Weighting

Overview of weighting

The same weighting approach was taken in Wave 4 as in Waves 1, 2 and 3. Weights were initially calculated separately for each country in two stages:

1. Calculation of selection weights (described in the section on selection weights)
2. Calibration of selection weights to country population totals (described in section on population weights)

Next, weights were created for use in analyses of combined-country data by scaling the weighted country sample sizes to be proportional to the corresponding country population values (for adults aged 16 and over). 

Because it was not possible to include all questions in the postal questionnaires (see the section called ‘Questionnaire development and cognitive testing’), four separate question-type weights were calculated in each country, and in the combined all-country sample.

These four question-type weights were designed to be used as follows:

1. All-questionnaire weights to be used for questions asked of all sample members in all online and postal questionnaires
2. Online questionnaire weights to be used for questions asked only of online participants (i.e., questions not asked in the postal questionnaires)
3. Online questionnaire plus Eating Out (EO) postal questionnaire weights to be used for questions asked only of online participants and postal questionnaire respondents receiving only the EO version (i.e., questions not asked in the EH postal questionnaires)
4. Online questionnaire plus Eating at Home (EH) postal questionnaire weights to be used for questions asked only of online participants and postal questionnaire respondents receiving only the EH version (i.e., questions not asked in the EO postal questionnaires)

Four additional weights (one for each of these question types) were calculated for the combined all-country sample. Once the main weights were calculated as described above, supplementary ‘Wales & Welsh-England’ weights were calculated. These were designed to allow comparisons to be made between Wales and England (excluding London) after controlling for country profile differences in age within gender, ethnic group, number of adults per household, and urban-rural mix.

Calculation of selection of weights

Selection weights were created to compensate for (i) variations in within-household individual selection probabilities and response propensities and (ii) the fact that, by design, some questions were not included in all questionnaires. As a maximum of two eligible adults were interviewed per household, adults in larger households are less likely to be included in the survey. So without this weight, individuals living in households in which some eligible adults were not interviewed would be underrepresented relative to individuals living in households in which all eligible adults were interviewed. They were calculated in the following stages: 

1. The all-questionnaire selection weight was calculated as: (number of eligible people aged 16 years or over in the household)/(number of participants in the household). 
2. The online questionnaire selection weight was calculated as: (number of eligible people aged 16 years or over in the household)/(number of online participants in the household). 
3. Next the Online questionnaire plus EO questionnaire weight and the online questionnaire plus EH questionnaire weight were calculated by doubling the value of the all-questionnaire selection weight for postal respondents relative to the corresponding value for online respondents (because the relevant questions were only asked in half the postal questionnaires).

Values were capped to the range 1-3 for the all-questionnaire and online selection weights, and to the range 1-6 for the online questionnaire plus EO questionnaire and online questionnaire plus EH questionnaire weights to restrict variance inflation.

Calibration to population values

Next, selection weights were applied to the three individual country samples and each was calibrated to the corresponding country population values for the number of adults aged 16 or over by: 

(i)    age band within gender 
(ii)    geographic area (defined separately for each country) 
(iii)    deprivation quintile (calculated using each country’s multiple deprivation index). 

These weighting variables are often used as standard in social surveys because they correlate reliably with both response propensity and a wide range of survey variables. We note that in some previous rounds of the face-to-face Food and You survey, working status was used as a weighting variable instead of deprivation quintile. In Waves 1 to 4 of Food and You 2 it was decided not to use this variable for weighting the sample because survey fieldwork took place during the Covid-19 pandemic, during which rates of employment were likely to be unstable.  Deprivation quintile was used as a substitute indicator of general economic prosperity. 
Weighting targets are shown in the next section, taken from ONS Mid 2020 Population Estimates and NISRA Mid 2020 Population Estimates.

Table 7: Population totals for age within gender in England

Table 8: Population totals for age within gender in Wales

Table 9: Population totals for age within gender in Northern Ireland

Table 10: Population totals for regions in England

Table 11: Population totals for regions in Wales

Table 12: Population totals for regions in Northern Ireland

Table 13: Population totals for deprivation quintiles in England

Table 14: Population totals for deprivation quintiles in Wales

Table 15: Population totals for deprivation quintiles in Northern Ireland

Initial calibration was carried out separately in each country for each of the four questionnaire type weights described above. For each questionnaire type weight, calibration adjustment factors were calculated by dividing the individual country weights by the selection weights. These adjustment factors were then capped at the 99th percentile value to limit variance inflation and applied to selection weight to produce final individual country weights.  

After calibration and adjustment factor capping, the individual country level weights were scaled to equalise unweighted and weighted sample sizes in each country.

The aim of these within-country calibration procedures was to match the profile of the weighted sample to that of the population aged 16 or over on gender, age band, geographic region, and deprivation quintile.  In practice, there will be slight discrepancies between weighted sample totals and population figures as a result of the adjustment factor caps.

Creation of all-country weight

An all-country version of each questionnaire type weight was then constructed by combining the individual country samples and rescaling final individual country weights so that weighted sample country proportions matched the respective country population (aged 16 years or over) proportions.

Wales and Welsh England standardisation weight

This weight was designed to calibrate English sample estimates to Welsh population characteristics for comparative purposes. It was calculated from the England sample as follows:

1. London cases were dropped (London being in many ways unique in the UK)
2. The non-London England sample proportions were calibrated to the weighted Wales sample proportions for four variables: number of adults in the household, ethnic group, urban-rural and age by gender. These four variables were selected when the ‘Wales & Welsh-England’ weights were first constructed in Wave 1. Weighted estimates for Wales and non-London England were compared across a range of candidate variables and statistically significant differences were found for urban-rural, ethnic group, household size and age within gender.

The final weighing variables were defined as follows:

Age within gender (male and female)

Number of adults in household

• 1 adult
• 2 adults
• 3+ adults
• Question not answered

Ethnic group

• White
• Asian
• Black 
• Mixed
• Other/not answered

Urban-rural

Urban: OA falls into a built-up area with a population of 10,000 or more
Rural: All other OAs

‘Wales & Welsh-England’ weights were calculated only for respondents in England outside London and in Wales (where they were the same as the individual country weight for Wales). 

Table 16: Summary of list of weights and when to use each one