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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–NFI4
fellings
tree species (5 classes) · higher/lower altitude zone
regional demarcation: canton
unit: 1000 m³/yr
evaluation area: accessible forest without shrub forest NFI3/NFI4
grid: 1.4-km grid
change 2004/06–2009/17
		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
tree species (5 classes)	higher/lower altitude zone	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	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	.
	lower altitude zone	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	0	0	0	0
	higher altitude zone	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	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	0	0	0	0
spruce	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	.
	lower altitude zone	147	18	2	100	72	51	524	12	24	72	127	30	0	0	0	0	16	73	56	31	203	21	17	33	11	83	11	59	137	27	43	40	75	25	24	63	137	22	4	100	2	71	261	22	3	71	5	60	263	16	2206	6
	higher altitude zone	0	.	32	68	17	84	328	22	0	.	51	34	0	.	37	45	334	17	41	50	92	25	88	23	2	78	73	41	50	40	0	.	4	97	81	29	0	.	16	49	14	50	114	27	69	32	48	55	15	72	1546	8
	total	147	18	33	63	91	44	856	11	24	72	181	24	0	0	38	45	351	17	97	28	295	16	105	20	14	71	84	36	189	22	43	40	79	24	105	27	137	22	20	44	16	45	381	17	72	30	54	50	278	16	3767	5
fir	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	.
	lower altitude zone	70	27	4	100	18	80	363	16	12	59	41	48	0	.	0	0	1	100	80	33	106	25	28	36	1	100	2	100	46	31	2	95	33	31	6	71	50	39	0	0	1	100	116	30	3	100	5	55	63	31	1073	9
	higher altitude zone	0	.	0	0	10	57	117	22	0	.	37	56	0	.	2	65	4	100	6	56	42	38	35	26	0	0	0	0	20	64	0	.	8	61	18	37	0	.	2	71	2	89	55	33	13	53	9	72	0	0	387	12
	total	70	27	5	100	28	55	487	14	12	59	78	37	0	.	2	65	5	84	85	31	148	21	63	21	1	100	1	100	66	29	2	95	41	28	23	33	50	39	2	71	3	75	173	23	16	47	14	49	63	31	1475	7
other conifers	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	.
	lower altitude zone	43	40	0	0	1	100	38	38	11	48	17	79	2	100	0	0	26	45	8	55	5	60	0	100	0	0	0	100	5	75	5	62	8	47	0	0	18	35	1	100	0	0	17	48	10	70	0	0	42	31	256	13
	higher altitude zone	0	.	0	0	0	0	5	100	0	.	0	.	0	.	0	0	56	27	0	0	0	0	0	0	0	.	0	0	2	100	0	.	0	0	0	0	0	.	10	65	0	0	5	100	51	28	0	.	0	0	125	18
	total	43	40	0	0	1	100	44	35	11	48	18	79	2	100	0	0	80	23	8	55	5	60	0	100	0	0	0	100	7	61	5	62	8	47	0	0	18	35	11	60	0	0	22	43	62	26	0	0	42	31	384	11
beech	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	.
	lower altitude zone	132	19	0	0	12	66	252	16	42	39	46	50	0	.	17	79	6	58	55	25	61	31	21	45	1	100	11	68	79	35	29	39	66	22	15	52	59	30	0	100	-1	100	102	22	3	83	3	100	107	20	1144	7
	higher altitude zone	0	.	0	0	3	100	28	38	0	0	4	72	0	.	4	75	2	100	3	100	7	71	15	37	0	0	1	100	5	46	0	.	7	50	2	76	0	.	0	0	0	0	30	35	0	100	4	81	2	100	119	16
	total	132	19	0	0	15	57	287	15	42	39	52	47	0	.	19	66	7	50	57	25	67	29	36	30	1	100	12	64	87	33	29	39	73	21	18	47	59	30	0	100	-1	100	135	19	3	74	7	63	109	19	1284	6
other broadleaves	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	.
	lower altitude zone	81	17	0	0	2	81	82	24	34	36	18	40	10	56	1	81	12	55	23	26	33	42	1	73	5	100	3	70	46	29	7	72	38	29	5	89	46	23	49	25	4	100	68	30	7	56	12	49	63	22	661	7
	higher altitude zone	0	.	4	74	3	100	10	59	0	0	1	61	0	.	2	62	9	69	0	0	1	74	0	100	0	0	3	86	9	62	0	.	3	80	3	62	0	.	1	100	1	71	2	46	2	68	0	0	0	0	53	22
	total	81	17	4	74	5	68	94	22	34	36	20	37	10	56	2	50	20	43	23	26	34	41	1	61	5	100	6	56	56	26	7	72	41	27	8	60	46	23	49	25	5	88	73	29	9	48	12	49	63	22	727	7
indeterminable	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	.
	lower altitude zone	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
	higher altitude zone	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	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	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	.
	lower altitude zone	472	12	6	76	105	49	1259	9	122	27	250	23	12	50	18	77	60	34	221	19	409	16	67	24	18	64	27	45	314	18	86	28	220	16	49	52	310	16	54	24	5	89	564	15	26	50	25	41	538	13	5341	4
	higher altitude zone	0	.	35	64	33	69	488	17	0	0	93	33	0	.	44	40	405	16	49	44	142	26	139	18	2	78	77	39	86	31	0	.	22	45	104	26	0	.	29	39	17	44	207	21	136	22	60	50	17	66	2231	7
	total	472	12	42	54	140	41	1769	8	122	27	350	19	12	50	62	36	464	15	270	18	549	14	206	15	21	58	103	32	405	16	86	28	242	15	154	25	310	16	83	21	23	40	784	12	161	20	86	37	555	12	7636	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. 1266074. Birmensdorf, Swiss Federal Research Institute WSL

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