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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
merchantable timber harvested
ownership (2 categories) · conifers and broadleaves
regional demarcation: canton
unit: 1000 m³/yr
evaluation area: accessible forest without shrub forest NFI1-NFI5
grid: 1.4 km grid, subgrids 1-5
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
ownership (2 categories)	conifers and broadleaves	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	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	.
	conifers	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	.
	broadleaves	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	.
	indeterminable	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	.
	total	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	.
public	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	.
	conifers	215	25	21	85	28	91	335	18	14	69	178	40	4	100	19	74	325	21	58	52	146	33	92	27	4	100	20	57	59	44	71	38	71	33	63	45	61	42	30	60	16	62	318	26	113	35	21	64	157	30	2496	7
	broadleaves	232	31	2	100	25	100	204	25	73	48	15	58	11	73	31	81	15	53	74	33	39	38	26	37	0	0	6	89	66	50	26	51	57	35	9	79	27	39	3	82	0	0	124	29	12	97	7	86	141	26	1284	10
	indeterminable	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	.	0	0	0	0	0	0	0	0	0	.	0	0	0	0
	total	448	22	23	86	53	95	539	16	87	42	193	38	14	61	51	58	340	21	132	32	185	29	118	24	4	100	27	48	125	35	97	33	128	28	72	41	88	35	33	55	16	62	442	21	125	33	28	55	297	24	3779	6
private	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	.
	conifers	26	52	6	79	48	81	736	18	42	100	44	55	0	0	21	100	13	100	36	59	332	25	73	40	0	0	21	100	150	39	2	81	23	89	42	50	143	36	0	0	3	100	47	57	3	100	9	80	131	29	1994	10
	broadleaves	37	36	0	0	0	0	329	30	0	0	30	66	0	0	5	74	1	72	6	91	60	43	12	52	0	0	0	0	63	47	0	0	41	51	8	54	100	48	25	53	1	100	16	59	0	0	7	100	99	43	853	15
	indeterminable	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	.	0	.	0	0	0	.	0	0	0	0	0	.	0	.	0	0
	total	63	38	6	79	48	81	1065	17	42	100	74	42	0	0	26	94	14	98	42	54	392	23	85	36	0	0	21	100	212	34	2	81	64	53	51	46	243	31	25	53	4	100	63	50	3	100	16	72	230	29	2848	9
total	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	.
	conifers	239	22	27	68	75	61	1066	14	52	74	220	33	4	100	41	64	337	21	94	39	478	20	165	23	4	100	41	58	210	31	73	37	93	33	106	34	204	28	29	60	20	54	368	24	116	34	29	51	287	21	4498	6
	broadleaves	268	27	2	100	25	100	532	21	75	48	45	49	10	73	36	70	15	51	80	31	99	30	38	30	0	0	6	89	129	34	26	51	97	29	17	47	126	39	29	48	1	100	141	27	12	97	14	66	240	23	2139	8
	indeterminable	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	0	0	.	0	0	0	0	0	.	0	0	0	0	0	0	0	0	0	.	0	0	0	0
	total	507	20	29	70	101	63	1599	12	127	42	265	30	14	61	77	50	353	20	174	27	577	18	203	21	4	100	47	51	339	25	100	32	191	26	123	31	330	25	58	39	21	53	509	20	128	32	44	43	527	18	6637	5

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. 1399132. Birmensdorf, Swiss Federal Research Institute WSL

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