Like Driving a Car-Hypothesis Testing
Most introductory statistics courses are organized in a similar way to driving a car. Basic, component skills are taught first so that these skills can be applied to inferential statistics later in the course.
For example, consider hypothesis testing, a very common and very important application in statistics. There are many skills students must learn, and master, before we can even begin to talk about a hypothesis test. These skills include:
- Calculating descriptive statistics such as mean and standard deviation.
- Working with probability distributions, specifically the normal distribution.
- Calculating probabilities related to the normal distribution.
- Working with sampling distributions.
- Calculating probabilities associated with sampling distributions.
Once students have learned these skills, students must apply these skills in the context of a hypothesis test to calculate the p-value for the test. The p-value is basically a probability associated with a particular sampling distribution, which often requires the calculation of some descriptive statistics followed by the calculation of a probability using a normal distribution. The p-value is the evidence that is used to either reject or not reject the null hypothesis. The ability to calculate the p-value for the hypothesis test correctly is critical to the outcome of the hypothesis test: an incorrect p-value will lead to an incorrect conclusion for the hypothesis test.
Learning to calculate a p-value for a hypothesis test is akin to learning the different skills to drive a car, such as learning the rules of the road and learning to operate a vehicle. Calculating the p-value is the “middle” step in any hypothesis test but is the step that involves the most prior knowledge and skills. Once students have mastered the ability to calculate a p-value, this idea is applied within the context of a hypothesis test, similar to applying the knowledge of operating a vehicle and the rules of the road to actually driving on the road in traffic.
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