15 – Conclusions In Hypothesis Testing

When making a decision about whether you’re choosing the null or alternative hypothesis, you might see certain professionals, specifically statisticians, cringe, with concluding remarks like, “So based on the data, we accepted the null hypothesis to be true,” or, “Based on the data, we accepted the alternative.” Remember, when setting up our null and alternative hypotheses, we automatically set the null to be true before any data were collected. Therefore, this statement is a default. It isn’t like we’re uncertain about what hypothesis we’ll choose and then we choose one, rather, you are by default choosing the null. Going back to the judicial example, everyone is innocent until proven guilty. You don’t choose someone as innocent. By default, everyone is innocent. Therefore, in hypothesis testing, we say, “Based on the data, we have evidence to reject the null hypothesis,” or alternatively, if we don’t have enough evidence to reject the null, we say, “Based on the data, we fail to reject the null hypothesis.” Many people will only care about making the right decision. So this distinction might seem just a bit picky. But it stresses that the null is much more likely to be chosen as you start with the statement being true.

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