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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
number of stems
altitude (in 200 m classes) · number of cases of damage
regional demarcation: economic region
unit: n/ha
evaluation area: accessible forest without shrub forest NFI1-NFI5
grid: 1.4 km grid, subgrids 1-5
state 1993/95
		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
altitude (in 200 m classes)	number of cases of damage	n/ha	±%	n/ha	±%	n/ha	±%	n/ha	±%	n/ha	±%	n/ha	±%	n/ha	±%	n/ha	±%	n/ha	±%	n/ha	±%	n/ha	±%	n/ha	±%	n/ha	±%	n/ha	±%	n/ha	±%
n/a	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	one visible damage	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	two or more visible damages	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	dead or lying tree	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	total	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
>1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	0	.	0	.	0	.	0	.	0	.	580	0	0	.	331	34	0	.	0	.	222	12	298	8	258	14	271	6
	one visible damage	0	.	0	.	0	.	0	.	0	.	0	.	20	0	0	.	47	33	0	.	0	.	85	11	73	9	58	27	74	7
	two or more visible damages	0	.	0	.	0	.	0	.	0	.	0	.	110	0	0	.	8	58	0	.	0	.	28	22	9	27	16	34	17	16
	dead or lying tree	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	3	65	7	52	14	59	6	36
	total	0	.	0	.	0	.	0	.	0	.	0	.	710	0	0	.	386	32	0	.	0	.	339	10	387	7	346	12	368	5
1601-1800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	0	.	0	.	0	.	0	.	0	.	328	40	545	26	520	0	236	22	230	34	259	35	348	14	300	10	239	12	307	7
	one visible damage	0	.	0	.	0	.	0	.	0	.	99	44	70	20	70	0	82	30	81	37	97	21	117	15	62	16	49	17	78	8
	two or more visible damages	0	.	0	.	0	.	0	.	0	.	30	76	6	73	20	0	60	44	37	48	16	60	26	23	22	29	13	24	24	16
	dead or lying tree	0	.	0	.	0	.	0	.	0	.	0	.	5	97	100	0	0	.	0	.	0	.	6	70	2	61	2	69	3	37
	total	0	.	0	.	0	.	0	.	0	.	457	42	625	24	710	0	378	18	347	19	372	26	496	13	386	9	303	11	413	6
1401-1600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	195	28	0	.	288	30	0	.	0	.	342	26	332	14	251	26	206	19	279	32	148	37	250	11	281	10	308	12	271	5
	one visible damage	46	35	0	.	57	31	0	.	0	.	110	31	64	19	100	47	78	15	67	29	47	29	94	12	69	11	77	17	77	7
	two or more visible damages	7	48	0	.	8	90	0	.	0	.	18	53	11	32	20	43	46	26	24	46	16	37	33	20	19	19	15	27	23	11
	dead or lying tree	0	.	0	.	0	.	0	.	0	.	4	97	0	.	0	.	2	99	0	.	0	.	5	51	1	70	2	69	2	33
	total	247	20	0	.	352	30	0	.	0	.	474	22	407	14	372	30	333	13	370	27	212	31	383	9	369	8	402	10	373	5
1201-1400 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	256	10	0	.	277	51	0	.	0	.	448	16	346	13	274	15	375	10	295	22	269	20	343	16	321	13	307	12	321	5
	one visible damage	58	18	0	.	42	75	0	.	0	.	105	12	80	16	83	15	83	17	79	23	128	17	108	17	114	17	63	16	85	6
	two or more visible damages	19	29	0	.	21	66	0	.	0	.	63	38	34	24	27	31	24	28	36	26	41	31	28	28	25	31	23	22	30	11
	dead or lying tree	0	.	0	.	0	.	0	.	0	.	0	.	4	72	0	.	0	.	3	97	6	96	2	79	0	.	0	99	1	41
	total	333	8	0	.	341	46	0	.	0	.	616	14	463	11	384	13	482	7	413	20	445	15	482	12	460	11	393	10	437	4
1001-1200 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	372	7	0	.	195	20	284	19	279	7	475	16	300	9	399	13	269	24	428	16	421	32	321	14	273	18	336	15	351	4
	one visible damage	75	9	0	.	66	14	91	39	109	67	114	21	108	12	97	18	74	21	117	23	123	31	86	19	108	21	58	14	89	5
	two or more visible damages	19	17	0	.	14	83	0	.	7	82	24	31	47	20	32	24	22	50	32	34	47	23	35	38	50	27	21	35	30	9
	dead or lying tree	1	100	0	.	0	.	0	.	0	.	0	.	1	100	1	99	2	98	14	75	3	97	2	98	2	98	4	56	2	32
	total	466	6	0	.	275	21	375	5	395	22	612	14	456	7	529	12	368	19	591	14	594	26	445	12	433	15	419	12	472	4
801-1000 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	365	7	348	17	424	17	322	18	354	19	478	18	389	8	484	12	303	21	542	15	259	22	399	15	267	18	395	12	384	4
	one visible damage	100	9	102	29	89	22	70	20	144	25	111	21	112	13	99	20	79	23	195	22	130	23	135	26	72	18	115	17	105	5
	two or more visible damages	40	19	46	30	10	56	20	36	26	44	31	33	40	21	18	25	16	33	68	42	107	25	38	28	42	31	48	22	38	8
	dead or lying tree	0	.	0	.	0	.	0	.	0	.	0	.	1	99	0	.	3	98	0	.	3	97	2	98	10	57	5	72	2	35
	total	505	6	496	17	523	15	411	14	525	16	619	14	543	7	602	11	400	17	805	11	498	15	574	13	392	14	563	9	529	3
601-800 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	373	7	386	13	390	9	334	7	393	8	471	24	376	11	374	9	401	13	226	19	398	29	230	21	297	17	370	13	368	3
	one visible damage	97	10	78	25	55	12	67	10	63	11	48	66	81	14	69	15	50	29	86	43	115	32	131	17	66	19	112	19	78	5
	two or more visible damages	25	18	31	48	14	29	17	20	13	23	23	61	22	29	25	37	6	77	51	36	59	29	63	20	30	53	71	20	26	9
	dead or lying tree	0	.	0	.	1	99	0	.	1	100	0	.	0	.	0	.	0	.	0	.	0	.	10	95	8	89	1	99	1	50
	total	495	6	495	11	460	8	419	6	471	8	542	19	478	9	468	8	458	12	364	20	572	25	434	14	402	13	554	11	472	3
=600 m	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	389	9	338	9	488	10	394	8	332	6	0	.	417	38	524	12	521	34	360	35	375	14	267	27	208	0	413	11	373	3
	one visible damage	82	17	51	13	69	14	68	9	49	9	0	.	47	56	155	44	103	39	221	33	45	39	57	44	0	.	110	14	67	5
	two or more visible damages	22	22	10	26	8	48	21	17	11	22	0	.	45	48	33	67	13	85	47	40	0	.	0	.	0	.	59	20	19	10
	dead or lying tree	0	.	1	100	1	99	1	75	1	100	0	.	0	.	0	.	0	.	12	89	0	.	0	.	0	.	4	84	1	44
	total	492	8	400	8	566	8	483	6	393	5	0	.	509	36	711	16	637	28	640	13	420	17	324	22	208	0	586	9	460	3
total	n/a	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.	0	.
	no visible damage	354	4	349	7	416	6	365	5	350	5	432	8	363	5	393	6	291	7	350	10	299	13	295	6	292	4	335	5	343	1
	one visible damage	83	5	62	11	65	8	68	6	57	7	105	10	92	6	94	10	76	9	111	12	109	12	101	6	76	6	81	7	82	2
	two or more visible damages	25	10	18	22	11	21	19	12	12	16	35	22	33	11	25	14	31	18	39	16	52	15	30	10	22	12	35	10	26	4
	dead or lying tree	0	100	0	100	1	70	0	75	1	80	1	99	1	46	1	78	1	61	5	57	2	58	4	30	4	30	3	28	2	14
	total	463	3	429	6	493	5	452	4	419	4	574	7	488	4	513	5	400	6	505	8	463	10	429	5	395	4	454	4	453	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. 1198818. Birmensdorf, Swiss Federal Research Institute WSL

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