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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.

NFI2
growing stock (stemwood)
aspect (9 classes)
regional demarcation: canton
unit: 1000 m³
evaluation area: accessible forest without shrub forest NFI1-NFI5
grid: 1.4 km grid, subgrids 1-5
state 1993/95
	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
aspect (9 classes)	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%	1000 m³	±%
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	.
indetermined	4569	21	0	.	0	.	12736	13	930	46	2081	34	709	45	5	100	504	48	1945	31	2918	28	1308	33	0	.	212	89	1916	35	697	50	1730	37	162	76	4653	21	277	91	0	.	4976	19	209	63	319	61	6094	18	48950	6
N	3420	27	388	75	689	63	13330	13	1334	39	3223	26	0	.	628	52	6055	17	3758	21	1578	39	1182	37	661	56	1064	52	3464	24	1060	41	2936	26	1537	40	915	42	3272	19	656	39	1782	33	3385	20	153	100	2467	27	58938	6
NE	1262	40	0	.	992	50	5276	19	540	67	1265	48	0	.	618	60	5527	15	356	61	4004	25	394	62	182	100	641	51	2972	31	295	71	584	53	1060	46	1176	40	2291	23	719	50	1096	39	1015	33	184	100	2851	25	35299	7
E	1352	38	358	90	792	57	5257	21	472	56	1133	41	0	.	640	52	6532	16	643	56	2174	31	810	43	379	58	582	55	2818	29	328	77	569	55	205	63	416	57	2944	19	730	51	3132	24	3125	20	142	100	1340	34	36873	7
SE	1613	36	1006	42	490	64	9623	14	772	44	3320	28	0	.	287	88	3610	19	377	50	1914	30	2955	26	206	75	1038	40	2598	30	521	59	2517	27	1345	34	360	57	2346	20	579	73	6221	17	1944	23	0	.	1665	36	47306	6
S	781	46	505	71	182	100	6869	15	438	61	1748	35	0	.	1238	45	3577	20	849	36	1396	49	987	43	0	.	450	55	1129	48	269	64	1554	30	1453	36	865	52	1486	24	488	65	2306	27	2721	24	152	94	1485	34	32927	7
SW	1028	43	0	.	145	100	3633	22	347	59	905	47	0	.	669	52	4660	19	1550	38	2251	36	569	57	9	100	989	51	1320	36	213	72	92	100	1065	41	628	59	3108	21	223	59	1909	34	1440	28	76	86	1209	42	28035	8
W	1112	39	49	100	634	77	5697	20	649	47	1383	47	0	.	395	52	7611	15	692	54	1758	37	213	75	207	71	710	51	1876	33	1069	41	509	59	1149	48	204	76	1806	24	708	46	1756	28	3847	18	217	100	1785	34	36036	7
NW	2012	30	329	71	1004	49	10347	14	694	58	3547	25	0	.	1128	59	5834	17	2614	29	3584	27	1813	26	471	64	1104	61	3309	28	182	96	829	44	1800	30	314	72	1902	23	1222	42	5189	20	5635	17	226	75	1535	33	56622	6
total	17149	10	2635	28	4929	22	72768	5	6174	17	18604	11	709	45	5610	20	43910	5	12783	11	21576	10	10231	12	2115	28	6789	18	21401	10	4633	18	11320	12	9776	14	9530	14	19433	6	5323	19	28366	8	23321	7	1468	31	20430	9	380985	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. 1195577. Birmensdorf, Swiss Federal Research Institute WSL

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