Appendix U - Statistical methods NI Report NDNS 2019-2023
Source: data.gov.uk (2025-10-10)

National Diet and Nutrition Survey 2017 to 2023 Report for Northern Ireland. This report presents results from 2017-2023 of the National Diet and Nutrition Survey (NDNS) for Northern Ireland. NDNS is a continuous cross-sectional survey, designed to assess the diet, nutrient intake and nutritional status of the general population aged 18 months and over living in private households in the UK.

National Diet and Nutrition Survey: 2019 to 2023 (years 12 to 15) 
 
 
 
Appendix U Statistical methods for 
National Diet and Nutrition Survey 2019 
to 2023 
U.1 Introduction 
 
This appendix provides an outline description of the statistical methods used for the following: 
• usual intake estimation of nutrient and food intakes 
• descriptive statistics used in this report 
• assessment of trends over time from Years 1 to 15 (2008 to 2023) 
• trends in relation to socio-economic status of the participant’s household (using 
equivalised income and index of multiple deprivation (IMD)). 
 
The National Diet and Nutrition Survey (NDNS) sample requires weights to adjust for differences 
in sample selection and response relative to the UK population distribution. The statistical 
analysis of data generated from this complex survey design requires taking the sample design 
(that is the sample stratification, clustering and weighting) into account to yield valid estimates 
of the population parameters. Details of the weighting and sampling procedures are provided in 
appendix BB. 
 
U.2 Definitions of statistical terms used in this report 
 
97.5th percentile   
97.5% of the data are below this value and 2.5% are above it. 
 
2.5th percentile 
2.5% of the data are below this value and 97.5% are above it. 
 
Confidence intervals 
The range of plausible values for the true population estimate. Values outside this interval are 
statistically significantly different from the sample estimate. 
 
Positive and negative skew 
A skewed distribution does not have a symmetric shape. Positive skew occurs when there is a 
long tail on the right (a wide spread of extreme high values compared to the majority of the 
data) and negative skew occurs when there is a long tail on the left (a wide spread of extreme 
low values compared to the majority of the data). 
 
Transformation  
The application of a function to each data point such that the transformed data more closely 
follow a desired distribution (i.e. log transformation for positively skew data). 
 
Arithmetic mean (mean) 
The average of a set of numerical values, as calculated by adding them together and dividing by  
the number of values. 

National Diet and Nutrition Survey: 2019 to 2023 (years 12 to 15) 
 
 
 
Geometric mean 
An alternative to the arithmetic mean to estimate the average value for data that are positively 
skewed (one alternative to not having a symmetric shape). 
 
Median 
The middle value in a dataset when the data is ranked by size 
 
U.3 Usual intake estimation of nutrient and food intakes   
 
This report is the first NDNS report to present dietary data collected using Intake24, an online 
24-hour dietary recall tool. The move to non-consecutive day dietary recalls for years 12 to 15 
(2019 to 2023) provided the opportunity to estimate nutrient and food intakes by calculating 
‘usual intakes’ which is the accepted method to estimate population habitual nutrient and food 
intakes. Dietary data for years 1 to 11 (2008 to 2018) were collected over 4 consecutive diary 
days and so nutrient and food intakes were estimated by calculating the ‘day average’. 
 
When calculating ‘day average’ nutrient and food intakes the variance of the usual group intake 
is inflated by day-to-day variation in individual intake, resulting in misleading estimates of the 
prevalence of low or high intakes. With the collection of repeated 24-hour recalls in years 12 to 
15, it is possible to eliminate the intra-individual variability of the data and thereby to obtain an 
estimate of the population usual intake distribution (Souverein and others, 2011). Several 
statistical procedures for estimating the usual intake distribution from repeated 24 hour recalls 
are available to enable the estimation of ‘habitual’ intakes. This enables more appropriate 
estimation of ‘percentiles’ or ‘proportions above or below a threshold’ compared with the ‘day 
average’ method. See National Cancer Institute Diet Assessment Primer and National Cancer 
Institute: Usual Dietary Intakes, the NCI method for more information. 
 
Usual intakes of frequently consumed foods such as meat, fruit and vegetables and sources of 
protein, can be estimated well with short-term measures (2 or more days of a 24-hour recall). 
Short-term measures for infrequently consumed foods such as fruit juice, fish and sugar-
sweetened soft drinks can result in zero intake being reported for many participants. Including 
an additional long-term measure such as a Food Frequency Questionnaire (FFQ) can help to 
more accurately capture usual intake for such foods. For example, with a dietary assessment 
protocol of collecting up to 4 recalls, a participant may record zero intake for a particular food on 
all recording days but may record in an FFQ that they consume the same food on average once 
a week. FFQ information has therefore been collected in Computer Assisted Personal Interview 
(CAPI) for a limited number of infrequently consumed foods (fish, white meat, fruit juice and 
sugar-sweetened soft drinks) and will be factored in alongside the short-term measure to 
improve the estimation of ‘usual intake’. 
 
The Multiple Source Method (MSM, Germany) is a web-based application which uses R code to 
perform the statistical analysis and was used to estimate ‘usual intakes’ of nutrients and foods 
for years 12 to 15. All valid recalls from all participants, regardless of the number of recalls 
obtained, were included in the analysis. The inclusion of participants with only 1 or 2 dietary 
recalls was made possible by the usual intake method ‘borrowing’ day-to-day variation 
estimates from other similarly aged participants with 3 or 4 recalls. This provides an advantage 
over the previous diary method which required at least 3 diet collection days for a participant to 
be included. 
 

National Diet and Nutrition Survey: 2019 to 2023 (years 12 to 15) 
 
 
For some foods there were insufficient participants with 2 or more consumption days and so it 
was not possible to estimate the day-to-day variation required in the calculation of ‘usual 
intakes’. The threshold set for this was 15% or more participants with 2 or more consumption 
days. For foods which did not meet this threshold intakes were estimated by calculating the ‘day 
average’. 
 
U.4 Descriptive statistics used in this report   
 
The choice of descriptive statistic is mainly driven by the statistical distribution of the data for 
each variable: 
 
• 
A numerical variable which follows a symmetric and ‘bell-shaped’ distribution is best 
described using an arithmetic mean (to represent the typical value) and standard deviation 
(to represent the spread). 
• 
This report also provides the median and 2.5th and 97.5th percentiles which provide robust 
(not outlier influenced) estimates of the typical value and spread of the distribution for the 
case when the numerical variable deviates from a symmetric and ‘bell-shaped’ distribution 
due to extreme outliers or a high proportion of zeros. 
• 
A numerical variable which is positively skewed (bunched for low values and widely spread 
for high values) is best described using a geometric mean (to represent the typical value) 
and 2.5th and 97.5th percentiles (to represent the spread) as the arithmetic mean will be 
strongly influenced by the relatively few high outlier values. 
• 
A numerical variable which has a high proportion of values below the limit of quantitation1 
is best described using a median (to represent the typical value) and 2.5th and 97.5th 
percentiles (to represent the spread). 
 
Evidence from literature was used to confirm the choice of descriptive statistic for each variable 
before it is used in this report. 
 
U.4.1 Descriptive statistics used for food, nutrient intake and blood and urine analyte 
variables   
The majority of food, nutrient intake and blood and urine analyte variables reported follow a 
symmetric and ‘bell-shaped’ distribution and so the descriptive statistics used are arithmetic 
mean, median, standard deviation, 2.5th and 97.5th percentiles. Exceptions to this are outlined in 
table U.1 along with the reported descriptive statistics: 
 
 
 
1 The limit of quantitation is the lowest amount that can reliably and consistently be detected and measured. 

National Diet and Nutrition Survey: 2019 to 2023 (years 12 to 15) 
 
 
Table U.1 
Descriptive statistics reported for variables that deviate from a symmetric 
and ‘bell-shaped’ distribution  
Analyte 
Distribution 
Descriptive 
statistics 
Descriptive 
statistics 
Blood: Red cell blood 
folate 
Positively skewed 
Geometric 
mean 
2.5th and 97.5th 
percentiles 
Blood: Serum folate 
Positively skewed 
Geometric 
mean 
2.5th and 97.5th 
percentiles 
Blood: 
Unmetabolised (free) 
folic acid 
High proportion of values 
below the limit of quantitation 
Median 
2.5th and 97.5th 
percentiles 
Urine: Iodine 
concentration 
Positively skewed but 
following WHO guidance on 
descriptive statistics 
(Institutional Repository for 
Sharing (https://iris.who.int/)) 
Median 
20th and 80th 
percentiles 
 
The variables listed below show some evidence of deviating from a symmetric and ‘bell-
shaped’ distribution and so the more robust (not outlier influenced) median and 2.5th and 97.5th 
percentiles should be used for interpretation rather than the arithmetic mean and standard 
deviation. 
 
• Foods: Sugar-sweetened soft drinks, Sugar confectionery, Chocolate confectionery, 
Sweet or savoury biscuits and cereal bars, Buns, cakes and pastries and Crisps and 
other savoury snacks. 
• Nutrients: Vitamin A, Vitamin D. 
• Blood analytes: Ferritin, Vitamin B6 (PLP), Vitamin B12. 
 
U.5 Trends over time   
 
This section outlines the statistical methods used to estimate the ‘average change per year’ in 
each outcome for urinary iodine and self-reported physical activity energy expenditure from 
years 1 to 15 of NDNS. Trends over time for foods and nutrients and blood analytes were not 
estimated due to the dietary assessment method change to Intake24 occurring from year 12 
and the blood sample postal model change from year 13. These time trends are investigated in 
the Stage 3 evaluation report of the dietary method change and the blood sample transport 
report. The same weights and design variables as those used in the years 1 to 4 (combined), 
years 5 and 6 (combined), years 7 and 8 (combined) and years 9, 10 and 11 (combined) 
reports (with additional weights and design variables for years 12, 13, 14 and 15 (combined)) 
were applied in these analyses. The weights for each data set were re-scaled based on 
sample size, such that each set of data is in the correct proportion (4:2:2:3:4) to give a 
standardised sample size per survey year.2 
 
2 Although the weights were not specifically designed for this type of sub-group analysis, it was possible to use the 
years 1 to 15 weights and design variables for just 2 to 4 years’ data (years 1 and 2, years 3 and 4, years 5 and 6, 
years 7 and 8, years 9, 10 and 11 or years 12, 13, 14 and 15), as:  
• 
the selection weights correct for any differences in sampling strategy across survey years    
• 
there was no evidence that response behaviour had changed significantly between the 6 survey periods   
However, to use subsets of any other combination of years of the dataset, the weights and design variables would 
 

National Diet and Nutrition Survey: 2019 to 2023 (years 12 to 15) 
 
 
 
The ‘average change per year’ were estimated through linear regression models across the 
age groups, overall and by sex (for all but the 1.5 to 3 years age group). Participants were 
grouped into quarters of a calendar year according to when their urine sample physical activity 
questionnaire data was collected, and this time variable was used as the explanatory variable 
in the regression models. 
 
The statistical analyses were undertaken using the following 3 stages: exploratory analyses, 
estimation of ‘changes per year’ and the ‘diet method change’ and diagnostic procedures (i.e. 
assessment of model assumptions and goodness of fit). All the analyses, including the 
graphical tools and diagnostic procedures, took into account the complex survey design. 
 
U.5.1 Exploratory analyses 
The observed distributions of the continuous variables were screened through histograms, Q-Q 
plots and boxplots. These graphical tools showed the shape of the distribution and highlighted 
the presence of outliers. These were investigated as well as their impact on the regression 
analyses. 
 
U.5.2 Estimation of the ‘average change per year’ 
Linear regression models were used and the regression coefficients (which estimate the 
intercept and slope parameters for each age and sex group) use probability weighted least 
squares (Holt and others, 1980) and their covariance matrix was estimated using a Taylor 
linearization method (Binder, 1983). The slope parameter (along with the associated 95% 
confidence interval) estimates the ‘average change per year’ for each variable. 
 
U.5.3 Diagnostic procedures 
 
The goodness of fit of the linear models was examined using the concept of explained variation 
(R-squared). 
 
U.6 Socio-economic regression analysis   
 
This section outlines the statistical methods used to estimate the average change per £10,000 
of equivalised income in each outcome of key foods, nutrients and blood and urine analytes 
from NDNS years 12 to 15 combined. 
 
The ‘average change per £10,000 of equivalised income’ for the continuous variables were 
estimated through linear regression models and for proportions (such as the percentage of the 
sample meeting the 5 A Day guideline for fruit and vegetable intake) through logistic regression 
models across 6 age groups, overall and by sex (for all but the youngest age group). The age 
groups were 1.5 to 3 years (sex-combined only), 4 to 10 years, 11 to 18 years, 19 to 64 years, 
65 to 74 years and 75 years and over. 
 
The statistical analyses were undertaken using the following 3 stages: exploratory analyses, 
 
have to be reviewed to ensure that the subset of data is still representative of the UK population when the years 1 
to 15 weights and design variables have been applied.  
 

National Diet and Nutrition Survey: 2019 to 2023 (years 12 to 15) 
 
 
estimation of ‘changes per £10,000 of equivalised income’ and diagnostic procedures (i.e. 
assessment of model assumptions and goodness of fit). All the analyses, including the 
graphical tools and diagnostic procedures, took into account the complex survey design. 
 
U.6.1 Exploratory analyses 
The observed distributions of the continuous variables were screened through histograms, Q-Q 
plots and boxplots. These graphical tools showed the shape of the distribution and highlighted 
the presence of outliers. These were investigated as well as their impact on the regression 
analyses. 
 
U.6.2 Estimation of the ‘average change per £10,000 of equivalised income’ for 
continuous variables 
Linear regression models were used for continuous measurements of foods, nutrients and blood 
and urine analytes. The regression coefficients (which estimate the intercept and slope 
parameters for each age and sex group) use probability weighted least squares (Holt and 
others, 1980) and their covariance matrix was estimated using a Taylor linearization method 
(Binder, 1983).  The slope parameter (along with the associated 95% confidence interval) 
estimates the ‘average change per £10,000 of equivalised income’ for each variable. 
 
U.6.3 Estimation of the ‘average change per £10,000 of equivalised income’ for 
proportions 
Logistic regression models (with an identity link function) were used for binary variables. The 
regression coefficients (which estimate the intercept and slope parameters for each age/sex 
group) use a pseudo-likelihood approach (Holt and others, 1980) and their covariance matrix 
was estimated using a Taylor linearization method (Binder, 1983). The slope parameter (along 
with the associated 95% confidence interval) estimates the ‘average change per £10,000 of 
equivalised income’ for each variable. 
 
U.6.4 Diagnostic procedures 
The goodness of fit of the linear models was examined using the concept of explained variation 
(R-squared). 
 
U.7 Socio-economic quintile summary for England 
 
To assess the relationship between each outcome of key foods, nutrients and blood and urine 
analytes from years 12 to 15 combined of the NDNS with the Index of Multiple Deprivation for 
England (EIMD) descriptive statistics were calculated (using the same methods as described in 
section U.3 above) for each quintile of EIMD. These descriptive statistics were then compared 
with descriptive statistics calculated for each quintile of equivalised income for England 
participants. 
 
 
 

National Diet and Nutrition Survey: 2019 to 2023 (years 12 to 15) 
 
 
U.8 General 
 
The statistical analyses described above were performed using the survey package in the 
statistical program R (Lumley, 2012) (Lumley, 2004). 
 
The statistical analyses described in this appendix are for descriptive purposes rather than 
analytical, that is, they are not intended to estimate the associations among many variables. 
Therefore, corrections for multiple comparisons were not necessary (or practical since 
thousands of statistical tests have been performed). Bonferroni procedures may be applicable 
in other situations involving simultaneous testing of regression coefficients when the number of 
independent variables in the regression analysis is large compared to the number of sampled 
Primary Sampling Units (PSUs) (Korn and Graubard, 1990). 
 
Unless stated otherwise, only trends and differences found to be statistically significant at the 
five per cent level are identified as `significant`. In other words, differences as large as these 
have no more than a five per cent probability of occurring by chance. The term ‘significant’ is 
not intended to imply substantive importance. 
 
References 
Binder D A. `On the Variances of Asymptotically Normal Estimators from Complex Surveys`. 
International Statistical Review 1983: volume 51, pages 279–292 
 
Holt D, Smith TMF and Winter PD. `Regression analysis of data from complex surveys`. Journal 
of the Royal Statistical Society A 1980: volume 143, pages 474 –487 
 
Korn EL and Graubard BI. `Simultaneous testing of regression coefficients with complex survey 
data: Use of Bonferroni t statistics`. The American Statistician (1990): volume 44, pages 270 –
276 
 
Lumley T. `Survey: analysis of complex survey samples`. R package 2012, version 3.28-2. 
 
Lumley T. `Analysis of complex survey samples`. Journal of Statistical Software (2004): volume 
9, issue 1, pages 1-19 
 
Souverein O, Dekkers A, Geelen A and others. Comparing four methods to estimate usual 
intake distributions. European Journal of Clinical Nutrition 2011: Volume 65, Supplement 1), 
pages S92–S101.