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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.

NFI2
number of stems
altitude (in 200 m classes) · number of cases of damage
regional demarcation: production region
unit: 1000 n
evaluation area: accessible forest without shrub forest
grid: 1.4-km grid
state 1993/95
		production region
		Jura		Plateau		Pre-Alps		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	±%
n/a	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	0	.	0	.	0	.	0	.	0	.
	one visible damage	0	.	0	.	0	.	0	.	0	.	0	.
	two or more visible damages	0	.	0	.	0	.	0	.	0	.	0	.
	dead or lying tree	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	.	0	.	0	.	0	.	0	.	0	.
>1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	0	.	494	47	15965	7	1953	18	18412	7
	one visible damage	0	.	0	.	108	49	4358	8	459	21	4926	7
	two or more visible damages	0	.	0	.	53	66	951	13	158	25	1162	12
	dead or lying tree	0	.	0	.	0	0	324	39	57	62	382	35
	total	0	.	0	.	655	44	21599	7	2627	17	24881	6
1601-1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	0	.	2975	22	17816	7	3480	15	24270	6
	one visible damage	0	.	0	.	617	21	4994	9	782	17	6392	7
	two or more visible damages	0	.	0	.	120	39	1593	13	214	24	1927	11
	dead or lying tree	0	.	0	.	35	72	109	44	29	58	173	33
	total	0	.	0	.	3747	21	24512	7	4504	14	32763	6
1401-1600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	693	28	347	45	8173	12	17168	8	5195	13	31576	6
	one visible damage	197	32	76	43	2022	15	4699	7	1167	15	8161	6
	two or more visible damages	47	51	18	72	368	21	1675	11	303	23	2411	9
	dead or lying tree	0	0	0	0	55	71	183	28	66	46	305	24
	total	937	26	441	43	10618	12	23726	7	6730	12	42452	5
1201-1400 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	5532	11	333	46	12874	9	17227	8	6111	13	42076	5
	one visible damage	1316	15	51	71	3803	11	4858	8	1344	16	11371	6
	two or more visible damages	362	21	12	75	1498	16	1693	15	360	20	3925	9
	dead or lying tree	0	0	0	0	69	47	136	33	4	100	209	27
	total	7209	10	397	45	18244	8	23913	7	7819	12	57582	4
1001-1200 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	14411	7	692	28	17430	7	13446	9	7518	12	53498	4
	one visible damage	3017	9	241	34	4693	9	4243	11	1475	13	13669	5
	two or more visible damages	750	14	28	54	1579	12	1508	13	585	19	4451	7
	dead or lying tree	25	61	0	0	39	63	131	33	97	44	291	23
	total	18203	7	962	27	23741	7	19328	8	9675	11	71908	4
801-1000 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	13213	8	5632	14	20937	7	12159	10	5796	14	57737	4
	one visible damage	3700	9	1221	16	5138	9	3749	10	1494	17	15302	5
	two or more visible damages	1621	14	242	22	1673	13	1633	13	651	19	5819	7
	dead or lying tree	19	71	0	0	47	47	93	41	34	73	192	27
	total	18552	8	7094	13	27794	7	17635	9	7975	13	79050	4
601-800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	15696	7	27416	6	12747	9	6798	12	5418	14	68075	4
	one visible damage	3856	9	4756	7	2407	11	1909	15	1692	17	14620	5
	two or more visible damages	1126	14	1109	11	828	17	700	18	1274	18	5037	7
	dead or lying tree	0	0	70	38	12	100	86	52	10	100	178	30
	total	20678	7	33351	5	15994	8	9493	11	8394	13	87910	3
=600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	16946	7	48834	4	3965	20	2926	19	7383	12	80054	3
	one visible damage	3148	9	7135	6	749	32	854	26	2096	14	13981	5
	two or more visible damages	872	17	1875	11	170	43	136	32	1187	17	4240	8
	dead or lying tree	32	52	128	57	0	0	10	100	39	84	209	40
	total	20997	7	57971	4	4884	20	3927	18	10705	11	98484	3
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	66491	2	83254	2	79594	3	103506	2	42853	4	375699	1
	one visible damage	15232	3	13479	3	19536	4	29665	3	10508	5	88421	2
	two or more visible damages	4778	7	3284	7	6289	6	9889	5	4733	7	28973	3
	dead or lying tree	75	35	198	39	257	26	1072	16	336	23	1938	11
	total	86577	2	100216	2	105676	2	144132	2	58430	3	495030	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. 1198721. Birmensdorf, Swiss Federal Research Institute WSL

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