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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
fellings
altitude (in 400 m classes) · main tree species
regional demarcation: production region
unit: 1000 m³/yr
evaluation area: accessible forest without shrub forest NFI2/NFI3
grid: 1.4-km grid
change 1993/95–2004/06
		production region
		Jura		Plateau		Pre-Alps		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	±%
n/a	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	0	.	0	.	0	.	0	.	0	.	0	.
	fir	0	.	0	.	0	.	0	.	0	.	0	.
	pine	0	.	0	.	0	.	0	.	0	.	0	.
	larch	0	.	0	.	0	.	0	.	0	.	0	.
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	0	.	0	.	0	.	0	.	0	.	0	.
	beech	0	.	0	.	0	.	0	.	0	.	0	.
	maple	0	.	0	.	0	.	0	.	0	.	0	.
	ash	0	.	0	.	0	.	0	.	0	.	0	.
	oak	0	.	0	.	0	.	0	.	0	.	0	.
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.
	other broadleaves	0	.	0	.	0	.	0	.	0	.	0	.
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	.	0	.	0	.	0	.	0	.	0	.
>1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	0	.	0	.	0	0	27	32	0	0	27	32
	fir	0	.	0	.	0	.	0	.	0	.	0	.
	pine	0	.	0	.	0	0	0	0	0	0	0	0
	larch	0	.	0	.	0	.	15	53	1	100	16	51
	Arolla pine	0	.	0	.	0	0	13	51	0	0	14	51
	other conifers	0	.	0	.	0	.	0	0	0	.	0	0
	beech	0	.	0	.	0	.	0	.	0	.	0	.
	maple	0	.	0	.	0	.	0	0	0	.	0	0
	ash	0	.	0	.	0	.	0	.	0	.	0	.
	oak	0	.	0	.	0	.	0	.	0	.	0	.
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.
	other broadleaves	0	.	0	.	0	.	0	0	0	.	0	0
	indeterminable	0	.	0	.	0	.	0	0	0	.	0	0
	total	0	.	0	.	0	0	56	27	1	100	57	26
1401-1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	7	83	4	80	79	27	276	16	19	59	386	13
	fir	1	100	0	0	1	100	2	82	0	0	4	55
	pine	0	.	0	.	0	0	2	55	0	0	2	55
	larch	0	.	0	.	0	.	38	26	1	71	40	25
	Arolla pine	0	.	0	.	0	0	3	73	0	.	3	73
	other conifers	0	.	0	.	0	0	1	100	0	0	1	100
	beech	0	100	0	.	1	100	0	0	0	0	1	72
	maple	0	100	0	0	0	100	0	100	0	0	0	65
	ash	0	.	0	.	0	.	0	.	0	.	0	.
	oak	0	.	0	.	0	.	0	.	0	.	0	.
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.
	other broadleaves	0	0	0	.	0	0	1	79	0	59	2	65
	indeterminable	0	.	0	.	0	0	0	0	0	0	0	0
	total	8	70	4	80	80	27	322	14	20	54	438	12
1001-1400 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	159	15	29	73	574	12	286	17	12	51	1050	9
	fir	69	25	13	48	109	18	27	36	0	100	211	13
	pine	0	0	0	.	0	0	18	50	1	100	21	48
	larch	0	0	0	.	0	0	28	61	0	0	30	61
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	0	0	0	.	0	100	0	100	0	.	0	72
	beech	51	24	6	52	34	33	6	44	8	54	100	17
	maple	1	69	0	0	9	64	4	46	0	100	14	43
	ash	0	0	0	0	1	89	2	68	0	100	4	52
	oak	2	100	0	.	0	0	0	100	0	0	2	97
	sweet chestnut	0	.	0	.	0	.	0	.	0	0	0	0
	other broadleaves	1	46	0	0	3	37	4	36	4	55	12	24
	indeterminable	0	0	0	.	0	0	0	0	0	0	0	0
	total	283	14	48	48	730	11	376	15	25	36	1444	7
601-1000 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	156	16	744	11	450	13	76	25	0	0	1403	7
	fir	134	15	246	14	332	13	9	58	0	0	705	8
	pine	12	35	20	30	1	100	16	52	0	.	50	23
	larch	0	0	6	60	3	72	20	50	1	100	32	37
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	0	100	13	53	0	0	0	0	0	.	13	52
	beech	221	13	174	17	111	16	38	36	6	93	538	9
	maple	14	29	18	31	13	37	4	38	0	100	49	17
	ash	20	30	22	25	16	31	8	66	1	100	67	17
	oak	1	65	17	39	0	100	0	0	0	0	18	36
	sweet chestnut	0	.	0	100	0	.	0	0	4	46	5	45
	other broadleaves	8	49	14	47	12	42	9	34	6	70	50	22
	indeterminable	0	0	0	0	0	0	0	0	0	0	0	0
	total	567	9	1273	8	939	9	181	18	19	52	2929	5
=600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	157	25	1020	8	27	40	7	80	0	0	1189	8
	fir	38	30	222	14	2	88	3	71	0	.	260	13
	pine	20	34	55	18	1	100	1	88	0	0	77	16
	larch	7	91	48	42	0	0	0	100	0	0	55	38
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	1	74	8	54	0	0	0	0	0	0	9	47
	beech	194	17	310	11	11	45	3	75	0	0	512	9
	maple	22	33	21	23	2	100	2	82	0	0	47	19
	ash	27	29	61	20	2	66	1	80	0	0	89	16
	oak	27	42	61	19	0	0	0	0	0	100	87	19
	sweet chestnut	0	.	0	0	0	.	1	100	12	39	13	37
	other broadleaves	21	30	64	24	2	78	7	93	6	37	102	18
	indeterminable	0	0	0	0	0	.	0	0	0	0	0	0
	total	514	12	1869	6	46	34	25	43	18	30	2439	5
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	481	11	1796	6	1127	8	671	10	31	41	3988	4
	fir	241	12	482	10	438	10	40	28	0	100	1146	6
	pine	33	25	75	15	2	75	37	33	1	100	144	13
	larch	7	91	54	37	3	72	101	23	3	51	173	19
	Arolla pine	0	.	0	.	0	0	17	43	0	0	18	43
	other conifers	1	69	21	39	0	100	1	87	0	0	21	36
	beech	468	10	489	9	152	14	47	30	14	51	1109	6
	maple	37	22	40	19	24	32	10	30	0	81	107	13
	ash	47	21	83	16	19	27	11	51	2	88	153	11
	oak	31	38	77	17	0	100	0	100	0	100	102	16
	sweet chestnut	0	.	0	100	0	.	1	100	16	31	17	29
	other broadleaves	29	25	78	21	17	31	22	35	17	32	159	13
	indeterminable	0	0	0	0	0	0	0	0	0	0	0	0
	total	1376	6	3193	4	1783	6	957	8	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. 1242163. Birmensdorf, Swiss Federal Research Institute WSL

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