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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
increment (gross increment)
site quality · conifers and broadleaves
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 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
site quality	conifers and broadleaves	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	.
	conifers	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	.
	broadleaves	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	.
	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	.
	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	.
low	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	.
	conifers	3	66	2	185	0	.	103	25	-2	241	26	49	0	.	35	43	161	18	17	39	14	44	16	52	6	94	39	38	22	54	0	0	3	79	31	32	5	100	10	49	25	60	52	28	84	30	0	.	11	80	664	9
	broadleaves	3	131	4	100	0	.	62	38	10	49	19	66	0	.	7	63	0	95	43	42	7	51	13	50	-3	111	28	58	8	67	-2	100	16	55	2	112	0	.	0	100	11	89	16	33	13	54	0	.	4	83	268	16
	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
	total	7	90	6	73	0	.	165	23	9	71	45	42	0	.	42	40	161	18	60	35	21	37	29	41	4	189	67	34	30	44	-2	100	19	53	32	32	5	100	10	49	36	52	68	25	97	27	0	.	16	68	932	8
moderate	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	.
	conifers	0	.	3	206	-2	100	310	16	0	.	69	36	0	.	13	66	478	14	19	68	13	41	61	29	10	74	20	51	56	34	0	.	13	62	48	35	0	.	199	21	17	47	112	24	463	13	8	71	0	.	1914	6
	broadleaves	0	.	-1	145	0	.	19	148	0	.	20	37	0	.	5	62	68	30	7	75	4	91	11	58	11	67	2	95	18	49	0	.	2	204	5	61	0	.	31	81	1	71	34	46	50	38	0	.	0	100	295	18
	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
	total	0	.	2	416	-2	100	329	18	0	.	89	31	0	.	18	56	546	13	26	57	17	46	72	26	21	70	22	49	74	28	0	.	15	71	53	34	0	.	230	20	18	46	146	22	513	12	8	71	0	100	2209	6
good	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	.
	conifers	47	32	44	42	103	31	439	13	-4	222	151	24	0	.	38	39	171	23	33	35	206	18	126	23	14	51	26	36	103	24	30	69	33	39	81	30	31	48	20	65	65	32	242	16	23	63	14	48	73	31	2138	6
	broadleaves	68	29	4	90	27	38	175	18	21	54	52	43	0	.	3	188	51	34	26	40	83	27	17	50	17	56	16	73	60	46	25	48	62	28	41	37	24	33	326	17	25	36	113	27	16	69	7	91	64	31	1305	7
	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
	total	115	23	48	43	130	28	614	11	16	106	202	22	0	.	40	40	223	20	60	28	289	16	143	22	31	42	41	42	163	25	54	47	95	25	122	25	56	34	347	17	90	27	355	15	38	53	21	48	137	24	3443	5
very good	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	.
	conifers	151	21	0	.	3	226	474	12	15	70	84	34	2	95	15	67	0	.	76	28	250	19	43	32	16	100	15	63	94	26	51	33	64	29	6	52	173	20	0	.	0	100	134	21	0	0	5	71	217	17	1902	6
	broadleaves	181	17	0	.	2	137	238	15	34	39	109	32	1	220	5	104	0	.	77	30	93	29	32	43	-1	100	8	63	45	58	34	41	46	32	8	129	129	28	5	169	5	100	126	23	8	70	9	75	154	17	1333	7
	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
	total	332	14	0	.	5	188	712	10	49	34	193	25	4	118	20	69	0	.	153	21	343	18	75	30	15	105	23	50	140	27	85	28	110	25	14	86	302	19	5	169	5	100	260	17	8	70	13	60	371	13	3236	4
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	.
	conifers	201	17	49	41	105	32	1332	7	9	164	329	16	2	95	99	25	811	10	146	19	486	13	245	15	48	45	100	22	275	15	82	32	113	21	165	19	209	18	229	19	106	25	543	10	570	12	27	36	302	14	6636	3
	broadleaves	254	14	7	81	29	37	512	12	65	28	199	22	1	220	20	45	119	22	153	20	187	19	73	25	24	51	53	38	131	30	58	32	128	19	55	33	153	24	362	17	42	34	296	16	84	27	17	58	222	15	3282	4
	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
	total	455	12	57	40	134	28	1845	6	74	33	528	14	4	118	118	24	930	9	299	14	673	11	319	13	71	38	153	21	407	15	140	25	241	16	219	17	362	16	592	12	148	22	839	9	654	11	43	33	524	11	9919	2

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. 1403919. Birmensdorf, Swiss Federal Research Institute WSL

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