Quality Analysis in a Survey on Transportation of Goods by Road
Juris Breidaks1
1 University of Latvia
e-mail: Juris.Breidaks@gmail.com
Central Statistical Bureau of Latvia
e-mail: Juris.Breidaks@csb.gov.lv
Abstract
The paper is devoted to the quality analysis of the ongoing survey “Transportation and Turnover of Goods by Road” organised by the Central Statistical Bureau of Latvia (CSB). This is a continuous survey. The stratified simple random sampling is used.
Starting from 2005 stratification is changed to improve the quality. The stratification from 2002 till 2004 is compared with the stratification from 2005 in the paper. These stratifications are compared by the sample error, bias and mean square error.
1 Introduction

The Survey on Transport of Goods by Road was initiated in January 1997 as a pilot project organized by Eurostat under the Phare Programme. It is a continuous survey where information about the vehicles in the sample is obtained through questionnaires mailed to respondents. The target of survey is to obtain the information about transportation of goods by road performed by transport vehicles registered in Latvia. The main variables of interest are tonnes transported, tonne-kilometres performed and kilometres travelled loaded for total goods road transport.
The survey covers transport vehicles that are owned by legal and natural persons and which at the moment of sample formation had undergone technical inspection and could be lawfully used. The data of the Road Traffic Safety Directorate about vehicle registrations and the number of vehicles that had undergone technical inspection reveal that only 43.2% of all the registered transport vehicles had passed the yearly technical inspection and could be legally used. Special vehicles such as fire-fighting engines, crane lorries, tower cranes, road repair vehicles and other special vehicles were not included in the survey.
Simple random stratified sampling is used. The weekly sample size is 120 vehicles.

2 Stratification
From 1st January of 2002 till 1st January of 2005 stratification has been made by capacity, place of registration of vehicles and year of release of vehicles.

Table 1 – Stratification in 2004 

Stratum	
Capacity and place of registration of vehicles	
Year of release of the vehicles	
1	cap. 1,5t, Riga(including the district of Riga)	All	
2	cap. 1,5t, all Latvia without Riga and the district of Riga	All	
3	1,5t<cap.  5t, Riga(including the district of Riga)	All	
4	1,5t<cap.  5t, all Latvia without Riga and the district of Riga	All	
5	5t<cap. 10t, Riga(including the district of Riga)	1998-2004	
6	5t<cap.  10t, Riga(including the district of Riga)	1991-1997	
7	5t<cap.  10t, Riga(including the district of Riga)	1990	
8	5t<cap.  10t, all Latvia without Riga and the district of Riga	1998-2004	
9	5t<cap.  10t, all Latvia without Riga and the district of Riga	1991-1997	
10	5t<cap.  10t, all Latvia without Riga and the district of Riga	1990	
11	cap.>10t, Riga(including the district of Riga)	1998-2004	
12	cap.>10t, Riga(including the district of Riga)	1991-1997	
13	cap.>10t, Riga(including the district of Riga)	1990	
14	cap.>10t, all Latvia without Riga and the district of Riga	1998-2004	
15	cap.>10t, all Latvia without Riga and the district of Riga	1991-1997	
16	cap.>10t, all Latvia without Riga and the district of Riga	1990	
17	the trucks, Riga(including the district of Riga)	1998-2004	
18	the trucks, Riga(including the district of Riga)	1991-1997	
19	the trucks, Riga(including the district of Riga)	1990	
20	the trucks, all Latvia without Riga and the district of Riga	1998-2004	
21	the trucks, all Latvia without Riga and the district of Riga	1991-1997	
22	the trucks, all Latvia without Riga and the district of Riga	1990	

After 1st January of 2005 stratification is made by capacity, place of registration of vehicles, year of release of the vehicles and status.

Table 2 – Stratification after 1st January of 2005 

Stratum	
Capacity and place of registration of vehicles	
Year of release of the vehicles	
Status of person	
1	cap. 1,5t, Riga(including the district of Riga)	All	Legal	
2	cap. 1,5t, all Latvia without Riga and the district of Riga	All	Legal	
3	1,5t<cap.  5t, Riga(including the district of Riga)	All	Legal	
4	1,5t<cap.  5t, all Latvia without Riga and the district of Riga	All	Legal	
5	5t<cap. 10t, Riga(including the district of Riga)	1999-2005	Legal	

Stratum	
Capacity and place of registration of vehicles	
Year of release of the vehicles	
Status of person	
6	5t<cap.  10t, Riga(including the district of Riga)	1992-1998	Legal	
7	5t<cap.  10t, Riga(including the district of Riga)	1991	Legal	
8	5t<cap.  10t, all Latvia without Riga and the district of Riga	1999-2005	Legal	
9	5t<cap.  10t, all Latvia without Riga and the district of Riga	1992-1998	Legal	
10	5t<cap.  10t, all Latvia without Riga and the district of Riga	1991	Legal	
11	cap.>10t, Riga(including the district of Riga)	1999-2005	Legal	
12	cap.>10t, Riga(including the district of Riga)	1992-1998	Legal	
13	cap.>10t, Riga(including the district of Riga)	1991	Legal	
14	cap.>10t, all Latvia without Riga and the district of Riga	1999-2005	Legal	
15	cap.>10t, all Latvia without Riga and the district of Riga	1992-1998	Legal	
16	cap.>10t, all Latvia without Riga and the district of Riga	1991	Legal	
17	the trucks, Riga(including the district of Riga)	1999-2005	Legal	
18	the trucks, Riga(including the district of Riga)	1992-1998	Legal	
19	the trucks, Riga(including the district of Riga)	1991	Legal	
20	the trucks, all Latvia without Riga and the district of Riga	1999-2005	Legal	
21	the trucks, all Latvia without Riga and the district of Riga	1992-1998	Legal	
22	the trucks, all Latvia without Riga and the district of Riga	1991	Legal	
23	1,5t<cap.  5t, all Latvia	All	Private	
24	5t<cap., all Latvia	All	Private	
25	the trucks, all Latvia	All	Private	

There are two types of vehicle. The status of the owner of a vehicle is legal or natural person.

Table 3 – Level of response by status in 2005
Status	Number of respondents	Sample size	Level of response (%)	
Legal	5085	5772	88.10	
Private	255	468	54.49	
Total	5340	6240	85.58	

Table 4 – Mean of indicators value in 2005 population

Capacity of vehicles	TONN	TKM	KML2	
	Legal	Private	Legal	Private	Legal	Private	
1,5t<cap.  5t	13.4	1.0	971.0	78.8	1253.9	213.3	
5t<cap.	330.5	81.5	24233.9	2500.5	1795.6	287.0	
the trucks	231.1	244.9	77330.1	23328.2	4232.5	1157.0	

Capacity of vehicles	TO_N	TK_N	KM_N	
	Legal	Private	Legal	Private	Legal	Private	
1,5t<cap.  5t	13.2	1.0	913.0	78.8	1190.6	213.3	
5t<cap.	321.7	81.5	16307.5	2500.5	1199.8	287.0	
the trucks	179.3	223.1	12722.4	19027.1	612.7	937.1	

	Notations for this and further tables					
	TONN	Tonnes transported for total goods road transport	
	TKM	Tonne-kilometres performed for total goods road transport	
	KML2	Kilometres travelled loaded for total goods road transport	
	TO_N	Tonnes transported for national goods road transport	
	TK_N	Tonne-kilometres performed for national goods road transport	
	KM_N	Kilometres travelled loaded for total national road transport	

Comparing the mean indicator of ton-kilometres performed and kilometres performed per vehicle in above mentioned vehicle groups, it is obvious that for vehicles owned by legal persons these indicators are higher. The non-response level of natural persons is higher compared to legal persons.
The status (legal or private) of the owner of a vehicle was not used as a stratification indication in the previous stratification. So the combination of these essential differences in these two vehicle groups can lead to biased estimates. The estimates of total indicators of private persons are underestimated if these differences are not taken into account. The estimates of total indicators of legal persons are overestimated because of the same reason. The estimates of total indicators are also overestimated because legal persons have higher response rate and the values of indicators for legal persons are also higher.

3 Comparing of the stratification
3.1 Sample errors of estimates
The variance of estimates was estimated for six indicators – total tonnes transported, total tonne-kilometres performed and total kilometres travelled loaded for total goods road transport and for national goods road transport.

Table 5 – The coefficients of variation for estimates of indicators in year 2004 and 2005
Year	TONN	TKM	KML2	TO_N	TK_N	KM_N	
2004	4.210	2.086	2.688	4.575	3.500	4.175	
2005	3.666	2.123	2.506	4.038	3.426	3.858	

It is obvious from Table 5 that the quality of estimates of indicators concerning to tonnes and ton-kilometres, kilometres has improved, expect sample error of one indicator is worsen
In next capter sample error for the survey in 2005 will be estimated with stratification from 2002 till 2004, and this stratification will be compared with stratification from 2005. The comparison is inconsiderate in table 5, because are compared different population. In next chapter one population of survey was taken.

3.2 The estimation of the sample error with different stratification
It is possible to estimate the sample error if the different stratification is used. Assume that there are two stratification, new stratification with G strata and previous stratification with H strata. It is possible to compute population size Mg from sampling frame. The standard deviation of g-th stratum is
	
 and  have to be estimated to estimate . Estimate of  is , where  ; θg is the index group of successfully surveyed vehicles belonging to g-th stratum. Estimate of  is

	
	
So the estimate of  is

Two conditions have to realize to estimate :  and .
Variance of  is
	
Estimate of  is

Table 6 – The coefficients of variation of estimates of indicators using two stratifications
	TONN	TKM	KML2	TO_N	TK_N	KM_N	
Stratification from 2002 till 2004	3.740	2.139	2.711	4.122	3.484	4.213	
Stratification from 2005	3.666	2.123	2.506	4.038	3.426	3.858	

It is obvious that if previous stratification would be used in 2005, than the sample error would be largercomparing with current situation.

3.3 Bias
In this survey there is bias of the estimates. The bias is caused by different reasons. One of the reasons (caused by two types of vehicles – legal and private) is discussed in the paper. Using stratification from 2002 till 2004, the estimation of those indicators are biased for these three indicators – total tonnes transported, total tonne-kilometres performed and total kilometres travelled loaded for total goods road transport.
An estimates of biases in percentage was taken from M. Liberts paper. I assume that the bias of estimates of indicators in percentage has not changed.
Table 7 – Estimates of biases (%) for totals ( in 2003)
TONN	TKM	KML2	
1.8	0.8	6	

Table 8 – Bias of estimates of indicators in 2005 using stratification from 2002 till 2004
TONN	TKM	KML2	
938 610.94	67 171 847.49	49 594 073.83	

Using stratification from 2005, the estimation of those indicators are unbiased for these three indicators, because the status (legal or natural) of the owner of a vehicle is used as a stratification indication.

3.4 Mean square error (MSE)
Mean square error is 
	
where  is variance of  and  is bias of .

Table 9 – MSE of estimates of indicators in 2005 using stratification from 2002 till 2004
	TONN	TKM	KML2	
Variance	3 803 715 422 997	32 260 798 183 220 800	502 018 849 797 176	
Bias	938 611	67 171 847	49 594 074	
MSE	4 684 706 032 318	36 772 855 212 612 200	2 961 591 025 714 650	

Table 10 – MSE of estimates of indicators in 2005 using stratification from 2005
 	TONN	TKM	KML2	
Variance	3 654 513 335 476	31 782 088 614 413 800	429 064 493 734 578	
Bias	0	0	0	
MSE	3 654 513 335 476	31 782 088 614 413 800	429 064 493 734 578	

4 Conclusion
Comparing the mean square error of tons transported, ton-kilometres performed and kilometres performed per vehicle, it became obvious that stratification from 2005 is better than previous stratification. The sample error is improved for all indicator, expect sample error of one indicator is worsen. The bias is considerably dominished.

5 References
Särndal C.-E., Swensson B., Wretman J. (1992) Model Assisted Survey Sampling. Springer-Verlag, New York.
Lapins, J. (1997) Sampling surveys in Latvia: Current situation, problems and future developments. Statistics in Transition: Journal of the Polish Statistical Association, 3, 281-292.
Pandutang V, Sukhatme, Balkrishna V. Sukhatme , Shashikala Sukhatme, C. Asok., Sampling Theory of Surveys with Applications, IOWA State University press and Indian Society of Agricultural Statistics, 14-15
Lohr S. L. (1999) Sampling: Design and Analysis. Brooks/Cole Publishing Company, Pacific Grove, Calif.
SPSS Inc. (2002) SPSS® Syntax Reference Guide
Liberts. M. (2004) Quality Analysis of a Sample Survey on Transportation of Goods by Road. http://www.stat.jyu.fi/~knissine/nordstatabs/Sess07SurvSamp.pdf, 9.