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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
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	214	25	21	85	28	91	334	18	14	69	178	40	4	100	19	74	325	21	58	52	146	33	91	27	4	100	20	57	59	44	70	38	70	33	63	45	61	42	30	60	16	62	317	26	113	35	21	64	156	30	2490	7
	broadleaves	171	28	2	100	21	100	161	24	58	43	12	57	10	73	27	81	13	53	65	32	34	37	24	37	0	0	6	88	57	49	25	51	51	35	7	78	24	39	3	81	0	0	107	28	10	96	7	86	106	26	1051	9
	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	385	21	23	86	48	95	496	16	72	38	190	39	14	61	46	57	338	21	123	32	180	29	116	24	4	100	26	49	117	34	95	33	122	28	71	41	86	35	33	55	16	62	424	22	123	33	28	55	262	24	3541	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	51	6	79	48	81	733	18	42	100	44	55	0	0	21	100	13	100	35	59	331	25	73	40	0	0	21	100	149	39	2	81	23	89	42	50	142	36	0	0	3	100	47	57	3	100	9	80	130	29	1989	10
	broadleaves	33	37	0	0	0	0	273	29	0	0	24	64	0	0	5	74	1	72	6	90	47	39	11	52	0	0	0	0	57	46	0	0	34	52	8	55	71	41	23	52	1	100	15	59	0	0	6	100	77	44	701	14
	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	59	39	6	79	48	81	1005	17	42	100	68	42	0	0	26	94	14	98	41	55	378	23	84	36	0	0	21	100	207	34	2	81	57	54	50	47	214	30	23	52	4	100	62	49	3	100	15	71	207	29	2691	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	238	22	27	68	75	61	1063	14	52	74	219	33	4	100	41	64	337	21	94	39	477	20	164	23	4	100	41	58	210	31	73	37	93	33	106	34	203	28	29	60	20	54	367	24	116	34	29	51	286	21	4488	6
	broadleaves	203	24	2	100	21	100	433	20	59	43	37	47	10	73	32	69	14	50	71	30	81	27	35	30	0	0	6	88	115	34	25	51	84	29	16	47	95	32	27	48	1	100	123	26	10	96	13	65	183	24	1754	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	441	18	28	70	96	63	1496	12	111	42	256	30	14	61	73	50	351	20	164	28	558	18	199	21	4	100	47	52	325	25	98	32	177	25	122	31	299	24	56	39	21	53	490	20	126	32	42	43	469	18	6242	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. 1387378. Birmensdorf, Swiss Federal Research Institute WSL

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