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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
tree state (living/dead) · diameter at breast height (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
tree state (living/dead)	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	.
living	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	65530	4	32895	6	16553	9	18513	8	20008	8	27009	7	180509	2
	21-30 cm	35314	3	19806	6	12135	8	10985	9	11749	8	16877	6	106866	2
	31-40 cm	22233	4	12361	6	8665	7	5879	9	7343	7	8116	7	64597	2
	41-50 cm	14955	3	7699	6	5383	7	3469	9	4909	7	4085	7	40500	2
	51-60 cm	8737	3	4782	6	3365	7	2027	10	2873	8	2228	10	24013	2
	61-70 cm	3583	5	2039	8	1488	11	835	13	1198	10	818	10	9961	3
	71-80 cm	1393	8	926	10	706	14	398	19	502	13	414	16	4338	5
	81-90 cm	441	14	217	20	219	19	128	28	199	22	188	24	1393	8
	91-100 cm	133	24	52	38	63	33	73	31	63	37	81	37	465	13
	>100 cm	59	40	36	45	28	50	14	71	37	45	76	41	251	20
	total	152379	2	80813	4	48605	6	42322	7	48881	6	59893	5	432892	2
dead	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	8388	6	7404	9	4818	12	4970	12	4225	12	7362	10	37166	4
	21-30 cm	3547	8	3133	12	2376	13	1708	14	2025	14	2474	12	15263	5
	31-40 cm	1871	12	1930	11	990	15	1104	14	991	16	919	17	7807	6
	41-50 cm	936	12	979	11	444	16	430	15	516	18	440	17	3744	6
	51-60 cm	462	14	448	16	262	20	245	20	361	18	225	26	2003	7
	61-70 cm	177	22	229	23	78	30	84	29	84	29	103	37	756	11
	71-80 cm	86	32	87	32	29	50	22	58	13	71	67	40	304	17
	81-90 cm	13	71	7	100	6	100	7	100	7	100	29	50	70	32
	91-100 cm	7	100	0	.	7	100	7	100	0	.	8	100	29	50
	>100 cm	7	100	0	.	0	.	0	.	0	.	0	.	7	100
	total	15495	5	14217	7	9011	9	8577	10	8222	10	11627	8	67148	3
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	12-20 cm	73918	3	40299	6	21371	8	23483	8	24233	8	34370	6	217675	2
	21-30 cm	38861	3	22939	6	14511	8	12693	9	13773	8	19351	6	122129	2
	31-40 cm	24104	3	14292	6	9655	7	6983	8	8335	7	9035	7	72404	2
	41-50 cm	15891	3	8678	5	5827	7	3899	9	5424	7	4525	6	44244	2
	51-60 cm	9200	3	5229	6	3627	7	2272	9	3234	7	2454	11	26016	2
	61-70 cm	3761	5	2268	8	1566	10	919	13	1282	10	921	10	10717	3
	71-80 cm	1479	8	1012	9	734	14	419	18	515	13	482	15	4641	5
	81-90 cm	454	13	224	19	225	19	136	27	206	21	217	23	1462	8
	91-100 cm	140	23	52	38	70	32	80	30	63	37	89	35	494	13
	>100 cm	66	38	36	45	28	50	14	71	37	45	76	41	258	19
	total	167874	2	95030	4	57615	6	50898	7	57103	6	71520	5	500040	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. 1230435. Birmensdorf, Swiss Federal Research Institute WSL

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