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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 NFI1-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	39	42	32	64	454	13	17	40	149	18	0	75	29	62	516	14	17	84	108	24	69	25	27	49	60	35	183	18	0	170234	39	36	56	36	76	26	65	45	58	40	210	17	162	25	21	41	145	23	2652	5
fir	37	38	17	43	29	50	382	12	14	38	51	44	1	100	3	157	25	53	87	25	197	20	127	19	6	69	29	37	77	35	6	62	37	38	54	29	43	41	20	40	-5	161	200	16	37	31	11	45	47	29	1536	6
pine	-2	179	0	.	0	100	4	213	8	53	3	93	-2	100	0	.	31	42	8	88	5	71	4	69	0	100	4	90	2	71	7	108	-2	150	2	96	4	87	-2	201	3	80	-3	104	-3	301	0	.	6	62	78	31
larch	2	387	0	.	0	.	5	57	0	94	3	62	0	.	-1	100	93	26	0	100	1	58	0	100	0	.	0	100	3	59	1	86	0	100	1	100	4	86	63	27	0	0	20	42	82	25	2	100	6	39	283	13
Arolla pine	0	.	0	.	0	.	2	100	0	.	0	.	0	.	0	.	26	40	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	100	0	.	0	.	8	69	0	.	0	.	37	33
other conifers	10	52	0	.	1	71	19	39	7	100	0	.	0	.	0	100	-1	119	2	90	9	64	0	100	0	.	0	100	7	70	4	100	4	69	0	100	0	86	2	92	0	100	9	61	0	93	0	.	4	53	78	20
beech	82	26	11	58	4	149	297	12	23	68	64	29	0	.	5	203	26	36	42	28	77	27	32	31	8	93	-3	243	112	24	29	38	55	28	23	38	49	23	107	22	16	54	114	19	-5	174	8	62	111	17	1287	6
maple	20	30	1	99	4	166	56	23	2	203	11	43	0	.	7	93	14	44	4	177	7	80	22	37	-1	439	-1	219	46	39	3	53	24	39	10	37	10	90	8	62	3	82	41	27	13	38	1	105	47	24	351	10
ash	14	39	0	.	-4	191	16	54	0	2798	29	60	1	100	1	516	5	134	-15	80	5	115	3	39	4	141	5	92	11	156	4	86	1	509	2	260	10	75	18	65	7	56	32	45	6	66	6	57	22	32	182	22
oak	16	54	0	.	0	.	15	38	0	194	8	41	11	77	0	.	2	78	-3	97	5	81	0	139	0	100	0	.	4	67	3	89	0	2451	0	100	13	64	-1	1416	0	10741	17	37	5	48	0	.	10	34	104	20
sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	8	50	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	-5	536	0	.	0	106	1	64	0	.	0	.	4	630
other broadleaves	22	30	0	100	2	109	32	30	4	94	4	457	1	79	-4	104	14	145	1	315	10	45	-2	110	1	334	2	66	3	196	2	50	10	74	7	46	14	68	42	48	-3	142	9	133	9	91	1	75	22	31	201	21
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	322	14	67	32	67	53	1283	8	74	33	322	16	12	61	40	68	759	11	143	24	425	15	255	14	46	41	97	29	448	15	57	51	169	20	154	19	224	16	317	17	79	33	649	10	315	17	50	33	421	11	6794	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. 1398937. Birmensdorf, Swiss Federal Research Institute WSL

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