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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 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
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	6	61	3	89	0	.	94	18	2	111	29	34	0	.	27	30	179	12	15	33	10	49	10	42	10	44	55	23	33	31	0	0	5	52	21	29	3	100	15	37	22	40	60	21	105	16	0	.	7	80	711	6
	broadleaves	8	42	1	170	0	.	41	28	16	35	10	63	0	.	11	42	0	69	41	27	3	51	13	40	0	504	13	54	8	48	-1	100	21	38	5	60	0	.	0	100	6	89	19	24	11	38	0	.	3	83	236	11
	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
	total	14	39	4	71	0	.	135	16	18	36	39	31	0	.	39	26	179	12	56	24	13	41	23	32	10	56	68	22	41	27	-1	100	27	36	27	28	3	100	15	37	28	38	78	19	117	15	0	.	9	68	947	6
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	.	7	62	0	690	313	10	0	.	73	25	0	.	21	43	637	8	18	42	15	32	49	23	11	50	23	31	59	29	0	.	11	54	60	25	0	.	224	11	33	28	165	15	504	8	7	58	0	.	2235	4
	broadleaves	0	.	0	206	1	100	50	33	0	.	11	36	0	.	11	44	67	18	11	46	3	65	13	33	5	64	5	47	19	39	0	.	2	136	7	54	0	.	77	23	-1	201	40	23	75	19	0	100	3	97	401	8
	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
	total	0	.	7	73	2	149	363	11	0	.	83	23	0	.	32	40	704	7	29	36	18	32	62	20	16	49	27	30	78	24	0	.	12	58	67	24	0	.	301	10	33	28	205	14	579	8	7	58	3	97	2636	4
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	54	27	31	34	106	25	466	9	6	89	180	16	0	.	26	34	209	15	54	20	202	13	131	16	8	43	37	31	162	17	29	42	33	27	99	19	31	40	30	33	38	29	251	12	20	39	36	28	80	21	2338	4
	broadleaves	72	19	8	51	24	28	173	12	23	32	77	23	0	.	7	61	63	25	54	21	68	19	25	30	15	40	19	40	86	23	30	33	64	24	38	24	34	28	343	10	20	32	135	18	20	33	8	53	78	21	1476	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
	total	126	17	39	33	130	22	639	8	29	36	257	14	0	.	32	31	272	13	108	17	270	12	155	15	23	32	55	29	248	15	59	28	97	20	138	17	65	28	373	10	58	25	386	10	39	29	44	26	158	17	3814	3
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	190	14	7	67	9	65	469	9	27	35	86	23	2	72	8	56	7	100	108	19	194	16	55	35	9	100	15	47	108	20	31	27	98	20	14	44	142	17	0	.	3	62	141	15	2	57	7	48	223	12	1956	4
	broadleaves	183	12	3	68	3	86	236	10	39	26	112	20	9	55	11	53	0	100	63	19	69	23	18	39	0	660	15	52	47	30	44	26	68	18	12	49	118	20	4	97	4	61	143	14	13	48	8	47	160	12	1375	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
	total	373	10	10	62	12	61	705	8	66	22	199	16	11	52	19	44	7	100	171	15	262	14	73	30	8	101	30	37	154	18	75	21	165	15	26	36	260	14	4	97	7	52	284	12	15	43	14	42	384	10	3331	3
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	249	12	48	26	115	23	1350	5	36	32	367	11	2	72	82	19	1030	6	194	12	421	10	246	12	37	30	129	15	362	11	61	24	146	15	195	13	176	15	266	10	98	18	618	7	629	7	49	23	310	10	7255	2
	broadleaves	262	10	12	42	29	26	511	7	77	17	217	14	9	55	40	24	129	15	170	12	143	14	68	17	19	36	51	25	160	16	73	20	157	14	63	19	152	16	427	9	28	30	343	10	117	15	16	35	243	10	3555	3
	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
	total	511	8	60	26	144	21	1861	5	113	17	584	9	11	52	122	17	1160	5	363	9	563	9	313	11	56	25	180	14	522	10	134	17	303	11	258	12	328	12	694	7	126	16	961	6	747	6	65	21	553	8	10810	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. 1344182. Birmensdorf, Swiss Federal Research Institute WSL

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