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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.

NFI4–NFI5
net increment
main tree species
regional demarcation: canton
unit: 1000 m³/yr
evaluation area: accessible forest without shrub forest NFI4/NFI5
grid: 1.4 km grid, subgrids 1-5
change 2009/17–2018/26
	canton
	AG		AI		AR		BE		BL/BS		FR		GE		GL		GR		JU		LU		NE		NW		OW		SG		SH		SO		SZ		TG		TI		UR		VD		VS		ZG		ZH		Switzerland
main tree species	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%
n/a	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	.
spruce	120	23	43	39	32	64	469	13	17	39	173	18	0	75	35	53	632	12	17	84	107	25	69	25	30	45	65	33	198	17	0	170234	40	35	72	30	76	26	88	35	68	35	237	17	196	21	38	39	147	23	2968	5
fir	38	38	17	43	29	50	388	12	14	36	51	44	0	100	3	157	25	53	87	25	197	20	127	19	6	69	29	37	87	32	6	62	37	38	55	28	43	41	23	36	-3	240	201	16	36	32	14	42	47	29	1564	6
pine	-2	179	0	.	0	100	4	205	8	53	3	93	-2	100	0	.	34	39	8	88	5	71	4	69	0	100	4	90	1	192	7	108	-2	150	2	73	4	87	-3	147	3	79	-3	104	-3	361	0	.	6	62	80	31
larch	2	387	0	.	0	.	7	50	0	94	3	62	0	.	-1	100	145	19	0	100	1	58	0	100	0	.	0	100	3	63	1	86	0	100	1	100	4	86	85	23	0	0	20	42	102	22	1	100	6	39	379	11
Arolla pine	0	.	0	.	0	.	2	100	0	.	0	.	0	.	0	.	35	31	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	100	0	.	0	.	11	51	0	.	0	.	49	26
other conifers	10	52	0	.	1	71	18	42	7	100	0	.	0	.	0	100	0	124	2	90	9	64	0	100	0	.	1	84	7	70	4	100	4	69	0	100	0	86	2	92	0	100	9	61	0	93	0	.	4	53	77	21
beech	84	26	11	58	4	149	316	12	30	54	64	29	0	.	5	203	31	33	42	28	77	27	32	31	8	93	-3	243	129	23	29	38	55	28	24	37	49	23	111	21	17	51	115	19	-4	187	8	60	110	17	1345	6
maple	20	30	1	99	4	166	59	22	6	85	11	43	0	100	8	81	16	40	4	177	7	80	25	34	0	3860	2	204	51	36	3	53	22	44	10	37	10	90	17	39	4	63	41	27	19	33	1	139	48	23	390	10
ash	14	39	0	.	-4	191	19	49	2	256	29	60	1	100	1	579	8	84	-15	80	5	115	3	39	4	141	5	90	14	131	4	86	1	509	2	228	10	75	18	66	7	52	32	46	-1	1330	6	57	23	31	187	22
oak	19	48	0	.	0	.	17	35	0	194	8	41	11	77	0	.	4	62	-3	97	5	81	0	139	0	100	0	.	4	65	3	89	0	2451	0	100	13	64	0	18134	0	1026	17	37	5	59	0	100	11	33	113	19
sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	8	50	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	1	2148	0	.	0	106	-2	155	0	.	0	.	7	371
other broadleaves	22	30	0	100	2	109	24	62	4	86	6	274	0	1049	-4	104	29	77	1	315	11	43	-2	110	1	234	2	56	4	138	2	50	11	72	10	56	9	121	59	38	-4	115	11	112	18	53	1	75	22	30	239	20
indeterminable	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	0	0	0	0	0	0	0	0	0	0	0	0	0	0	.	0	0	0	0
total	326	14	71	31	67	53	1323	7	89	29	348	15	12	63	47	59	967	9	143	24	424	15	258	14	51	37	106	27	497	14	57	51	169	21	177	18	219	17	400	14	93	30	680	10	379	15	71	32	425	11	7398	3

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. 1299318. Birmensdorf, Swiss Federal Research Institute WSL

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