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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.

NFI5
number of stems
tree age (in 40-year classes) · conifers and broadleaves
regional demarcation: economic region
unit: 1000 n
evaluation area: accessible forest without shrub forest
grid: 1.4 km grid, subgrids 1-5
state 2018/26
		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 age (in 40-year classes)	conifers and broadleaves	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%
n/a	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	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
	broadleaves	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
	indeterminable	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
=40 years	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	5211	16	1222	35	3075	27	8242	15	5592	16	1947	36	5992	19	3346	27	1955	25	831	34	974	36	3620	17	6956	15	3091	19	52054	5
	broadleaves	7793	12	4125	18	3729	21	5472	15	9831	10	1818	24	4470	16	2515	21	3098	20	592	30	1535	30	3452	18	3998	20	9589	13	62017	4
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	13004	10	5347	17	6804	18	13714	12	15423	9	3765	23	10462	13	5861	19	5052	17	1423	27	2509	25	7072	13	10954	12	12680	11	114070	3
41-80 years	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	13654	8	2190	22	1605	22	5869	16	6863	15	6267	18	12201	10	6343	13	6355	13	4318	17	2499	22	15597	11	21385	9	10831	11	115979	3
	broadleaves	14684	8	4761	14	3162	18	4767	13	7260	9	2733	22	7605	13	6550	13	4689	16	3140	23	3061	22	7881	14	3388	23	32479	7	106159	3
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	28337	6	6950	13	4767	16	10636	11	14123	9	9000	15	19806	8	12893	10	11044	12	7458	16	5560	18	23478	9	24774	8	43310	6	222138	2
81-120 years	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	7269	9	687	24	1141	25	1959	17	2459	13	2707	16	6127	13	4251	13	2843	16	1859	19	1347	22	7556	12	10343	11	4812	13	55360	4
	broadleaves	5569	9	1624	18	2065	21	1563	15	2530	11	1201	26	1886	18	2805	17	1773	27	1128	26	834	20	603	24	671	29	3080	13	27333	5
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	12838	7	2310	16	3206	17	3523	12	4989	9	3908	15	8013	11	7057	11	4616	15	2987	17	2181	17	8159	12	11014	10	7892	9	82693	3
121-160 years	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	2797	11	168	36	294	35	531	23	612	21	1507	22	3452	14	1886	18	2395	20	1197	29	994	26	4895	13	6532	12	3115	13	30374	5
	broadleaves	1597	18	473	27	255	38	428	26	430	22	105	40	600	24	465	23	329	31	110	36	158	34	428	59	134	50	884	39	6398	9
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	4394	10	640	24	549	27	960	19	1043	17	1612	21	4052	12	2351	16	2724	19	1307	27	1151	24	5323	13	6666	11	3999	13	36771	4
>160 years	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	1225	17	56	61	212	52	116	37	0	.	1213	40	2123	17	1091	24	2475	17	1183	26	868	32	5536	13	7452	11	2521	13	26071	5
	broadleaves	530	47	42	62	13	100	150	50	106	44	0	.	297	42	36	52	128	36	98	46	38	69	146	60	18	74	898	28	2501	16
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	1756	19	98	46	225	50	266	38	106	44	1213	40	2420	16	1127	23	2603	16	1280	24	905	31	5683	13	7470	11	3419	11	28572	5
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	conifers	30156	5	4322	16	6327	16	16718	10	15526	9	13641	12	29896	8	16917	9	16023	10	9388	14	6681	16	37204	7	52668	6	24370	8	279837	2
	broadleaves	30173	6	11024	11	9224	13	12380	9	20157	7	5857	16	14858	10	12373	11	10017	13	5067	18	5627	16	12511	11	8210	15	46930	6	204406	2
	indeterminable	0	0	0	.	0	.	0	.	0	0	0	.	0	0	0	.	0	0	0	.	0	.	0	0	0	0	0	.	0	0
	total	60329	4	15346	10	15551	11	29098	7	35684	6	19498	11	44753	6	29290	8	26039	8	14455	13	12307	13	49715	6	60878	5	71300	4	484244	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. 1303970. Birmensdorf, Swiss Federal Research Institute WSL

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