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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.

NFI1
growing stock (stemwood)
ownership (2 categories) · diameter at breast height (10 classes)
regional demarcation: protection forest region
unit: 1000 m³
evaluation area: accessible forest without shrub forest
grid: 1.4-km grid
state 1983/85
		protection forest region
		Jura + Plateau		Northwestern Alps		Northeastern Alps		Southwestern Alps		Southeastern Alps		Southern Alps		Switzerland
ownership (2 categories)	diameter at breast height (10 classes)	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%
n/a	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	21-30 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	31-40 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	41-50 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	51-60 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	61-70 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	71-80 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	81-90 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	91-100 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	>100 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	.	0	.	0	.	0	.	0	.	0	.	0	.
public	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	8025	4	2724	7	2308	9	1927	8	2046	7	2207	7	19237	2
	21-30 cm	16124	3	5280	7	4842	8	3678	8	4893	7	2998	7	37815	2
	31-40 cm	24873	3	8428	7	7043	7	4338	7	7657	6	3344	8	55682	2
	41-50 cm	23301	4	7940	7	6830	7	4110	8	7607	6	3117	8	52904	2
	51-60 cm	14722	5	5728	8	4557	10	3159	10	5656	8	2356	9	36178	3
	61-70 cm	5499	7	2650	11	2466	13	1199	15	2655	11	1289	14	15758	4
	71-80 cm	2451	12	778	20	880	19	784	18	1249	15	821	20	6963	7
	81-90 cm	1030	19	179	42	418	27	257	29	411	25	248	31	2544	11
	91-100 cm	331	32	150	51	172	44	73	59	198	48	124	47	1048	18
	>100 cm	89	72	52	72	71	77	47	74	90	51	536	32	886	23
	total	96446	2	33907	5	29588	6	19572	6	32463	5	17040	5	229016	2
private	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	4659	6	2797	7	1493	10	520	16	342	19	1514	10	11325	3
	21-30 cm	11884	5	5858	6	4279	9	880	16	798	16	1420	11	25118	3
	31-40 cm	16915	5	9587	6	4975	9	776	17	1157	17	992	13	34403	3
	41-50 cm	14729	5	10120	6	4666	9	711	19	1184	18	641	17	32051	3
	51-60 cm	7074	7	6720	8	2747	12	685	22	806	18	302	23	18334	4
	61-70 cm	2570	11	2518	11	721	20	163	30	288	30	92	35	6352	7
	71-80 cm	773	21	1215	18	600	31	114	39	177	39	230	30	3108	11
	81-90 cm	100	50	422	27	48	79	58	58	21	100	67	56	717	20
	91-100 cm	20	100	67	78	21	100	20	100	40	72	79	47	248	32
	>100 cm	37	100	70	100	0	.	0	.	0	.	299	51	406	42
	total	58760	4	39374	5	19552	8	3926	13	4812	13	5637	9	132062	2
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	12684	3	5520	5	3801	6	2446	7	2388	6	3722	5	30562	2
	21-30 cm	28008	2	11138	4	9121	6	4558	7	5691	6	4418	5	62933	2
	31-40 cm	41788	2	18015	4	12018	6	5114	7	8814	6	4336	6	90085	2
	41-50 cm	38030	2	18059	4	11496	6	4821	7	8790	6	3758	7	84955	2
	51-60 cm	21796	3	12448	5	7304	7	3845	9	6462	7	2657	8	54512	2
	61-70 cm	8069	6	5168	8	3188	11	1362	14	2943	10	1381	14	22110	4
	71-80 cm	3224	10	1993	13	1480	17	897	17	1426	14	1051	17	10071	6
	81-90 cm	1130	18	602	23	467	25	314	26	432	24	315	27	3261	10
	91-100 cm	352	31	217	43	193	41	94	51	238	42	203	34	1296	16
	>100 cm	126	59	122	65	71	77	47	74	90	51	835	28	1292	21
	total	155207	1	73281	3	49140	4	23499	5	37275	4	22677	4	361078	1

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. 1371501. Birmensdorf, Swiss Federal Research Institute WSL

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