Let’s start from the end: I do not know how to make children eat more vegetables or even eat some vegetables. At least with my children, success is minimal. But two researchers from the University of Colorado had an idea: we would serve them the vegetables on plates with pictures of vegetables. To test whether the idea works, they conducted an experiment whose results were published in the prestigious journal JAMA Pediatrics . Because the results have been published you can guess that the result of the experiment was positive. But, did they really prove that their idea works?

**Design of the experiment and its results**

18 kindergarten and school classes (children aged 3–8) were selected in one of the suburbs of Denver. At first the children were offered fruits and vegetables when they were given white plates. In each class a bowl of fruits and a bowl of vegetables were placed, and each child took fruit and vegetables for himself or herself and ate them as he pleased. The weights of the vegetables and fruits were recorded before they were served to the children, and when the children had finished their meal, the researchers weighed the remaining fruits and vegetables. The difference between the weights (before and after the meal) was divided by the number of children, and thus the average amount of fruit and vegetables each child ate was obtained. Fruit and vegetables averages were also calculated separately. The researchers repeated these measurements three times per class.

After a while, the measurements were repeated the same way, but this time the children were given plates with pictures of vegetables and fruits. The result was an average increase of 13.82 grams in vegetables consumption, between 3 and 5 years of age. This result is statistically significant. In percentages it sounds much better: this is an increase of almost 47%.

So, what’s the problem? There are several problems.

**First problem — extra precision**

I will start with what is seemingly not a problem, but a warning: over-precision. When super precise results are published, you have to start worrying. I would like to emphasize: I mean precision, not accuracy. Accuracy refers to the distance between the measured value and the real, unobserved value, and is usually measured by standard deviation or confidence interval. The issue here is about precision: the results are reported at the level of two decimal places; they are very precise. I’m not saying it’s not important, but from my experience, when someone exaggerates, you have to look more thoroughly at what’s going on. Precision of two digits after decimal when it comes to grams seems excessive to me. You can of course think differently, but that’s the warning signal that made me read the article to the end and think about what was described in it.

**Second problem — on whom was the experiment conducted?**

The second problem is much more fundamental: the choice of the experimental unit, or unit of observation . **The experimental units here are the classrooms**. The observations were made at the class level. The researchers measured how many vegetables and fruits were eaten by all the children in the class. They did not measure how many vegetables and fruits each child ate. Although they calculated an average for a child, I suppose everyone knows that the average alone is a problematic measure: it ignores the variation between the children. Before experimental intervention, Each child ate an average of about 30 grams of vegetables at a meal, but I do not think there will be anyone who disagrees with the statement that each child ate a different amount of vegetables. What is the standard deviation? We do not know, and the researchers do not know, but this is essential, because the difference between the children affects the final conclusion. Because the researchers ignored (regardless of the reason) the variation between the children, they practically assumed that the variance was very low, in fact zero. Had the researchers consider this variation, the conclusions of the experiment would be different: the confidence intervals would be different, **and wider than the confidence intervals calculated by the researchers**.

Another type of variance that was not considered is the variation **within** children. Let me explain: Even if we watched one child and saw that on average he ate 30 grams of vegetables at every meal, at different meals he eats a different amount of vegetables. The same the question arises again: What is the standard deviation? This standard deviation also has an impact on the final conclusion of the experiment. Of course, each child has a different standard deviation, and this variability should also be taken into consideration.

A third type of variation that was not considered is the variation between children of different ages: it is reasonable to assume that an 8-year-old will react differently to a painted plate than a 3-year-old. An 8-year-old will probably eat more vegetables than a 3-year-old.

I think that the researchers did not pay attention to all these issues. The words variation, adjust or covariate do not appear in the article. Because the researchers ignored these sources of variation, the confidence intervals they calculate are too narrow to reflect the real differences between the children and the types of successes.

Finally, although the experimental unit was the class, the results were reported as measurements were made at the child’s level. In my opinion, this also shows that the researchers were not aware of the variation between and within the children. For them, class and child are one and the same.

**Third problem — what about the control?**

There is no control group in this experiment. At a first sight, there is no problem: according to the design of the experiment, each class constitutes its own control group. After all, the children received the vegetables in white plates as well as plates with paintings of vegetables and fruits. But I think that’s not enough.

There are lots of types of plates for children, with drawings by Bob the Builder, Disney characters, Adventure Bay, Thomas the engine, and the list goes on. Could it be that the change was due to the very fact of the paintings themselves, and not because they are paintings of vegetables and fruits? Maybe a child whose meal is served on a plate with pictures of his favorite superhero will eat even more vegetables? The experimental design does not answer this question. A control group is needed. In my opinion, two control groups are needed in this experiment. In one of them the children initially get white plates, and then plates of Thomas the engine, Disney or superheroes, depending on their age and preferences. In the second control group there will be children who will initially receive “ordinary” plates (i.e. Thomas, Disney, etc.) and then plates with paintings of vegetables and fruits.

**Fourth problem — subgroup analysis**

Although the age group of the children in the study was 3–8, the researchers discuss the results for children in ages 3–5. What happened to children at age 6–8? Was the analysis for the two (or more) age groups pre-defined? The researchers do not provide this information.

**Fifth Problem — What does all this mean?**

First, it was found that there was a statistically significant change in the consumption of vegetables, but no significant change was observed in the fruit. The researchers referred to this in a short sentence: a possible explanation, they said, is the ceiling effect . Formally they are right. ceiling effect is a statistical phenomenon, and that is what happened here. The really important question they did not answer: Why did this effect occur?

And the most important question: Is the significant change also meaningful? What does the difference of 14 grams (sorry, 13.82 grams) mean? The researchers did not address this question. I’ll give you some food for thought. I went to my local supermarket and weighted one cucumber and one tomato (yes, it’s a small sample, I know). The weight of the cucumber was 126 grams, and the weight of the tomato was 124 grams. In other words, each child ate on average an extra half a bite of a tomato or a cucumber. Is this amount of vegetables meaningful in terms of health and / or nutrition? The researchers did not address this question, nor did the editors of the journal.

**Summary**

It is possible that plates with vegetables and fruit paintings cause children to eat more vegetables and fruits. This is indeed an interesting hypothesis. The study that was described here does not answer this question. The manner in which it was planned and implemented does not allow even a partial answer to this question, apparently due to the lack of basic statistical thinking.