	14	38	0	.	8	71	0	.	299	13
thinning of mountain forest	0	.	0	.	0	.	46	38	0	.	11	71	0	.	0	0	5	59	9	72	31	47	0	.	0	100	10	66	1	100	0	.	0	.	18	51	0	.	2	100	9	74	0	0	64	29	0	.	16	100	219	17
coppice cut	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	0	0	.	0	.	0	.	0	.	0	.	6	54	0	.	0	.	0	.	0	.	0	.	6	54
conversion	0	.	0	.	0	.	32	49	5	100	0	.	0	.	0	.	0	.	0	.	0	.	1	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	0	0	.	5	100	42	40
transformation	0	.	0	.	0	.	0	.	4	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	1	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	5	89
sanitary felling	62	31	4	100	18	100	160	23	22	86	42	32	0	100	2	100	64	43	18	53	56	32	7	59	0	.	1	100	29	42	11	91	13	53	51	41	38	45	12	45	4	66	86	29	12	41	10	52	17	45	732	10
thinning of continuous cover forest	34	31	0	.	1	100	39	39	9	47	0	.	0	.	20	56	0	.	0	.	0	.	6	64	0	.	0	.	6	69	8	59	34	34	0	.	0	.	0	.	0	.	2	100	0	.	18	45	93	25	273	13
tending of forest edge	6	76	0	.	0	.	38	55	10	99	0	0	0	.	2	100	0	0	0	0	9	56	0	.	0	.	0	.	32	63	16	72	1	100	0	.	8	71	5	67	0	.	4	87	0	100	0	.	7	59	141	26
planting	0	.	0	.	0	.	0	.	0	.	10	100	0	.	0	.	0	.	0	.	0	0	0	.	0	.	0	.	6	74	0	.	0	.	0	.	0	.	0	.	0	.	22	83	0	.	18	100	0	0	58	53
agrosilvicultural treatments	6	74	0	.	41	82	53	64	0	.	5	59	0	.	0	100	20	66	16	65	3	85	23	52	0	100	8	96	9	58	0	.	0	100	5	77	0	.	12	51	3	97	41	56	8	60	0	.	5	100	260	22
total	409	12	31	53	123	42	1439	8	110	28	286	19	10	48	49	38	347	15	211	17	449	14	172	14	15	63	80	31	343	17	71	27	199	15	123	25	243	17	66	22	20	36	632	12	133	20	69	35	467	12	6235	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. 1299592. Birmensdorf, Swiss Federal Research Institute WSL

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