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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
altitude (in 400 m classes) · main tree species
regional demarcation: protection forest region
unit: 1000 m³/yr
evaluation area: accessible forest without shrub forest NFI4/NFI5
grid: 1.4 km grid, subgrids 1-5
change 2009/17–2018/26
		protection forest region
		Jura + Plateau		Northwestern Alps		Northeastern Alps		Southwestern Alps		Southeastern Alps		Southern Alps		Switzerland
altitude (in 400 m classes)	main tree species	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	.
	spruce	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	fir	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	larch	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	beech	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	maple	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	ash	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	oak	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other broadleaves	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	.	0	.	0	.	0	.	0	.	0	.	0	.
>1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	0	.	26	42	4	92	19	51	80	31	13	118	143	23
	fir	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	pine	0	.	0	71	0	.	1	121	1	697	-1	154	1	761
	larch	0	.	2	100	0	100	39	36	54	27	34	56	129	22
	Arolla pine	0	.	0	.	0	.	9	60	37	29	0	87	47	26
	other conifers	0	.	0	.	0	.	0	0	-1	103	0	.	-1	103
	beech	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	maple	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	ash	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	oak	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other broadleaves	0	.	0	.	0	.	0	95	0	74	0	78	1	49
	indeterminable	0	.	0	.	0	.	0	0	0	0	0	0	0	0
	total	0	.	28	39	3	97	68	28	172	19	47	69	319	16
1401-1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	11	86	221	18	75	36	147	24	325	18	55	54	834	11
	fir	6	64	38	36	-1	510	5	91	2	173	18	62	68	28
	pine	0	.	6	62	2	76	2	186	11	37	-4	91	18	46
	larch	0	.	8	58	1	94	46	33	38	31	59	26	153	16
	Arolla pine	0	.	2	100	0	.	2	74	-2	158	0	.	2	150
	other conifers	0	.	-1	128	0	100	0	100	0	99	0	.	-1	162
	beech	1	71	0	.	0	.	0	100	1	100	21	34	23	32
	maple	4	78	2	345	0	96	1	70	-1	186	4	68	10	68
	ash	0	.	0	100	0	100	0	.	0	.	0	.	0	1013
	oak	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other broadleaves	0	136	4	47	1	88	6	67	16	54	4	127	31	35
	indeterminable	0	.	0	0	0	0	0	0	0	0	0	0	0	0
	total	21	68	280	16	80	34	211	20	391	16	156	24	1138	9
1001-1400 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	117	29	248	16	234	18	32	63	134	24	49	39	814	10
	fir	207	13	171	23	71	28	28	37	8	73	12	58	496	11
	pine	0	116	0	0	-1	258	-1	602	15	69	1	408	14	94
	larch	0	.	1	96	0	100	16	42	21	46	16	59	54	28
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	0	100	0	79	2	96	0	100	0	.	0	.	3	75
	beech	77	17	57	33	71	28	-2	164	4	127	75	27	284	13
	maple	31	28	31	32	31	33	8	45	3	70	6	69	109	16
	ash	2	55	2	211	11	51	-4	220	3	71	13	80	28	55
	oak	0	.	0	97	0	100	1	129	0	.	3	70	4	51
	sweet chestnut	0	.	0	.	0	.	0	.	0	.	-1	113	-1	113
	other broadleaves	5	64	-2	627	0	19803	0	3710	11	76	7	249	22	114
	indeterminable	0	0	0	0	0	0	0	0	0	0	0	0	0	0
	total	439	11	508	13	420	14	79	36	200	19	179	20	1827	6
601-1000 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	421	11	115	25	152	21	-2	408	51	25	12	66	749	9
	fir	427	11	211	16	113	26	3	56	8	73	1	100	763	9
	pine	5	166	6	114	4	70	-1	233	8	56	0	.	23	56
	larch	14	42	0	860	2	88	0	3484	4	109	3	93	24	39
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	37	28	2	77	0	142	0	0	0	.	0	.	39	27
	beech	419	11	135	21	62	31	2	243	12	42	28	44	659	9
	maple	95	17	6	142	48	39	6	64	12	46	4	51	171	16
	ash	46	44	20	76	1	1206	3	115	2	340	0	2547	72	41
	oak	15	42	6	66	0	76	5	63	2	78	1	379	30	31
	sweet chestnut	0	100	0	100	0	.	1	100	0	89	24	84	25	81
	other broadleaves	32	27	13	46	1	432	8	50	-2	292	12	114	65	31
	indeterminable	0	0	0	0	0	0	0	0	0	0	0	0	0	0
	total	1511	7	514	11	385	16	26	57	97	21	86	32	2620	5
=600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	401	13	16	74	10	87	0	.	0	.	3	73	429	13
	fir	226	15	7	100	2	123	0	.	0	.	0	.	235	14
	pine	28	46	0	.	0	158	-3	76	0	.	0	.	25	53
	larch	18	54	2	80	1	100	0	0	0	.	0	100	20	49
	Arolla pine	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other conifers	34	34	0	.	0	133	0	.	0	.	2	92	36	33
	beech	348	10	4	69	30	42	-5	95	0	.	1	186	379	10
	maple	90	20	0	1847	3	139	2	96	0	.	4	98	99	19
	ash	81	29	4	50	-6	138	0	1706	1	100	6	72	87	29
	oak	79	22	0	.	3	98	0	2741	0	.	-2	331	80	24
	sweet chestnut	0	.	0	.	0	.	-2	118	0	.	-15	96	-17	84
	other broadleaves	79	33	-7	114	5	89	3	77	4	100	35	49	120	27
	indeterminable	0	0	0	0	0	0	0	0	0	.	0	0	0	0
	total	1384	6	26	57	48	47	-5	160	5	100	34	73	1493	6
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	spruce	950	8	626	10	474	13	196	21	588	12	132	30	2968	5
	fir	866	7	426	12	185	19	36	32	17	50	31	43	1564	6
	pine	33	46	12	65	6	63	-3	361	35	38	-4	103	80	31
	larch	32	35	13	44	4	60	102	22	118	18	112	24	379	11
	Arolla pine	0	.	2	100	0	.	11	51	35	31	0	87	49	26
	other conifers	72	22	1	147	3	76	0	93	0	124	2	92	77	21
	beech	845	7	196	18	163	19	-4	187	17	43	126	20	1345	6
	maple	219	12	38	37	82	26	19	33	14	42	18	37	390	10
	ash	129	24	26	61	6	276	-1	1330	6	101	19	61	187	22
	oak	94	20	6	61	3	75	5	59	2	78	2	451	113	19
	sweet chestnut	0	100	0	100	0	.	-2	155	0	89	8	300	7	371
	other broadleaves	117	23	9	170	8	132	18	53	30	47	58	49	239	20
	indeterminable	0	0	0	0	0	0	0	0	0	0	0	0	0	0
	total	3357	4	1357	7	935	10	379	15	864	9	504	14	7398	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. 1306479. Birmensdorf, Swiss Federal Research Institute WSL

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