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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 · main tree species
regional demarcation: economic region
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
		economic region
		Western Jura		Eastern Jura		Western Plateau		Central Plateau		Eastern Plateau		Western Pre-Alps		Central Pre-Alps		Eastern Pre-Alps		Northwestern Alps		Central Alps		Northeastern Alps		Southwestern Alps		Southeastern Alps		Southern Alps		Switzerland
site quality	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	±%
n/a	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	fir	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	larch	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	beech	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	maple	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	ash	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	oak	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other broadleaves	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	.
	total	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	.
	spruce	40	31	-4	100	5	58	6	49	12	78	27	49	85	23	25	35	64	33	40	40	47	39	38	43	104	23	10	41	498	10
	fir	25	44	2	97	0	.	3	95	8	82	1	93	-1	254	0	115	18	46	3	64	3	71	2	78	0	.	0	.	65	26
	pine	-2	221	0	464	0	.	1	244	0	220	0	.	7	98	0	.	0	100	-3	106	0	.	1	76	4	96	0	.	8	121
	larch	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	100	0	.	0	.	36	45	29	42	6	54	65	28
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	8	65	18	36	0	.	24	32
	other conifers	1	60	0	100	0	.	0	100	0	100	0	.	0	71	0	.	0	100	0	100	0	100	0	0	1	45	0	.	3	27
	beech	71	28	7	77	4	100	16	55	4	101	8	117	30	54	11	58	19	82	11	86	6	75	0	1003	0	.	0	.	197	19
	maple	-2	255	-2	127	0	100	1	72	1	79	4	51	13	74	1	50	1	238	-1	88	2	79	4	62	0	.	0	.	23	54
	ash	9	46	1	100	0	0	1	76	2	59	3	100	-2	170	-1	101	1	80	0	100	0	.	4	92	0	.	0	.	18	39
	oak	4	67	3	77	0	.	3	94	1	77	0	90	1	83	0	.	1	91	0	100	0	.	1	99	0	.	0	.	13	38
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	2	120	0	.	0	.	1	120
	other broadleaves	5	56	1	70	0	.	-1	346	1	99	1	84	1	53	0	122	1	52	2	87	0	100	3	97	0	95	0	100	15	34
	indeterminable	0	0	0	.	0	0	0	.	0	.	0	.	0	.	0	.	0	0	0	0	0	.	0	0	0	0	0	.	0	0
	total	151	21	8	88	9	68	29	40	30	45	44	42	134	22	35	29	107	27	53	37	57	35	97	27	156	19	16	36	932	8
moderate	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	120	19	0	.	22	45	1	100	0	100	137	23	63	23	62	32	136	26	12	59	33	39	260	17	297	17	226	19	1370	7
	fir	64	26	0	.	4	56	1	100	0	0	53	43	20	59	35	31	0	2289	11	50	1	83	35	48	18	32	38	36	288	14
	pine	0	100	0	.	0	.	0	.	0	.	0	.	0	.	0	100	1	70	1	100	0	.	42	42	-2	714	7	88	45	52
	larch	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	3	128	0	.	-1	115	122	19	42	41	47	44	203	17
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	-4	100	0	.	0	.	4	60	9	60	0	100	10	68
	other conifers	0	100	0	.	0	.	0	.	0	.	0	.	0	.	-3	100	0	.	0	.	0	.	0	130	0	90	0	.	-3	120
	beech	35	39	0	.	2	71	-3	100	6	100	12	58	8	72	1	500	-15	179	-3	114	4	95	19	70	6	147	10	222	90	46
	maple	9	58	0	.	1	159	0	100	0	.	7	57	6	69	5	43	9	80	2	84	5	60	6	49	12	63	2	52	67	21
	ash	1	74	0	.	0	.	0	.	0	.	6	44	2	121	1	94	13	80	2	79	2	62	-6	165	5	71	3	55	28	52
	oak	0	.	0	.	0	.	0	.	0	.	0	.	0	100	0	.	-1	100	0	.	0	.	1	247	1	100	6	47	6	58
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	0	0	.	12	82	11	82
	other broadleaves	2	64	0	.	0	.	0	.	0	.	6	38	4	89	1	102	4	45	1	64	2	53	30	25	30	37	14	55	92	17
	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
	total	233	16	0	.	29	38	-1	100	7	100	221	19	102	26	102	25	146	33	25	43	46	34	513	12	417	15	364	15	2209	6
good	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	200	15	37	50	54	37	45	33	79	28	121	26	196	15	206	20	31	52	71	32	51	30	7	135	115	28	38	46	1267	7
	fir	166	16	8	58	40	32	71	28	40	27	39	48	214	19	82	24	22	41	31	34	19	41	15	70	22	47	10	55	804	8
	pine	10	65	-3	363	0	120	1	69	1	318	0	.	4	86	2	58	0	.	1	96	0	.	0	.	0	.	0	.	18	76
	larch	0	71	1	60	2	78	1	74	5	88	2	100	0	100	0	100	5	94	0	100	3	68	0	.	0	472	1	848	20	52
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	2	176	1	62	7	97	13	52	3	82	0	0	0	75	0	75	0	.	0	0	0	100	0	.	0	.	2	100	30	39
	beech	139	15	28	67	18	63	78	22	113	20	34	43	81	25	85	28	12	99	27	33	18	41	18	55	6	93	95	33	764	8
	maple	13	44	8	70	3	45	0	2532	-5	204	9	67	8	102	27	30	-1	204	8	52	1	470	-4	108	1	218	5	80	73	30
	ash	24	39	12	43	2	495	29	42	5	149	5	115	26	43	11	137	3	232	9	98	-2	152	2	97	-4	152	33	44	155	22
	oak	5	56	7	102	-4	189	4	52	4	93	2	90	2	100	0	72	2	100	1	60	0	.	0	100	2	100	21	35	45	31
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	100	0	.	0	.	1	100	0	100	122	31	103	31
	other broadleaves	17	50	11	44	7	57	8	40	2	156	4	69	9	51	-3	161	10	55	6	61	9	55	-1	178	10	71	90	25	164	15
	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	576	10	110	32	129	29	249	16	246	18	216	22	541	11	411	14	85	26	154	22	99	26	38	53	153	25	417	14	3443	5
very good	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	93	23	56	28	108	26	362	14	385	12	13	50	57	39	27	53	5	89	1	100	12	63	0	0	0	.	0	.	1119	7
	fir	116	18	22	36	30	43	236	16	136	22	5	172	74	25	29	41	1	100	0	100	8	67	0	.	0	.	0	.	668	9
	pine	11	92	5	82	9	50	16	38	15	34	0	.	0	100	-1	100	0	.	0	.	0	.	0	.	0	.	0	.	55	26
	larch	0	87	-3	76	11	60	4	72	6	58	0	.	1	100	2	62	1	178	0	.	1	100	0	.	0	.	0	.	23	38
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	-3	103	12	81	6	100	9	61	15	63	0	.	0	.	0	70	0	.	0	.	0	.	0	.	0	.	0	.	37	42
	beech	125	20	80	26	85	27	174	18	180	15	2	62	49	28	21	70	8	68	2	241	15	36	2	100	0	.	8	96	755	8
	maple	14	55	12	43	0	2321	12	65	62	28	1	100	7	63	-1	2874	0	1303	1	100	1	54	0	100	0	.	0	.	109	24
	ash	26	30	27	34	47	38	19	50	83	29	-4	119	5	45	15	51	-4	136	0	.	-2	206	1	100	0	.	0	100	215	16
	oak	19	49	11	65	13	57	12	45	39	33	0	100	0	0	0	448	0	.	0	.	0	.	1	100	0	.	1	99	94	21
	sweet chestnut	0	.	0	.	0	100	0	.	0	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	100	1	63
	other broadleaves	10	30	7	81	42	43	39	56	50	30	0	0	0	4157	5	169	7	60	1	100	2	55	4	73	0	.	-4	96	160	21
	indeterminable	0	0	0	0	0	0	0	.	0	0	0	.	0	.	0	0	0	0	0	.	0	.	0	.	0	.	0	.	0	0
	total	410	12	228	16	352	16	884	10	970	8	17	91	193	20	98	36	19	54	5	91	37	44	8	70	0	.	5	169	3236	4
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	453	9	90	27	190	19	410	12	475	11	298	15	402	11	318	15	235	18	124	23	144	19	306	16	518	13	277	16	4249	4
	fir	373	10	32	29	74	25	309	14	184	17	98	31	307	14	146	17	42	39	45	26	30	31	50	39	40	30	47	31	1857	5
	pine	19	64	2	418	9	49	17	37	17	42	0	.	12	69	1	145	1	58	-2	208	0	.	43	41	2	809	7	88	127	25
	larch	0	55	-2	122	13	51	5	62	10	51	2	100	1	85	3	57	9	69	0	100	2	94	159	18	70	30	55	41	298	13
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	-3	100	0	.	0	.	12	48	27	31	0	100	34	30
	other conifers	-1	609	13	76	13	70	22	39	18	54	0	0	1	52	-2	143	0	100	0	100	0	71	0	130	1	40	2	100	71	29
	beech	371	10	115	24	110	23	265	14	303	11	57	34	170	17	117	24	28	118	37	39	43	25	37	44	12	84	113	34	1858	5
	maple	34	34	18	43	4	104	13	75	58	34	22	36	34	41	32	55	9	100	10	47	9	79	7	86	12	61	7	61	275	15
	ash	60	21	40	26	48	39	50	31	89	28	10	76	31	38	26	67	13	101	11	82	-2	283	1	1051	1	611	36	40	429	12
	oak	28	36	20	49	9	111	19	33	44	31	2	73	3	82	0	8975	2	118	0	158	0	.	2	115	3	83	28	29	165	16
	sweet chestnut	0	.	0	.	0	100	0	.	0	100	0	.	0	.	0	.	0	100	0	.	0	.	2	88	0	100	131	29	117	28
	other broadleaves	34	28	19	41	49	38	46	47	53	28	11	34	14	48	3	334	23	33	10	42	12	41	35	24	40	33	97	24	437	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
	total	1371	5	348	14	519	13	1158	8	1251	7	500	13	974	8	643	11	360	17	236	17	239	16	654	11	727	10	800	10	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. 1393170. Birmensdorf, Swiss Federal Research Institute WSL

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