Catherine Renne Insee Measuring sampling error in business surveys The case of the French monthly industry survey

Measuring sampling error in business surveys 2 Introduction Definitions Census : Exhaustive observation of all the elements of a population Sampling : Selection methods of the elements of a population Two types of sampling Probability sampling : each element of the population has a known non-zero probability of being selected. Stratified sampling, cluster sampling,… Non-probability sampling : elements are selected from the population in some non random manner Ex : quota sampling 17 MS 9 MS

Measuring sampling error in business surveys 3 Key issues of probability sampling 1. Selection of the sample Sampling method, selection process, sample size,… 2. How to aggregate the answers Calculation of the estimator In other words : how to draw conclusions from sampling data? Calculation of the random error In other words : how accurate is the aggregation procedure? Good sampling methods involve To have an exhaustive list of the units of the target population Sample frame issues To know exactly what we want to measure via the survey Variable of interest, notion of « true value »

Measuring sampling error in business surveys 4 Basic vocabulary of sampling Parameter It is a fonction of the individual unknown values Y i in the population of size N. This is the « true value » Example : {1,2,3,4) are the elements of the population. Y1=6000 ; Y2=12000 Y3=8000 ; Y4=6000 The estimator If n is the size of the sample, the formula that aggregates the n value y i is called the estimator of :

Measuring sampling error in business surveys 5 Sampling error The value of the estimator depends on the selected sample Bias If we could select all the possible samples, we would know the average value of the estimator The bias is the difference between this average and the true value Example : n=2. s1={1,2}, s2={1,3}, s3={1,4}, s4={2,3}, s5={2,4}, s6={3,4} The average of these six values is This is the « true value » The estimator is unbiased Variance

Measuring sampling error in business surveys 6 Sampling error in short Low bias, low variance Low bias, high variance High bias, low variance High bias, high variance

Measuring sampling error in business surveys 7 The statistical law of the estimator

Measuring sampling error in business surveys 8 Sampling plan The estimator Principle of calculation Unweighted questions Weighted questions The French business industry survey

Measuring sampling error in business surveys 9 Sampling plan Sampling frame: the statistical business register Stratification criteria : activity (3 digits of the NACE) enterprise size employees ; employees ; 500 or more Number of units per strata proportional to the shares of total turnover Exhaustive strata : >500 employees or >150 million turnover

Measuring sampling error in business surveys 10 The estimator Two kind of questions At the enterprise level : Ex : Your outlook for total French Industry ? Likely changes in next 3 months At the activity level : Ex : How has your production developed over the past 3 months? It has… + increased = remained unchanged - decreased Answers are not weighted Answers are weighted

Measuring sampling error in business surveys 11 Principle of calculation The answers of enterprises are associated with an auxiliary variable Y : yi=1 if + increased yi=0 if = remained unchanged yi=-1 if - decreased Balance of opinion is the average of Y. Yi=1Yi=0Yi=-1

Measuring sampling error in business surveys 12 Unweighted questions

Measuring sampling error in business surveys 13 Weighted questions

Thank you for your attention ! Contact Ms. Catherine Renne Tél. : Courriel : Insee 18 bd Adolphe-Pinard Paris Cedex 14 Informations statistiques : / Contacter lInsee (coût dun appel local) du lundi au vendredi de 9h00 à 17h00