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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–NFI3
bolewood harvested
type of last silvicultural treatment
regional demarcation: economic region
unit: 1000 m³/yr
evaluation area: accessible forest without shrub forest NFI1-NFI5
grid: 1.4 km grid, subgrids 1-5
change 1993/95–2004/06
	economic region
	Western Jura		Eastern Jura		Western Plateau		Central Plateau		Eastern Plateau		Western Pre-Alps		Central Pre-Alps		Eastern Pre-Alps		Northwestern Alps		Central Alps		Northeastern Alps		Southwestern Alps		Southeastern Alps		Southern Alps		Switzerland
type of last silvicultural treatment	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%	1000 m³/yr	±%
n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
no treatment	56	30	12	52	9	42	54	29	24	39	10	58	28	50	7	48	10	57	5	68	25	66	6	63	39	39	15	81	289	13
tending	81	34	101	43	52	56	161	31	110	32	29	100	53	69	44	61	28	52	1	100	9	100	6	75	48	49	0	100	725	14
thinning	146	21	64	26	59	27	192	19	190	17	44	34	53	34	20	53	1	81	8	89	15	63	12	46	29	44	13	54	846	8
secondary felling	115	28	28	60	46	45	26	57	78	43	52	55	71	41	11	58	9	100	7	71	16	100	31	50	32	47	0	0	523	14
final felling	111	32	42	56	11	100	69	54	14	81	14	71	28	73	35	82	32	65	7	100	1	100	11	90	27	59	23	68	416	18
selection felling	51	27	0	.	8	100	2	100	0	.	0	.	76	38	0	.	0	.	0	.	0	.	0	100	0	0	2	100	142	24
thinning of mountain forest	0	.	0	.	0	.	0	.	0	.	6	73	9	72	6	100	0	.	0	0	0	.	36	44	63	34	0	.	121	24
coppice cut	3	100	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	3	80	5	64
conversion	17	79	0	.	0	.	0	.	9	83	0	.	0	.	0	0	0	.	0	.	0	.	0	.	0	.	0	.	27	59
transformation	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	0	0	.	0	.	1	100	0	.	0	.	2	100	3	78
sanitary felling	196	22	47	41	195	26	462	16	564	17	144	33	388	18	135	30	57	34	13	93	16	49	18	39	46	40	4	100	2242	7
thinning of continuous cover forest	0	.	0	.	0	.	3	100	84	30	0	.	2	100	0	.	0	.	0	.	0	.	0	.	0	.	1	100	90	29
tending of forest edge	0	0	0	.	2	100	13	71	18	72	0	.	7	100	61	72	0	.	0	.	0	.	7	100	0	0	0	0	103	43
planting	5	100	43	81	69	70	21	62	49	59	0	.	6	100	12	100	0	.	0	.	0	0	0	.	0	.	3	100	210	33
agrosilvicultural treatments	19	53	2	100	8	77	2	100	2	71	0	0	9	72	8	61	14	100	0	.	0	0	5	52	0	100	8	59	78	28
total	799	9	343	20	459	17	1004	10	1148	10	298	22	741	12	346	22	150	24	42	41	81	33	133	21	283	16	74	30	5715	4

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. 1399087. Birmensdorf, Swiss Federal Research Institute WSL

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