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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
fellings
tree species (5 classes) · higher/lower altitude zone
regional demarcation: economic region
unit: 1000 m³/yr
evaluation area: accessible forest without shrub forest NFI3/NFI4
grid: 1.4-km grid
change 2004/06–2009/17
		economic region
		Western Jura		Eastern Jura		Western Plateau		Central Plateau		Eastern Plateau		Western Pre-Alps		Central Pre-Alps		Eastern Pre-Alps		Northwestern Alps		Central Alps		Northeastern Alps		Southwestern Alps		Southeastern Alps		Southern Alps		Switzerland
tree species (5 classes)	higher/lower altitude zone	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	.
	lower altitude zone	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
	higher altitude zone	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	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
spruce	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	lower altitude zone	184	18	92	26	296	21	568	12	576	11	47	53	172	19	147	28	19	53	7	58	15	54	3	71	7	45	14	90	2206	6
	higher altitude zone	255	16	0	.	2	100	4	100	10	72	126	31	281	21	232	21	93	38	40	51	42	41	69	32	303	18	48	45	1546	8
	total	440	12	92	26	298	21	572	12	585	11	173	27	453	15	380	17	112	32	47	44	57	33	72	30	310	17	62	40	3767	5
fir	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	lower altitude zone	238	20	24	38	65	32	234	19	175	18	34	56	188	20	71	32	0	0	3	86	3	100	3	100	1	100	0	0	1073	9
	higher altitude zone	100	18	0	.	1	100	0	0	0	0	67	39	114	23	54	30	9	71	2	89	6	65	13	53	4	100	2	71	387	12
	total	337	15	24	38	66	31	234	19	175	18	102	32	301	15	125	22	9	71	5	63	8	55	16	47	5	84	2	71	1475	7
other conifers	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	lower altitude zone	21	33	16	35	32	45	39	36	98	22	0	0	4	66	2	71	1	100	0	0	4	100	10	70	25	45	1	100	256	13
	higher altitude zone	0	0	0	.	0	.	0	.	0	.	0	0	0	0	0	0	11	71	0	0	2	100	51	28	54	28	11	58	125	18
	total	20	33	16	35	32	45	39	36	98	22	0	0	4	66	2	71	12	68	0	0	6	74	62	26	78	24	12	54	384	11
beech	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	lower altitude zone	159	14	123	20	96	26	220	16	246	14	12	67	82	29	87	31	45	44	3	119	39	52	3	83	5	58	0	100	1144	7
	higher altitude zone	65	22	0	0	4	100	0	0	1	100	5	59	12	46	13	38	2	76	0	100	5	62	0	100	2	100	0	0	119	16
	total	222	12	123	20	100	26	221	16	247	13	18	51	92	26	101	28	47	41	3	121	42	47	3	74	7	50	0	100	1284	6
other broadleaves	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	lower altitude zone	83	22	79	21	70	27	102	22	187	12	4	79	16	43	21	38	7	66	9	63	6	55	7	56	1	64	59	23	661	7
	higher altitude zone	6	46	0	0	0	0	0	0	0	0	4	43	9	60	18	38	0	71	1	71	2	57	2	68	9	69	1	100	53	22
	total	88	21	79	21	70	27	102	22	187	12	8	46	25	35	39	27	7	64	10	60	8	45	9	48	10	61	59	23	727	7
indeterminable	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	lower altitude zone	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
	higher altitude zone	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	0	0	0	0
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	lower altitude zone	684	11	334	14	558	15	1163	9	1282	8	97	42	461	14	329	21	72	36	22	64	67	41	26	50	39	39	74	25	5341	4
	higher altitude zone	426	12	0	0	7	82	4	100	11	65	202	27	416	17	317	18	116	36	43	48	56	34	136	22	372	17	61	37	2231	7
	total	1108	8	334	14	567	14	1167	9	1293	7	302	23	876	11	647	14	187	26	65	38	120	27	161	20	410	16	136	22	7636	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. 1266073. Birmensdorf, Swiss Federal Research Institute WSL

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