#set document(title: "11.9 Misconceptions", author: "OpenStax")
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== 11.9#h(0.6em)Misconceptions


    #notebox("Note", rgb("#8a94a6"), rgb("#556666"), rgb("#f7f8fa"))[
#emph[Prerequisites]


      Introduction
                to Hypothesis Testing, Statistical
                Significance, Type I and II Errors #linebreak()  #linebreak()
]


    #notebox("Note", rgb("#8a94a6"), rgb("#556666"), rgb("#f7f8fa"))[
#emph[Learning Objectives]


      + State why the probability value is not the probability the null hypothesis
        is false
+ Explain why a low probability value does not necessarily mean there
        is a large effect
+ Explain why a non-significant outcome does not mean the null hypothesis
        is probably true
]


    Misconceptions about significance testing are
               common. This section lists three important ones. #linebreak()


    + Misconception: The probability value is the probability that
                 the null hypothesis is false.  #linebreak() 
                  #linebreak() 
                 Proper interpretation: The probability value is the probability
                 of a result as extreme or more extreme given that the null hypothesis
                 is true.
It is the probability of the data given the null hypothesis. It is not the probability
                that the null hypothesis is false. #linebreak() 
                 #linebreak()
+ Misconception: A low probability
                 value indicates a large effect. #linebreak() 
                  #linebreak() 
                 Proper interpretation: A low probability value indicates that
                 the sample outcome (or one more extreme) would be very unlikely
                 if the null hypothesis were true. A low probability value can
                 occur with small effect sizes, particularly if the sample size
                 is large. #linebreak() 
                  #linebreak()
+ Misconception: A
                 non-significant outcome means that the null hypothesis is probably
                 true. #linebreak() 
                  #linebreak() 
                 Proper interpretation:
A non-significant outcome means that the data do not conclusively demonstrate
                 that the null hypothesis is false.