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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
total number of stems
tree state (living/dead) · diameter at breast height (10 classes)
regional demarcation: protection forest region
unit: 1000 n
evaluation area: accessible forest without shrub forest NFI4/NFI5
grid: 1.4 km grid, subgrids 1-5
state 2018/26
		protection forest region
		Jura + Plateau		Northwestern Alps		Northeastern Alps		Southwestern Alps		Southeastern Alps		Southern Alps		Switzerland
tree state (living/dead)	diameter at breast height (10 classes)	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	.
	12-20 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	21-30 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	31-40 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	41-50 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	51-60 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	61-70 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	71-80 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	81-90 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	91-100 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	>100 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	.	0	.	0	.	0	.	0	.	0	.	0	.
living	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	66728	3	36922	6	19447	8	21392	8	25231	7	32934	6	202653	2
	21-30 cm	35985	3	21798	6	13716	8	12530	8	14787	7	19654	6	118470	2
	31-40 cm	22504	3	13266	6	9430	7	6582	8	8444	7	9209	7	69435	2
	41-50 cm	15117	3	8308	5	5877	7	3744	9	5512	7	4443	6	43001	2
	51-60 cm	8913	3	5009	6	3641	7	2141	9	3100	7	2392	10	25195	2
	61-70 cm	3689	5	2172	8	1580	10	901	13	1283	10	877	10	10501	3
	71-80 cm	1447	8	987	10	727	13	438	17	527	13	435	15	4562	5
	81-90 cm	441	14	234	19	250	18	145	26	226	21	244	21	1541	8
	91-100 cm	140	23	77	32	63	33	80	30	73	35	95	33	529	12
	>100 cm	79	36	36	45	36	45	14	71	51	38	83	39	299	18
	total	155043	2	88808	4	54766	6	47968	6	59235	5	70366	4	476187	1
dead	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	8495	6	7722	9	5410	11	5703	11	5003	11	8149	9	40483	4
	21-30 cm	3580	8	3317	11	2572	12	1961	13	2313	13	2650	11	16393	5
	31-40 cm	1871	12	2008	11	998	15	1140	13	1049	16	1047	16	8113	5
	41-50 cm	951	11	1063	11	487	15	481	14	544	17	483	16	4010	5
	51-60 cm	485	14	469	16	278	19	252	20	400	18	246	25	2130	7
	61-70 cm	177	22	238	22	78	30	92	28	84	29	110	35	780	11
	71-80 cm	86	32	99	31	36	45	22	58	20	58	67	40	330	16
	81-90 cm	13	71	7	100	6	100	14	71	7	100	35	45	83	29
	91-100 cm	7	100	0	.	7	100	7	100	0	.	8	100	29	50
	>100 cm	7	100	0	.	0	.	0	.	0	.	0	.	7	100
	total	15673	5	14924	7	9872	9	9672	9	9421	9	12795	7	72357	3
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	75223	3	44643	5	24857	8	27095	7	30234	7	41082	6	243136	2
	21-30 cm	39565	3	25115	5	16288	7	14491	8	17100	7	22304	5	134863	2
	31-40 cm	24375	3	15275	5	10428	7	7722	8	9493	7	10256	6	77548	2
	41-50 cm	16067	3	9371	5	6365	7	4225	8	6056	6	4926	6	47010	2
	51-60 cm	9398	3	5477	6	3918	7	2392	9	3500	7	2639	10	27325	2
	61-70 cm	3866	5	2410	8	1658	10	993	12	1367	10	987	9	11281	3
	71-80 cm	1534	7	1086	9	763	13	460	17	548	13	502	14	4892	4
	81-90 cm	454	13	241	19	256	18	160	26	233	20	280	20	1624	7
	91-100 cm	147	22	77	32	70	32	87	29	73	35	103	32	558	12
	>100 cm	86	34	36	45	36	45	14	71	51	38	83	39	306	17
	total	170716	2	103731	4	64638	6	57640	6	68657	5	83161	4	548544	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. 1230442. Birmensdorf, Swiss Federal Research Institute WSL

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