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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 NFI4/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	.	1335	47	325	81	5408	16	11320	12	3932	17	22320	8
	fire	0	.	0	.	0	.	0	.	0	.	7	100	7	100
	rockfall	0	.	0	.	0	.	325	27	154	43	343	53	823	26
	various	0	.	50	54	28	100	243	36	623	25	215	26	1159	17
	indeterminable	0	.	418	39	115	71	1991	19	4453	14	1481	18	8456	9
	wood harvest	0	.	0	.	0	.	79	53	20	76	0	.	100	45
	other human activity	0	.	23	72	0	.	293	46	44	47	63	69	423	34
	weather	0	.	0	.	18	100	409	27	290	26	615	39	1332	21
	lying living trees	0	.	0	.	0	.	122	62	452	39	93	49	667	29
	dead trees	0	.	459	56	18	100	1827	21	2918	17	876	29	6099	12
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
1601-1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	6069	21	1599	40	6651	18	8080	14	4793	18	27192	8
	fire	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	rockfall	0	.	314	37	0	.	163	36	311	36	206	52	993	20
	various	0	.	392	40	178	73	196	30	424	29	339	34	1529	18
	indeterminable	0	.	1916	20	407	38	2384	17	2766	15	1129	21	8601	9
	wood harvest	0	.	55	100	0	.	7	100	41	46	27	100	130	50
	other human activity	0	.	80	54	7	100	227	52	222	40	43	61	579	27
	weather	0	.	206	35	24	77	453	42	310	33	260	25	1254	19
	lying living trees	0	.	114	71	22	100	68	48	18	100	16	100	238	39
	dead trees	0	.	1854	27	316	47	2233	25	1334	18	600	25	6338	13
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
1401-1600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	1065	29	10127	14	4224	20	5872	17	9563	14	7386	17	38238	7
	fire	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	rockfall	13	100	824	38	82	47	388	41	519	44	402	34	2227	20
	various	138	47	300	29	249	50	231	31	192	42	495	24	1605	14
	indeterminable	246	31	3422	13	1078	23	1685	19	2769	15	1504	19	10704	7
	wood harvest	8	100	105	48	44	85	37	56	131	42	18	100	342	26
	other human activity	0	.	338	36	86	84	172	47	199	37	42	71	838	22
	weather	26	78	333	25	171	51	313	32	279	29	402	26	1524	13
	lying living trees	0	.	55	58	162	58	198	60	88	53	84	59	586	29
	dead trees	185	63	3222	16	1254	32	1532	21	2385	23	1436	21	10015	10
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
1201-1400 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	5841	16	10532	13	6562	14	5748	19	3584	21	5141	18	37408	7
	fire	0	.	0	.	0	.	0	.	0	.	33	100	33	100
	rockfall	21	100	889	30	1128	33	459	40	265	54	699	27	3461	16
	various	305	30	487	29	660	26	743	47	114	47	445	29	2754	16
	indeterminable	946	19	2935	13	1752	16	931	23	1533	23	1468	18	9564	7
	wood harvest	111	44	158	42	191	46	0	.	109	45	60	50	629	21
	other human activity	83	41	302	45	143	47	18	100	159	49	26	76	730	24
	weather	260	44	366	26	274	40	101	51	186	47	340	28	1526	15
	lying living trees	0	.	36	71	254	55	78	47	0	.	108	43	475	32
	dead trees	828	26	2894	17	2310	20	1331	22	1237	24	1133	24	9732	9
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
1001-1200 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	13216	9	13114	11	7635	15	4041	19	2910	25	6343	17	47260	6
	fire	0	.	0	.	0	.	0	.	6	100	72	91	78	84
	rockfall	398	36	1216	28	825	33	328	52	447	44	819	28	4032	14
	various	449	28	398	28	752	29	218	37	281	48	440	40	2538	14
	indeterminable	1753	13	2259	15	2024	15	886	26	1285	28	1633	19	9841	7
	wood harvest	765	19	417	28	431	30	7	100	33	81	7	100	1660	14
	other human activity	191	37	217	50	314	39	15	71	55	58	25	100	817	22
	weather	200	36	606	25	222	32	144	35	172	63	377	26	1721	14
	lying living trees	0	.	70	63	131	64	139	66	18	100	134	71	492	33
	dead trees	1581	17	2567	15	2141	21	1096	26	682	28	1217	25	9283	9
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
801-1000 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	18653	9	12978	12	9120	13	2793	26	1987	27	6370	23	51901	6
	fire	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	rockfall	1107	33	427	50	1149	29	362	64	88	60	529	31	3662	17
	various	483	23	672	22	518	23	84	53	116	44	460	43	2333	13
	indeterminable	3183	12	1888	16	1782	17	762	28	804	29	1925	23	10343	8
	wood harvest	956	22	523	31	487	29	33	100	87	48	0	0	2087	14
	other human activity	361	33	300	43	224	35	7	100	50	74	69	48	1012	20
	weather	440	24	301	35	313	26	40	71	227	45	549	54	1870	19
	lying living trees	0	.	102	51	40	62	18	100	18	100	204	58	382	35
	dead trees	2285	14	2376	17	2159	18	744	31	452	28	1882	24	9898	8
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
601-800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	35535	7	8255	13	5262	19	1196	46	2132	25	4541	19	56920	5
	fire	0	.	0	.	0	.	0	.	0	.	424	69	424	69
	rockfall	675	35	613	44	336	45	147	62	147	71	391	30	2310	18
	various	1459	17	774	39	473	34	76	81	171	31	1238	40	4192	16
	indeterminable	5067	10	1439	17	1338	21	300	46	570	31	2052	20	10766	7
	wood harvest	2181	12	434	30	98	41	0	.	33	100	90	100	2836	11
	other human activity	521	27	85	45	26	75	0	.	14	71	28	77	674	22
	weather	718	17	129	39	111	45	42	61	38	83	774	43	1812	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	477	37	413	35	2317	21	10522	8
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
=600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	46245	5	1347	42	1991	29	1289	36	35	100	6550	18	57457	5
	fire	0	.	0	.	0	.	0	.	0	.	126	100	126	100
	rockfall	299	71	7	100	413	74	48	73	0	.	479	34	1247	33
	various	1864	13	74	72	122	68	112	59	0	.	831	34	3003	13
	indeterminable	6916	7	232	60	477	34	203	47	0	.	3027	18	10855	7
	wood harvest	2878	11	71	78	58	58	18	100	0	.	0	.	3025	11
	other human activity	674	28	0	0	52	55	75	100	0	.	192	41	994	22
	weather	1096	15	44	72	89	58	36	71	0	.	430	28	1695	12
	lying living trees	249	26	15	100	21	74	18	100	0	.	323	41	627	24
	dead trees	6000	9	212	42	492	31	431	42	0	.	3335	17	10471	8
	total	.	.	.	.	.	.	.	.	.	.	.	.	.	.
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	120555	2	63756	5	36718	6	32999	7	39610	6	45057	5	338696	2
	fire	0	.	0	.	0	.	0	.	6	100	662	50	669	49
	rockfall	2513	20	4290	15	3934	17	2219	18	1930	19	3868	11	18755	7
	various	4697	8	3148	13	2982	13	1903	20	1922	14	4462	14	19114	5
	indeterminable	18111	4	14508	6	8973	7	9140	8	14179	7	14219	6	79131	2
	wood harvest	6899	7	1762	15	1309	17	183	34	454	21	202	50	10809	5
	other human activity	1829	15	1346	19	853	21	806	26	744	20	489	22	6067	8
	weather	2739	9	1986	12	1221	16	1539	16	1502	15	3748	14	12735	6
	lying living trees	334	24	427	27	705	28	678	26	594	31	1060	21	3798	11
	dead trees	15673	5	14924	7	9872	9	9672	9	9421	9	12795	7	72357	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. 1346959. Birmensdorf, Swiss Federal Research Institute WSL

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