Selection from the list of topics

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
fellings
altitude (in 400 m classes) · main tree species
regional demarcation: protection forest region
unit: 1000 m³/yr
evaluation area: accessible forest without shrub forest NFI2/NFI3
grid: 1.4-km grid
change 1993/95–2004/06
		protection forest region
		Jura + Plateau		Northwestern Alps		Northeastern Alps		Southwestern Alps		Southeastern Alps		Southern Alps		Switzerland
altitude (in 400 m classes)	main tree species	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	.
	spruce	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	fir	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	larch	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	beech	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	maple	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	ash	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	oak	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other broadleaves	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	.	0	.	0	.	0	.	0	.	0	.	0	.
>1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	0	.	2	100	2	100	9	74	14	35	0	0	27	32
	fir	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	pine	0	.	0	0	0	0	0	0	0	0	0	0	0	0
	larch	0	.	0	0	0	.	13	63	3	61	1	100	16	51
	Arolla pine	0	.	0	0	0	0	4	91	10	61	0	0	14	51
	other conifers	0	.	0	.	0	0	0	0	0	0	0	.	0	0
	beech	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	maple	0	.	0	.	0	.	0	.	0	0	0	.	0	0
	ash	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	oak	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other broadleaves	0	.	0	.	0	.	0	0	0	0	0	.	0	0
	indeterminable	0	.	0	.	0	.	0	0	0	0	0	.	0	0
	total	0	.	2	100	2	100	25	47	27	31	1	100	57	26
1401-1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	11	60	129	27	33	40	37	31	155	19	19	59	386	13
	fir	1	100	1	100	0	0	0	100	2	85	0	0	4	55
	pine	0	.	0	0	0	0	0	0	2	55	0	0	2	55
	larch	0	.	0	0	0	100	21	39	16	33	1	71	40	25
	Arolla pine	0	.	0	0	0	0	3	73	0	0	0	.	3	73
	other conifers	0	.	0	.	0	0	1	100	0	0	0	0	1	100
	beech	0	100	0	100	0	0	0	.	0	0	0	0	1	72
	maple	0	100	0	74	0	0	0	0	0	0	0	0	0	65
	ash	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	oak	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other broadleaves	0	0	1	100	0	0	0	100	0	72	0	59	2	65
	indeterminable	0	.	0	0	0	0	0	0	0	0	0	0	0	0
	total	12	54	132	26	33	39	63	26	174	18	20	54	438	12
1001-1400 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	188	17	463	13	227	21	31	45	129	23	12	51	1050	9
	fir	82	22	77	19	35	38	12	60	8	57	0	100	211	13
	pine	0	0	0	0	0	0	16	53	1	71	1	100	21	48
	larch	0	0	0	0	0	0	26	61	0	0	0	0	30	61
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	0	0	0	100	0	100	0	0	0	.	0	.	0	72
	beech	57	22	25	39	13	39	0	0	1	71	8	54	100	17
	maple	1	69	10	56	2	53	0	0	0	0	0	100	14	43
	ash	0	0	1	89	1	100	1	89	0	0	0	100	4	52
	oak	2	100	0	0	0	.	0	100	0	0	0	0	2	97
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	0	0	0
	other broadleaves	1	46	3	35	2	59	2	55	0	62	4	55	12	24
	indeterminable	0	0	0	0	0	0	0	0	0	0	0	0	0	0
	total	332	14	579	12	280	19	89	31	140	22	25	36	1444	7
601-1000 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	906	9	330	15	174	20	3	59	13	36	0	0	1403	7
	fir	381	10	269	14	58	31	1	100	0	0	0	0	705	8
	pine	33	23	1	100	3	75	1	100	12	68	0	.	50	23
	larch	6	60	10	59	5	72	0	0	9	86	1	100	32	37
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	13	52	0	0	0	0	0	0	0	.	0	.	13	52
	beech	393	10	92	20	48	24	0	72	9	56	6	93	538	9
	maple	33	22	3	41	14	37	0	100	0	0	0	100	49	17
	ash	42	20	10	40	12	52	0	100	2	90	1	100	67	17
	oak	18	36	0	100	0	0	0	0	0	0	0	0	18	36
	sweet chestnut	0	100	0	0	0	.	0	0	0	0	4	46	5	45
	other broadleaves	22	35	6	38	12	44	1	88	2	69	6	70	50	22
	indeterminable	0	0	0	0	0	0	0	0	0	0	0	0	0	0
	total	1848	6	722	11	326	16	7	48	47	35	19	52	2929	5
=600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	1172	8	5	74	23	43	5	100	0	0	0	0	1189	8
	fir	258	13	0	0	5	55	0	.	0	.	0	.	260	13
	pine	75	16	0	0	1	100	1	100	0	100	0	0	77	16
	larch	55	38	0	0	0	0	0	.	0	100	0	0	55	38
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	9	47	0	.	0	0	0	0	0	.	0	0	9	47
	beech	506	9	3	71	11	46	0	0	0	0	0	0	512	9
	maple	43	20	4	72	1	100	0	0	0	.	0	0	47	19
	ash	88	16	1	73	1	77	0	0	0	100	0	0	89	16
	oak	88	19	0	0	0	0	0	0	0	.	0	100	87	19
	sweet chestnut	0	0	0	.	0	.	1	100	0	.	12	39	13	37
	other broadleaves	85	19	7	100	3	67	0	100	0	0	6	37	102	18
	indeterminable	0	0	0	.	0	.	0	0	0	.	0	0	0	0
	total	2380	5	20	57	44	33	7	74	1	76	18	30	2439	5
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	2277	5	925	9	456	13	86	24	311	14	31	41	3988	4
	fir	723	7	336	12	97	23	13	57	10	49	0	100	1146	6
	pine	108	13	1	100	4	64	19	47	15	54	1	100	144	13
	larch	61	35	10	59	6	66	60	33	28	35	3	51	173	19
	Arolla pine	0	.	0	0	0	0	7	60	10	61	0	0	18	43
	other conifers	22	37	0	100	0	100	1	100	0	0	0	0	21	36
	beech	956	7	117	18	71	19	0	72	10	50	14	51	1109	6
	maple	77	15	17	36	17	32	1	100	0	0	0	81	107	13
	ash	130	13	13	33	14	47	2	74	2	82	2	88	153	11
	oak	108	16	0	100	0	0	0	100	0	0	0	100	102	16
	sweet chestnut	0	100	0	0	0	.	1	100	0	0	16	31	17	29
	other broadleaves	107	17	17	43	17	35	4	45	3	55	17	32	159	13
	indeterminable	0	0	0	0	0	0	0	0	0	0	0	0	0	0
	total	4569	3	1436	7	681	11	192	18	388	12	85	22	7139	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. 1242152. Birmensdorf, Swiss Federal Research Institute WSL

back