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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)
regional demarcation: canton
unit: 1000 m³
evaluation area: accessible forest without shrub forest
grid: 1.4-km grid
state 1983/85
	canton
	AG		AI		AR		BE		BL/BS		FR		GE		GL		GR		JU		LU		NE		NW		OW		SG		SH		SO		SZ		TG		TI		UR		VD		VS		ZG		ZH		Switzerland
diameter at breast height (10 classes)	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%
n/a	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	.
12-20 cm	1426	10	187	29	368	22	4793	6	452	16	1377	11	138	44	438	22	2968	6	1047	12	1348	11	719	12	255	25	657	16	1555	10	477	18	910	12	773	14	676	15	3142	6	422	19	2605	8	2446	7	167	30	1218	11	30562	2
21-30 cm	2867	10	656	26	1080	22	10075	5	1129	14	3075	10	84	39	948	21	6651	6	2604	11	2799	10	1607	12	533	25	1130	16	3952	9	872	21	2251	11	1523	14	1397	14	3458	6	918	16	5406	7	4558	7	273	29	3084	10	62933	2
31-40 cm	4308	9	783	24	1293	19	16227	5	1514	14	4657	10	65	54	1144	18	10136	5	3378	10	4931	10	2336	12	626	24	1626	15	5355	9	1064	20	3153	11	2367	13	1998	15	3015	8	1026	18	7566	7	5114	7	620	26	5784	9	90085	2
41-50 cm	3991	10	588	27	1289	21	16974	5	1490	15	3847	10	54	84	1145	17	10046	5	2800	11	4529	10	2521	11	447	29	1420	17	5271	9	623	21	3005	11	2272	13	1974	15	2503	8	714	19	6362	7	4821	7	655	27	5615	8	84955	2
51-60 cm	2769	12	203	38	843	24	11442	6	825	18	2059	14	28	95	541	25	7268	6	1549	14	2890	12	1633	14	232	28	1045	18	3345	11	413	25	1182	18	1584	16	1189	18	1851	11	556	24	3992	9	3845	9	456	32	2772	11	54512	2
61-70 cm	801	19	62	78	35	71	4520	8	368	28	1113	19	0	.	441	32	3475	10	634	23	686	21	505	21	80	47	554	27	1496	16	124	38	513	29	766	21	466	24	849	16	331	38	1779	13	1362	14	78	62	1074	16	22110	4
71-80 cm	436	31	48	72	25	100	2122	13	89	58	275	32	0	.	211	37	1699	13	117	54	152	41	484	30	0	.	166	40	578	30	27	100	160	54	418	33	127	41	778	19	148	53	695	22	897	17	24	100	394	28	10071	6
81-90 cm	172	41	0	.	0	.	881	21	78	72	95	58	0	.	101	45	516	22	30	100	71	60	26	100	11	100	30	100	235	39	38	100	28	100	67	72	23	100	231	33	64	59	130	42	314	26	0	.	119	51	3261	10
91-100 cm	31	100	0	.	0	.	220	43	0	.	42	71	0	.	69	76	238	42	25	100	0	.	71	71	0	.	0	.	52	78	0	.	0	.	21	100	40	100	203	34	50	72	80	71	94	51	0	.	59	73	1296	16
>100 cm	36	100	0	.	0	.	70	100	54	100	0	.	0	.	52	100	177	40	0	.	0	.	37	100	0	.	0	0	0	.	0	.	0	.	20	100	0	.	748	30	0	.	52	72	47	74	0	.	0	.	1292	21
total	16836	7	2528	23	4933	17	67324	4	5997	12	16541	8	369	39	5089	15	43173	4	12184	8	17407	8	9938	9	2184	21	6628	13	21838	7	3638	15	11203	9	9812	10	7891	11	16779	4	4229	15	28667	5	23499	5	2274	22	20118	7	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. 1201159. Birmensdorf, Swiss Federal Research Institute WSL

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