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So, I have some survey data which asks different groups of consumers how favorable they view certain products (e.g., food products, clothes products, and beauty products). I want to compare the number of "very favorable" answers across product groups. For this, I plan to collapse individual products to retain these 3 main categories and then compare mean number of "very favorable" answers between product categories. Does this suffice as continuous data for a one-way ANOVA?

I know measuring strictly the number of "very favorable" answers without taking into consideration other answers sounds useless, but it is useful for the research I am doing.

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Counts are not continuous, but ANOVA does not require continuous data, it can still work reasonably well on discrete interval data and counts are interval (even ratio) data. The bigger issue is the equality of variances and the independence of mean and variance which counts which violate the assumptions of ANOVA. Unless your numbers are large enough that a normal approximation is reasonable.

It may be much better to model this using a Poisson regression or contingency table tools which better account for the mean variance relationship in count data.

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