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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.

NFI3
number of stems
altitude (in 200 m classes) · number of cases of damage
regional demarcation: protection forest region
unit: n/ha
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	n/ha	±%	n/ha	±%	n/ha	±%	n/ha	±%	n/ha	±%	n/ha	±%	n/ha	±%
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	.	280	33	0	.	288	11	324	9	276	14	305	6
	one visible damage	0	.	99	26	0	.	63	13	61	10	72	20	65	7
	two or more visible damages	0	.	32	45	0	.	22	20	15	24	22	40	19	14
	dead or lying tree	0	.	0	.	0	.	4	71	8	59	5	98	6	44
	total	0	.	410	27	0	.	378	9	408	8	375	11	394	5
1601-1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	349	16	301	26	366	16	294	10	267	13	317	7
	one visible damage	0	.	99	20	83	24	67	16	72	13	71	14	77	8
	two or more visible damages	0	.	23	21	3	65	22	27	22	24	17	26	20	12
	dead or lying tree	0	.	5	99	5	94	2	99	0	.	1	99	2	58
	total	0	.	477	15	391	21	456	13	388	8	357	11	416	6
1401-1600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	244	19	242	10	247	17	310	12	318	10	401	11	294	5
	one visible damage	32	33	97	11	49	20	74	14	88	13	70	17	79	6
	two or more visible damages	7	47	37	18	9	44	30	24	26	19	20	26	26	11
	dead or lying tree	0	.	1	99	2	73	11	77	1	99	0	.	2	60
	total	283	17	377	9	307	16	425	10	432	9	491	11	402	4
1201-1400 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	266	9	324	8	301	10	402	12	288	14	286	12	309	4
	one visible damage	61	13	94	9	74	13	75	17	132	14	88	15	85	5
	two or more visible damages	18	29	37	18	25	24	19	31	28	29	42	24	29	10
	dead or lying tree	0	99	0	100	9	60	2	99	0	.	3	99	3	45
	total	345	8	455	7	408	8	498	11	448	11	419	9	427	4
1001-1200 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	364	7	312	9	404	10	343	13	261	20	302	15	342	4
	one visible damage	72	9	91	9	109	11	88	22	114	21	103	15	91	5
	two or more visible damages	15	18	31	13	27	18	23	30	70	24	31	25	28	8
	dead or lying tree	0	100	2	53	1	99	8	80	2	98	0	.	2	38
	total	451	6	437	7	542	8	462	10	447	14	435	11	462	3
801-1000 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	369	6	303	9	401	9	436	13	310	18	439	11	364	4
	one visible damage	86	11	99	12	106	15	73	23	83	17	133	15	97	6
	two or more visible damages	25	16	20	19	29	22	28	34	27	24	39	23	26	9
	dead or lying tree	1	49	2	66	1	99	2	97	7	55	5	75	2	29
	total	482	5	424	7	537	8	539	11	426	13	617	9	489	3
601-800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	343	4	378	8	388	10	285	30	308	14	370	11	352	3
	one visible damage	68	6	70	13	105	27	125	25	75	16	143	16	80	6
	two or more visible damages	17	11	15	26	28	45	49	36	27	29	44	21	21	10
	dead or lying tree	0	64	1	99	0	99	15	67	3	74	0	.	1	40
	total	428	4	465	7	521	12	474	18	414	11	557	10	453	3
=600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	311	4	627	16	446	12	278	24	300	0	427	11	330	3
	one visible damage	59	6	49	51	134	37	48	45	0	.	130	12	67	5
	two or more visible damages	15	10	30	94	26	38	25	46	0	.	44	18	18	9
	dead or lying tree	1	34	0	.	3	98	0	.	0	.	4	60	1	29
	total	385	3	706	15	609	14	351	21	300	0	605	9	417	3
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	330	2	317	4	362	5	340	5	307	5	350	4	332	1
	one visible damage	66	3	92	5	95	8	73	7	83	6	103	6	81	2
	two or more visible damages	17	6	28	8	24	12	25	10	26	10	34	9	23	4
	dead or lying tree	1	25	2	36	3	41	5	37	3	42	2	38	2	16
	total	414	2	438	3	484	4	442	4	419	4	489	4	438	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. 1198843. Birmensdorf, Swiss Federal Research Institute WSL

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