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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
number of stems
conifers and broadleaves · diameter at breast height (10 classes)
regional demarcation: biogeographical region
unit: 1000 n
evaluation area: accessible forest without shrub forest NFI1-NFI5
grid: 1.4 km grid, subgrids 1-5
state 2018/26
		biogeographical region
		Jura		Plateau		Northern Alps		Western Central-Alps		Eastern Central-Alps		Southern Alps		Switzerland
conifers and broadleaves	diameter at breast height (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	.
	12-20 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	21-30 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	31-40 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	41-50 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	51-60 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	61-70 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	71-80 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	81-90 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	91-100 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	>100 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	.	0	.	0	.	0	.	0	.	0	.	0	.
conifers	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	13133	8	17758	8	27234	6	11544	10	16621	9	5992	14	92282	3
	21-30 cm	7673	7	10335	8	17408	6	8051	11	10176	8	4929	12	58571	3
	31-40 cm	5321	8	5970	8	12758	6	4936	10	6815	8	3329	11	39130	3
	41-50 cm	3791	6	4423	6	8821	5	2988	10	4689	7	2249	10	26962	3
	51-60 cm	2351	7	2869	7	5880	5	1769	10	2763	8	1545	12	17176	3
	61-70 cm	1122	11	1371	9	2905	7	690	15	1134	11	597	13	7819	4
	71-80 cm	420	14	670	12	1369	9	315	22	477	14	319	19	3569	5
	81-90 cm	104	30	316	16	304	17	101	32	198	22	135	31	1158	9
	91-100 cm	37	45	34	45	102	27	58	35	63	37	51	41	344	15
	>100 cm	22	58	21	58	57	35	14	71	30	50	40	52	184	21
	total	33972	5	43767	5	76837	4	30468	8	42964	6	19186	9	247194	2
broadleaves	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	16498	7	21191	6	19213	7	5682	14	4007	17	21635	8	88227	3
	21-30 cm	8980	7	10662	6	12048	7	2090	17	1921	20	12594	8	48294	3
	31-40 cm	6098	7	6416	6	6782	7	483	25	787	18	4900	9	25467	3
	41-50 cm	3659	7	4169	6	3263	7	201	33	343	24	1904	9	13538	3
	51-60 cm	1489	9	2755	7	1626	10	30	50	204	25	733	15	6837	4
	61-70 cm	379	16	960	10	477	16	15	71	54	35	256	19	2142	7
	71-80 cm	73	34	376	16	170	23	0	.	32	52	118	27	769	11
	81-90 cm	0	.	95	28	50	41	0	0	8	100	82	32	235	18
	91-100 cm	0	.	63	36	13	71	7	100	0	.	38	60	121	28
	>100 cm	0	.	24	76	0	.	0	.	0	.	44	57	68	46
	total	37176	5	46712	4	43643	5	8508	14	7356	15	42303	6	185698	2
indeterminable	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	0	0	0	.	0	0	0	.	0	.	0	.	0	0
	21-30 cm	0	0	0	.	0	.	0	0	0	.	0	.	0	0
	31-40 cm	0	0	0	0	0	0	0	.	0	0	0	.	0	0
	41-50 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	51-60 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	61-70 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	71-80 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	81-90 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	91-100 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	>100 cm	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	0	0	0	0	0	0	0	0	0	0	.	0	0
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	29631	5	38949	5	46447	5	17226	9	20628	8	27627	7	180509	2
	21-30 cm	16652	5	20997	5	29456	5	10141	9	12097	8	17522	6	106866	2
	31-40 cm	11419	5	12387	5	19539	4	5420	9	7602	7	8230	7	64597	2
	41-50 cm	7450	4	8591	4	12084	4	3189	10	5032	7	4154	6	40500	2
	51-60 cm	3840	5	5625	5	7506	4	1800	10	2966	8	2277	10	24013	2
	61-70 cm	1501	9	2331	6	3383	6	705	14	1188	10	853	10	9961	3
	71-80 cm	493	13	1046	9	1539	8	315	22	508	13	436	15	4338	5
	81-90 cm	104	30	411	14	355	15	101	32	206	21	217	23	1393	8
	91-100 cm	37	45	97	28	115	25	66	33	63	37	88	35	465	13
	>100 cm	22	58	45	48	57	35	14	71	30	50	84	39	251	20
	total	71148	4	90479	3	120480	3	38976	7	50320	6	61489	5	432892	2

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. 1348723. Birmensdorf, Swiss Federal Research Institute WSL

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