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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.

NFI5
total number of stems with two most important forms of damages
altitude (in 200 m classes) · cause of damage to trees (10 classes)
regional demarcation: protection forest region
unit: 1000 n
evaluation area: accessible forest without shrub forest NFI1-NFI5
grid: 1.4 km grid, subgrids 1-5
state 2018/26
		protection forest region
		Jura + Plateau		Northwestern Alps		Northeastern Alps		Southwestern Alps		Southeastern Alps		Southern Alps		Switzerland
altitude (in 200 m classes)	cause of damage to trees (10 classes)	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%	1000 n	±%
n/a	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	fire	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	rockfall	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	various	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	indeterminable	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	wood harvest	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	other human activity	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	weather	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	lying living trees	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	dead trees	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
>1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	799	48	0	.	5152	17	8599	14	1706	27	16256	10
	fire	0	.	0	.	0	.	0	.	0	.	7	100	7	100
	rockfall	0	.	0	.	0	.	294	28	74	45	217	67	584	29
	various	0	.	43	60	0	.	150	34	434	25	104	35	730	18
	indeterminable	0	.	357	44	0	.	1669	21	3413	16	523	30	5963	11
	wood harvest	0	.	0	.	0	.	79	53	20	76	0	.	100	45
	other human activity	0	.	23	72	0	.	293	46	44	47	47	86	406	35
	weather	0	.	0	.	0	.	290	30	192	32	119	67	601	22
	lying living trees	0	.	0	.	0	.	104	71	346	48	0	.	450	40
	dead trees	0	.	425	60	0	.	1673	22	2314	19	548	41	4959	13
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
1601-1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	5294	24	1556	41	5791	19	6259	16	4120	19	23019	9
	fire	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	rockfall	0	.	314	37	0	.	138	39	275	39	101	43	828	21
	various	0	.	338	46	160	81	182	31	274	31	300	37	1254	20
	indeterminable	0	.	1571	23	338	43	2152	19	2113	17	911	24	7085	10
	wood harvest	0	.	55	100	0	.	7	100	41	46	27	100	130	50
	other human activity	0	.	33	63	0	.	109	43	127	50	25	77	294	28
	weather	0	.	123	45	24	77	397	47	197	43	226	26	966	23
	lying living trees	0	.	79	92	22	100	49	54	0	.	0	.	151	53
	dead trees	0	.	1741	28	316	47	1915	28	1120	21	525	28	5617	14
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
1401-1600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	957	31	8947	15	3894	22	5378	18	8388	15	5943	19	33509	7
	fire	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	rockfall	13	100	483	40	82	47	363	44	327	53	366	36	1633	20
	various	110	56	300	29	240	52	214	33	192	42	408	26	1465	15
	indeterminable	225	33	3070	14	827	26	1537	20	2570	16	1203	22	9432	8
	wood harvest	8	100	105	48	44	85	37	56	131	42	18	100	342	26
	other human activity	0	.	243	41	86	84	118	58	150	37	42	71	640	24
	weather	19	100	333	25	171	51	260	32	225	34	336	27	1344	14
	lying living trees	0	.	55	58	35	71	181	65	53	58	18	100	341	38
	dead trees	177	65	3074	17	1047	35	1445	22	2198	25	1091	23	9033	10
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
1201-1400 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	5238	16	9974	13	5379	16	5075	20	3397	22	4695	20	33759	7
	fire	0	.	0	.	0	.	0	.	0	.	33	100	33	100
	rockfall	21	100	818	32	681	35	459	40	265	54	530	31	2774	16
	various	297	31	332	29	421	31	317	50	104	51	445	29	1915	15
	indeterminable	946	19	2638	14	1552	17	713	24	1466	24	1352	20	8667	8
	wood harvest	111	44	158	42	191	46	0	.	109	45	60	50	629	21
	other human activity	83	41	246	51	136	49	0	.	127	55	26	76	617	26
	weather	260	44	366	26	169	38	101	51	164	53	305	30	1365	15
	lying living trees	0	.	36	71	130	49	60	53	0	.	108	43	334	27
	dead trees	828	26	2858	17	2064	21	1066	23	1161	24	1116	25	9092	9
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
1001-1200 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	13208	9	11824	11	7047	15	3215	21	2226	29	5567	19	43088	6
	fire	0	.	0	.	0	.	0	.	6	100	72	91	78	84
	rockfall	398	36	1209	29	772	35	314	54	425	46	819	28	3937	15
	various	449	28	354	29	681	30	146	39	205	57	368	45	2203	15
	indeterminable	1753	13	1761	14	1849	16	744	28	786	33	1372	21	8265	8
	wood harvest	765	19	386	30	361	32	7	100	26	100	7	100	1553	14
	other human activity	191	37	115	56	271	43	7	100	35	71	25	100	645	24
	weather	200	36	502	25	110	35	117	39	145	72	312	29	1386	15
	lying living trees	0	.	70	63	61	76	122	74	18	100	43	71	314	37
	dead trees	1581	17	2430	16	2083	22	954	26	563	32	1114	27	8725	9
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
801-1000 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	17918	9	12215	12	8487	14	2645	27	1959	28	5562	26	48786	6
	fire	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	rockfall	1107	33	427	50	957	33	362	64	88	60	454	32	3395	17
	various	435	23	591	20	429	25	84	53	116	44	460	43	2115	13
	indeterminable	3091	12	1740	16	1491	18	755	28	775	30	1829	24	9680	8
	wood harvest	925	22	523	31	388	27	33	100	59	52	0	0	1928	15
	other human activity	277	36	300	43	214	37	0	.	50	74	69	48	910	21
	weather	440	24	247	36	244	29	40	71	227	45	530	56	1727	20
	lying living trees	0	.	102	51	22	77	18	100	18	100	188	63	348	38
	dead trees	2250	14	2138	17	1871	19	726	31	452	28	1746	26	9183	9
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
601-800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	35389	7	8160	14	5262	19	1137	48	2132	25	4497	20	56576	5
	fire	0	.	0	.	0	.	0	.	0	.	424	69	424	69
	rockfall	675	35	613	44	336	45	147	62	147	71	369	31	2287	18
	various	1413	17	774	39	473	34	76	81	171	31	1238	40	4147	16
	indeterminable	5036	10	1439	17	1338	21	300	46	570	31	2052	20	10734	7
	wood harvest	2181	12	434	30	98	41	0	.	33	100	90	100	2836	11
	other human activity	494	28	85	45	26	75	0	.	14	71	28	77	648	23
	weather	691	18	129	39	111	45	25	76	38	83	774	43	1769	20
	lying living trees	85	53	36	71	75	49	36	71	0	.	98	44	330	25
	dead trees	4795	10	1339	22	1181	23	401	40	413	35	2317	21	10446	8
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
=600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	45752	5	1347	42	1859	31	1243	37	35	100	6220	18	56456	5
	fire	0	.	0	.	0	.	0	.	0	.	126	100	126	100
	rockfall	299	71	7	100	413	74	30	100	0	.	426	37	1175	35
	various	1816	14	74	72	122	68	58	65	0	.	776	36	2846	14
	indeterminable	6836	7	232	60	432	36	131	48	0	.	2801	19	10432	7
	wood harvest	2861	11	71	78	58	58	18	100	0	.	0	.	3008	11
	other human activity	634	29	0	0	36	65	0	.	0	.	192	41	862	23
	weather	1096	15	44	72	89	58	36	71	0	.	412	29	1677	12
	lying living trees	249	26	15	100	21	74	18	100	0	.	323	41	627	24
	dead trees	5864	9	212	42	448	32	396	45	0	.	3172	18	10092	8
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	118463	2	58561	5	33484	7	29637	7	32994	7	38310	6	311449	2
	fire	0	.	0	.	0	.	0	.	6	100	662	50	669	49
	rockfall	2513	20	3871	15	3241	18	2106	19	1601	21	3282	12	16614	7
	various	4521	9	2806	14	2527	14	1226	17	1495	14	4099	15	16675	6
	indeterminable	17887	4	12809	6	7827	8	8001	9	11693	8	12042	7	70258	2
	wood harvest	6851	7	1731	15	1140	17	183	34	419	22	202	50	10526	5
	other human activity	1679	15	1045	21	770	23	527	30	547	22	455	23	5022	9
	weather	2706	9	1744	12	916	17	1266	18	1189	18	3014	16	10836	6
	lying living trees	334	24	392	28	366	26	589	29	436	39	779	24	2895	12
	dead trees	15495	5	14217	7	9011	9	8577	10	8222	10	11627	8	67148	3
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.

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. 1346951. Birmensdorf, Swiss Federal Research Institute WSL

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