Visual perceptions of portion size normality and intended food consumption: A norm range model

Highlights • Smaller portion sizes are associated with lower energy intake.• We test a norm range model of the portion size effect on intended intake.• A wide range of portion sizes were perceived as normal.• Portions perceived as normal did not prompt intended compensatory eating.• Portions perceived as smaller than normal prompted intended compensation.


Portion size stimuli
To select the five foods used in Study 1, participants completed an online study in which they answered questions about commonly eaten and commercially available food types. Foods containing a small number of discrete units per portion (e.g., biscuits, chocolate bars) were not included in order to prevent unit size or number from influencing normality judgments. A pilot sample of 22 participants (11 males, 11 females) aged between 20 and 60 years (M = 30.33, SD = 10.95) rated on 7-point Likert scales how regularly they consumed each of the candidate foods (from 1 = daily, to 7 = yearly or less frequently), their liking of the food, familiarity, and appropriateness of consumption for breakfast, lunch, dinner, dessert, and a snack. We selected foods which were generally well liked and regularly consumed by participants in the pilot study (Table S1).

Criteria for identifying the 'norm range'
For each food, the lower boundary of the norm range was identified as the smallest portion size judged as 'normal' by a clear majority of participants, and the upper boundary as the largest portion size judged as 'normal' by a clear majority of participants. We operationalised a clear majority as being ≥60% of participants. We initially planned to use a criteria of 50% of participants judging a portion size as 'normal' to identify the norm range in Study 1 (based on Tovée, Edmonds, & Vuong, 2012). However, for a number of foods there were portion sizes which clustered around 50%, suggesting a lack of consensus. We therefore increased the norm range criteria to 60% of participants judging a portion size as 'normal', in order to identify a range of portion sizes that was clearly considered normal by a majority of participants, and to differentiate from chance expectation (50%). This criteria was determined before hypothesis testing in Study 1 and was then used in the a priori selection of norm ranges in Study 2.

Calculation of differences in intended consumption
We calculated differences in intended consumption between pairs of portions that differed in size by 20% of the reference portion to allow a 'gap' between paired portion sizes. As participants reported intended consumption of portions sizes differing by 10% size increments, the 20% difference scores meant that each cross-boundary comparison would be expected to more reliably encompass a portion that was perceived by most participants as 'normal' and one that was 'not normal'. For example, if the 80% portion is considered the start of the norm range, a 20% difference score of 60% -80% provides more certainty that the comparison represents a cross-boundary comparison for the majority of participants (i.e., includes a 'smaller than normal' versus 'normal' comparison) than does a 10% difference score of 70 -80%.

Individual differences measures
Participants completed a standard battery of questionnaires that we routinely collect in laboratory studies to provide data for future exploratory analyses. See below. We did not intend to use these measures for analytical purposes in the planned analyses for Studies 1 and 2, and do not discuss these variables further in the present work.

Income and education
Participants were asked to indicate their highest level of education (did not complete high school, high school, some university, Bachelor's degree, Master's degree, Doctoral or professional degree), and to enter their total annual household income (free text entry).

Pilot check questions
Participants were asked to report how regularly they consume (Likert scale ranging

Dieting status
A single item was administered to assess whether participants were currently dieting (yes/no).

Plate clearing tendency
A 5-item measure with a 5-point Likert response format (1 [strongly disagree], to 5 [strongly agree]) was used to assess participants' tendencies to clear their plate when eating (e.g., " I always clear my plate when eating"; Robinson et al., 2015). The scale has been demonstrated to have good internal reliability (Robinson et al., 2015).

Self-control
The brief self-control scale was used to assess trait self-control (De Ridder et al., 2011).

Attitudes against food waste
Participants completed a 5 item measure with a 7-point Likert response format (1 [strongly disagree], to 7 [strongly agree]) assessing attitudes against wasting food (e.g., "Even if I felt full, I would rather finish what is on my plate than see it go to waste". Figure S1 displays the percentage of the sample judging each portion size as 'normal' across food types.  Figure S1. Percentage of participants in Study 1 judging each portion as 'normal' for 5 foods.

Study 2 analytic sample
One participant in Study 2 was missing intention data due to a technical fault, leaving an analytic sample size of 45 for the replication of Study 1 findings using collective norm ranges. The analytic sample size for the individual norm range analyses ranged from 29 to 37: four participants had missing reaction time data because they did not provide any correct relative size judgments within the time constraints for one or more portion size comparisons, and the remaining missing cases were excluded because participant 'norm ranges' included the minimum (40%) or maximum (300%) portion size stimulus, which meant that the participant was missing portion judgments that were categorised as 'below' or 'above' normal.

Replication of Study 1 findings in Study 2 using collective norm ranges
To determine the collective norm range (i.e., the range of portion sizes considered 'normal' by a majority of the sample) for Study 2, the lower boundary of the norm range for each food was marked by the smallest portion size falling within the norm range for at least 60% of participants, and the upper boundary as the largest portion size falling within the norm range for at least 60% of participants. In Study 2, the norm range for pasta was 90-140% (compared pairwise comparisons showed that intended consumption was significantly higher for portions that were 'smaller than normal' than for those considered 'normal', pasta: MD = 1.40, SE = 0.07, p <.001, curry: MD = 1.71, SE = 0.07, p <.001, and significantly higher for portions that were considered 'normal' than for those that were considered 'larger than normal', pasta: MD = 1.67, SE = 0.07, p < .001, curry: MD = 1.71, SE = 0.08, p <.001. Boundary category based on the collective norm range predicted differences in intended consumption between pairs of portion sizes, F(2, 88) = 5.70, p =.01, ηρ 2 = .12.
Pairwise comparisons revealed the mean difference in intended consumption was larger between portion sizes that crossed the lower norm boundary than between portion size pairs that fell inside of the norm range, MD = 0.19, SE = 0.09, p = .047, which was not statistically significant against Bonferroni-adjusted α = .025. However, unlike in Study 1, and in the main analyses reported in Study 2, differences in intended consumption were significantly larger between portion sizes that crossed the upper norm boundary than those that fell within the norm range boundary, MD = 0.31, SE = 0.08, p <.001. Type of food did not predict differences in intended consumption between portion size pairs, F(1,44) = 0.41, p = .525, ηρ 2 = .01, and there was no significant interaction between food and boundary category, F(1.73, 76.26) = 1.19, p = .309, ηρ 2 = .03. Neither cubic nor quadratic components were significant in any analysis, suggesting that a combination of linear and quartic functions best describe the pattern of discrimination performance observed across the 5 categories.

Additional post-hoc analysis: effect of norm range on discrimination performance polynomial trend analysis
Weber's law holds that as the size of a physical stimulus increases or decreases, discrimination performance diminishes or improves (Kingdom & Prins, 2016). Therefore, differences between smaller portion sizes should be easier to discriminate than differences between larger portion sizes. Because comparison position in the relative size judgment task (across lower boundary, within norm range, across upper boundary) is confounded with portion size, effects on discrimination performance could also be attributable to Weber's law and not only categorical perception.
To account for this possibility, we conducted additional post-hoc analyses to examine discrimination performance in 5 comparison positions: (a) below the norm range, (b) across the lower boundary, (c) within the norm range, (d) across the upper boundary, and (e) above the norm range. We conducted separate 5 (comparison position) ✕ 2 (food type) repeated measures ANOVAs on relative size judgment RT and accuracy (adjusted alpha = .0125).
Categorical perception would be evidenced by better discrimination performance for crossboundary comparisons (b) and (d), than within-category comparisons (a), (c), and (e).
We also conducted trend analysis, which tests the overall pattern of the relationship between comparison position ([a] to [e]) and discrimination performance. For our 5-level independent variable (comparison category), it is possible for the pattern of discrimination performance across levels to be described by up to 4 different trend components: linear (a straight line, such that performance increases or decreases steadily from the smallest to the largest comparison category), quadratic (a line with 1 change in direction), cubic (a line with 2 changes in direction), or quartic (a line with 3 changes in direction). For each trend component, we examined the associated F test for the polynomial contrast representing that trend. A statistically significant F test indicated that the pattern of discrimination performance across comparison positions conformed to that trend. A schematic of the trend components that we expected to describe the relationship between discrimination performance and comparison position is shown in Figure S2. In line with Weber's law, we expected a significant linear trend, such that discrimination performance would diminish as portion size increased. In line with the prediction that portion size normality would be categorically perceived, we also expected a significant quartic trend. A quartic trend describes a 'double peaked' pattern, whereby there are 3 changes in direction in the line describing the pattern of performance across sequential levels. In this case, we expected to observe an upward trend or 'peak' in discrimination performance at comparison positions (b) and (d), corresponding to the boundaries of the norm range.

Post-hoc analysis results
In line with the primary results reported in the manuscript, there was a significant effect of norm range position on both relative size judgment accuracy, F(2.56, 66.58) = 38.26, p <.001, ηρ 2 = .60, and RT, F(1, 24) = 43.48, p <.001, ηρ 2 = 64, and a significant category ✕ food interaction for RT. Results of pairwise comparisons are displayed in Figures   S3 (accuracy, collapsed across foods) and S4 (RT plotted for curry and pasta seperately). The norm range boundaries significantly facilitated discrimination performance relative to withincategory performance in 'across lower boundary' vs. 'within norm range' comparisons (for both accuracy and RT in both foods), and 'across upper boundary' vs. 'above norm range' comparisons (marginally significant for accuracy, and only significant for curry RT). These results are in line with the prediction that portion size normality is perceived categorically, but are also consistent with Weber's law. However, inconsistent with both accounts, discrimination performance was not significantly different across the upper norm range boundary than 'within the norm range' (or 'above the norm range' for pasta RT). Consistent with Weber's law (but not categorical perception), relative size judgment accuracy was marginally significantly better for portions in the 'below norm' category than those crossing the lower norm range boundary.