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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
growing stock (stemwood)
forest type (17 classes)
regional demarcation: canton
unit: 1000 m³
evaluation area: accessible forest without shrub forest
grid: 1.4-km grid
state 2004/06
	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
forest type (17 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	.
inaccessible forest	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	.
shrub forest	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	.
permanently unstocked forest area	633	36	23	100	385	78	1334	31	390	66	641	37	0	.	46	68	349	51	448	56	807	53	319	53	0	.	791	39	710	37	0	.	146	53	388	47	156	53	830	55	2	100	1179	41	397	36	78	100	422	44	10475	11
temporarily unstocked forest area	63	71	0	.	0	.	539	34	0	0	219	49	0	.	82	95	936	29	75	100	165	53	0	.	0	0	101	58	101	60	6	100	0	.	152	51	98	83	25	79	77	100	133	76	99	59	14	100	54	78	2941	14
aisle, embankment	0	.	0	.	0	.	15	149	28	100	36	100	0	.	89	100	203	45	111	63	0	.	0	.	0	.	7	88	20	100	0	.	155	78	3	100	0	.	85	78	52	100	386	66	71	71	0	.	0	.	1262	27
permanently open stand	15	100	11	100	38	100	1223	26	5	100	214	53	3	100	119	84	3409	12	563	61	183	51	444	41	146	55	441	35	544	39	0	.	256	100	409	40	0	.	1164	19	74	65	1334	21	1278	22	13	100	49	100	11934	8
(nut) orchard, plantation	0	.	0	.	0	.	0	.	0	.	40	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	435	44	0	.	149	100	52	81	0	.	0	.	675	37
coppice forest	279	68	0	.	0	.	176	48	119	100	59	52	0	.	33	81	453	37	10	100	16	100	27	100	0	.	0	.	0	.	0	.	43	100	0	.	0	.	3132	14	5	62	306	49	164	53	0	.	0	.	4821	11
coppice with standards	361	46	0	.	0	.	91	59	0	.	0	.	97	71	0	.	156	53	131	78	0	.	0	.	0	.	0	.	0	.	91	100	0	.	8	100	0	.	1310	23	63	100	341	53	0	.	0	.	42	100	2691	16
selection type high forest	89	83	121	100	91	100	8091	12	93	79	928	31	0	.	210	53	6801	10	542	38	998	33	3618	16	0	.	1706	24	542	37	0	.	41	100	397	48	85	100	1958	17	591	35	2476	20	2875	14	102	100	188	55	32544	5
non-uniform high forest	1924	29	0	.	334	62	5306	15	376	41	811	36	0	.	494	46	3116	16	169	72	1229	29	381	42	0	.	68	100	1062	38	51	100	294	47	0	.	607	41	3403	14	200	59	1910	23	3446	17	0	.	754	34	25935	6
young growth/ thicket	494	32	0	.	8	100	1133	24	230	53	272	41	0	.	139	59	813	23	159	77	271	52	23	100	16	55	62	71	279	48	114	62	217	44	66	72	35	100	206	31	100	72	395	37	339	31	10	100	603	30	5986	9
poletimber	1238	21	67	62	169	59	2482	17	114	61	1291	23	0	.	130	51	3176	13	553	36	1109	23	255	45	70	100	187	55	1004	25	316	38	664	29	633	29	1511	23	2808	12	296	43	1463	19	2312	15	227	63	1898	19	23971	5
young timber	1544	23	128	80	326	72	5780	12	884	32	2278	23	198	59	1734	42	3645	14	2040	22	1406	28	576	36	501	40	172	72	3443	18	1249	28	1636	22	675	35	768	32	3095	14	479	39	3344	15	4459	13	259	60	1563	22	42179	5
medium timber	3144	17	794	39	1017	37	16660	9	2914	20	4705	17	123	75	1467	29	11020	9	5316	14	3114	20	1393	22	888	34	578	40	6437	15	1828	23	5266	13	2110	24	2164	25	2927	16	1541	29	10473	10	6391	12	259	44	5028	15	97556	3
old timber	6352	13	1686	30	3526	23	27803	7	1867	26	5114	17	145	100	1743	29	17602	8	3666	19	9400	13	4067	18	344	52	2326	25	10115	12	862	37	3179	21	5742	16	3587	19	4140	14	1494	29	11577	11	8310	12	1491	31	8150	12	144288	3
total	16137	8	2830	22	5895	17	70632	4	7019	12	16608	8	565	39	6284	16	51680	4	13783	8	18697	8	11103	9	1964	21	6439	13	24258	7	4516	14	11896	9	10584	10	9010	11	25519	4	4974	14	35467	5	30193	5	2452	22	18752	7	407258	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. 1232820. Birmensdorf, Swiss Federal Research Institute WSL

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