Taking something specific and applying it more broadly is making a generalization. It's a generalization to say all dogs chase squirrels.

A generalization is taking one or a few facts and making a broader, more universal statement. If all the girls you know play with dolls, you might make the generalization that all girls play with dolls. Scientists try to make generalizations based on research — the more data they have, the more accurate the generalization. Generalizations can be similar to stereotypes in that they are sometimes wrong and harmful. Usually, it's best to stick with specifics and avoid generalizations.

Definitions of generalization
  1. noun
    the process of formulating general concepts by abstracting common properties of instances
    synonyms: abstraction, generalisation
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    type of:
    theorisation, theorization
    the production or use of theories
  2. noun
    reasoning from detailed facts to general principles
    synonyms: generalisation, induction, inductive reasoning
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    type of:
    the connection of isolated facts by a general hypothesis
  3. noun
    (psychology) transfer of a response learned to one stimulus to a similar stimulus
    synonyms: generalisation, stimulus generalisation, stimulus generalization
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    (Pavolvian conditioning) the elicitation of a conditioned response by stimulation similar but not identical to the original stimulus
    type of:
    carry-over, transfer, transfer of training
    application of a skill learned in one situation to a different but similar situation
  4. noun
    an idea or conclusion having general application
    synonyms: generalisation, generality
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    principle, rule, tenet
    a basic generalization that is accepted as true and that can be used as a basis for reasoning or conduct
    a fundamental principle or practice
    the bright positive masculine principle in Chinese dualistic cosmology
    the dark negative feminine principle in Chinese dualistic cosmology
    feng shui
    rules in Chinese philosophy that govern spatial arrangement and orientation in relation to patterns of yin and yang and the flow of energy (qi); the favorable or unfavorable effects are taken into consideration in designing and siting buildings and graves and furniture
    type of:
    idea, thought
    the content of cognition; the main thing you are thinking about
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