Selection from the list of topics

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
number of stems
altitude (in 200 m classes) · number of cases of damage
regional demarcation: protection forest region
unit: 1000 n
evaluation area: accessible forest without shrub forest NFI1-NFI5
grid: 1.4 km grid, subgrids 1-5
state 2004/06
		protection forest region
		Jura + Plateau		Northwestern Alps		Northeastern Alps		Southwestern Alps		Southeastern Alps		Southern Alps		Switzerland
altitude (in 200 m classes)	number of cases of damage	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	.
	no visible damage	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	one visible damage	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	two or more visible damages	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	dead or lying tree	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	.	0	.	0	.	0	.	0	.	0	.	0	.
>1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	690	50	0	.	5980	16	10113	14	1892	26	18675	9
	one visible damage	0	.	244	46	0	.	1317	18	1899	15	493	30	3953	10
	two or more visible damages	0	.	78	59	0	.	455	24	479	26	152	46	1164	16
	dead or lying tree	0	.	0	0	0	.	88	72	243	60	32	100	364	45
	total	0	.	1012	46	0	.	7841	16	12735	13	2569	24	24157	9
1601-1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	5168	23	1410	38	6661	21	6362	16	4059	19	23660	9
	one visible damage	0	.	1471	25	387	37	1213	21	1559	18	1082	20	5713	10
	two or more visible damages	0	.	344	26	14	71	400	30	479	27	266	29	1504	14
	dead or lying tree	0	.	72	100	22	100	35	100	0	0	18	100	147	58
	total	0	.	7055	21	1834	35	8309	19	8400	15	5425	18	31024	9
1401-1600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	1232	32	8000	14	3212	24	5414	18	8863	15	6259	18	32979	7
	one visible damage	161	42	3210	15	635	25	1294	19	2461	17	1089	22	8851	8
	two or more visible damages	36	54	1228	21	112	47	521	28	716	22	319	29	2932	12
	dead or lying tree	0	0	17	100	26	75	189	78	17	100	0	0	250	60
	total	1430	31	12454	13	3985	23	7418	17	12057	14	7667	18	45011	7
1201-1400 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	5296	15	10754	13	6825	16	5393	20	3586	22	4903	18	36757	7
	one visible damage	1220	18	3108	13	1670	18	1010	23	1642	22	1501	20	10149	7
	two or more visible damages	350	31	1221	20	574	27	259	35	343	33	719	28	3465	11
	dead or lying tree	8	100	15	100	205	61	23	100	0	0	54	100	306	46
	total	6873	14	15098	12	9274	15	6685	19	5570	20	7177	16	50677	6
1001-1200 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	15190	10	11601	12	10058	15	3570	22	2228	28	5463	20	48111	6
	one visible damage	2982	12	3386	13	2710	16	913	28	976	29	1857	20	12824	7
	two or more visible damages	629	20	1169	16	682	21	243	35	598	31	557	28	3878	9
	dead or lying tree	19	100	83	54	35	100	83	82	17	100	0	0	237	39
	total	18820	9	16239	11	13485	14	4809	20	3819	24	7878	17	65050	6
801-1000 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	19703	9	11442	12	11143	14	3185	25	2821	26	5894	19	54188	6
	one visible damage	4580	13	3750	15	2952	18	530	32	756	26	1786	22	14354	7
	two or more visible damages	1339	17	772	21	812	24	204	40	243	30	529	28	3900	10
	dead or lying tree	70	50	65	66	17	100	16	100	61	58	63	77	291	29
	total	25693	9	16028	11	14925	13	3936	24	3881	23	8270	18	72733	5
601-800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	39851	6	9236	14	7018	17	1000	43	2501	24	5752	18	65357	5
	one visible damage	7920	8	1716	17	1906	30	439	40	611	26	2219	21	14810	7
	two or more visible damages	1961	12	369	28	505	47	172	47	219	35	691	25	3918	10
	dead or lying tree	30	64	36	100	7	100	54	74	25	76	0	0	151	40
	total	49762	6	11357	13	9436	18	1665	36	3355	23	8662	17	84237	5
=600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	54089	5	2023	37	2940	26	1199	37	104	100	8026	17	68382	5
	one visible damage	10222	6	160	60	887	44	206	53	0	.	2453	17	13928	6
	two or more visible damages	2621	10	96	100	172	44	106	54	0	.	827	22	3821	9
	dead or lying tree	184	34	0	0	17	100	0	0	0	.	83	62	284	29
	total	67116	5	2279	36	4015	27	1511	35	104	100	11390	15	86416	4
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	135362	2	58913	5	42607	7	32403	7	36576	6	42247	5	348109	2
	one visible damage	27086	4	17045	6	11146	9	6923	8	9903	7	12480	6	84583	2
	two or more visible damages	6936	6	5276	9	2872	13	2361	12	3078	11	4060	9	24583	4
	dead or lying tree	311	25	288	36	329	41	487	38	364	42	251	38	2030	16
	total	169695	2	81522	4	56955	6	42174	7	49921	6	59038	4	459304	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. 1198734. Birmensdorf, Swiss Federal Research Institute WSL

back