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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: economic region
unit: 1000 m³
evaluation area: accessible forest without shrub forest NFI1-NFI5
grid: 1.4 km grid, subgrids 1-5
state 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
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	±%
n/a	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	.
shrub forest	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
permanently unstocked forest area	428	56	473	59	1067	50	1325	56	887	42	576	47	1417	36	448	61	395	50	0	.	108	100	355	63	209	51	130	74	7818	16
temporarily unstocked forest area	132	100	11	100	158	92	218	65	146	60	358	53	291	46	254	56	348	61	130	100	150	95	-4	100	183	53	250	81	2626	20
aisle, embankment	181	58	202	100	0	.	-15	100	0	.	133	71	11	88	0	.	0	.	0	.	164	100	79	100	122	70	246	67	1122	32
permanently open stand	1484	29	8	100	116	78	0	.	0	.	354	50	554	39	638	44	1257	44	71	100	293	73	882	36	2136	23	731	36	8525	12
(nut) orchard, plantation	0	.	0	.	65	100	0	.	0	.	0	.	0	.	0	.	245	100	0	.	0	.	0	.	0	.	522	58	833	48
coppice forest	66	78	209	100	80	100	0	.	0	.	31	100	26	100	0	.	233	54	0	.	59	82	160	64	196	65	3855	16	4916	14
coppice with standards	60	100	160	100	409	62	0	.	350	58	0	.	0	.	0	.	0	.	129	90	0	.	0	.	0	.	1835	26	2944	21
selection type high forest	5294	17	128	100	20	100	570	57	197	80	1836	34	6045	15	714	42	2103	25	843	41	396	56	3140	19	5901	14	2203	23	29389	7
non-uniform high forest	2508	24	1333	58	615	49	1005	49	2435	25	533	51	2756	28	1171	42	1440	34	301	68	554	52	3120	25	1921	25	3441	20	23131	9
young growth/ thicket	444	39	1024	32	383	50	655	36	1239	28	15	77	359	53	215	69	428	70	169	72	164	80	388	39	645	37	164	56	6292	12
poletimber	2034	25	651	36	730	36	2266	19	4493	17	1132	33	1138	34	1920	26	680	46	229	52	241	49	2147	24	2336	20	2652	17	22650	7
young timber	8459	13	2922	24	1701	33	4006	21	4109	18	1693	32	2317	27	3588	24	772	38	584	49	2770	43	3647	18	2016	25	3166	19	41751	6
medium timber	18606	9	5260	18	4361	21	6443	18	10573	13	3681	22	6112	18	7493	17	5228	19	2000	35	2174	28	5794	17	8844	14	5402	17	91970	4
old timber	13913	11	3202	23	6553	19	15750	12	16908	11	4317	25	18994	11	16984	12	5280	20	5009	22	4126	25	7069	16	14760	12	6751	16	139616	3
total	53609	4	15583	10	16257	11	32224	7	41337	5	14658	11	40020	6	33425	7	18409	10	9464	15	11201	15	26778	7	39268	6	31349	4	383583	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. 1232807. Birmensdorf, Swiss Federal Research Institute WSL

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