Because the thresholds are conventionalised, we need to recognise the apparent arbitrariness of the conventions and not make such black and white interpretations.

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The p value is the probability of the experiment having given the result it did purely by chance. 
The threshold of significance is almost always 0.05 so that if the probability of a chance outcome is less than 1 in 20, the experimental result is declared to be significant. There are other important thresholds as summarised in the following table

p value

Don't make such black and white interpretations

Always report effect sizes where possible. Effect sizes are measures of importance because they indicate how much effect the experimental manipulation had on the differences seen in the data. 

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