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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)
diameter at breast height (10 classes) · conifers and broadleaves
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
diameter at breast height (10 classes)	conifers and broadleaves	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	.
	conifers	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	broadleaves	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	.	0	.	0	.	0	.	0	.	0	.	0	.
12-20 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	5491	5	3351	6	1952	8	1822	8	2048	7	614	11	15278	3
	broadleaves	7194	4	2169	7	1849	9	624	13	340	15	3108	6	15284	3
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	12684	3	5520	5	3801	6	2446	7	2388	6	3722	5	30562	2
21-30 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	13373	4	8078	5	5668	8	4099	7	5308	7	1606	10	38132	2
	broadleaves	14634	3	3060	7	3453	8	459	18	383	21	2812	7	24801	2
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	28008	2	11138	4	9121	6	4558	7	5691	6	4418	5	62933	2
31-40 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	25791	3	14627	5	8637	7	4941	7	8496	6	2700	10	65193	2
	broadleaves	15997	3	3388	9	3381	9	172	24	318	26	1636	8	24892	3
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	41788	2	18015	4	12018	6	5114	7	8814	6	4336	6	90085	2
41-50 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	26193	3	15557	5	9365	6	4717	7	8496	6	2803	8	67132	2
	broadleaves	11837	4	2502	10	2131	10	104	35	294	27	955	11	17824	3
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	38030	2	18059	4	11496	6	4821	7	8790	6	3758	7	84955	2
51-60 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	15752	4	10900	6	6362	8	3792	9	6309	7	2108	10	45224	2
	broadleaves	6043	7	1548	14	942	16	53	61	153	44	549	17	9289	5
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	21796	3	12448	5	7304	7	3845	9	6462	7	2657	8	54512	2
61-70 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	5499	7	4751	8	2916	11	1332	14	2850	10	1128	16	18476	4
	broadleaves	2569	11	417	26	272	29	30	64	93	51	253	20	3635	9
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	8069	6	5168	8	3188	11	1362	14	2943	10	1381	14	22110	4
71-80 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	2313	12	1892	14	1364	18	868	17	1426	14	719	21	8582	6
	broadleaves	911	17	100	49	116	42	30	74	0	.	331	27	1488	13
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	3224	10	1993	13	1480	17	897	17	1426	14	1051	17	10071	6
81-90 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	503	26	566	24	448	26	314	26	404	25	230	33	2466	11
	broadleaves	627	23	35	58	19	100	0	.	28	78	85	49	795	19
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	1130	18	602	23	467	25	314	26	432	24	315	27	3261	10
91-100 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	242	38	217	43	193	41	94	51	222	44	74	60	1041	19
	broadleaves	110	52	0	.	0	.	0	.	16	100	129	41	255	31
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	352	31	217	43	193	41	94	51	238	42	203	34	1296	16
>100 cm	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	37	100	122	65	71	77	47	74	90	51	288	39	655	25
	broadleaves	89	72	0	.	0	.	0	.	0	.	548	37	637	33
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	126	59	122	65	71	77	47	74	90	51	835	28	1292	21
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	95194	2	60061	4	36978	5	22026	5	35648	5	12271	6	262178	1
	broadleaves	60013	2	13220	6	12163	7	1472	13	1627	18	10406	5	98900	2
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	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. 1353803. Birmensdorf, Swiss Federal Research Institute WSL

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