FAQ: Hypothesis Testing with R - Type I and Type II Errors

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This community-built FAQ covers the “Type I and Type II Errors” exercise from the lesson “Hypothesis Testing with R”.

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[rebecca5294488996]

I don’t understand how this exercise demonstrates type i and type ii errors.

Which set of data is the hypothesis and which is the actual data? To me, the actual data would be the data you collect in the experiment. Which of these is the “null hypothesis”?

Can someone clear this up for me?

Thank you!

[eves92]

I would also like some clarity. Thanks for asking this question.

[lisalisaj]

In hypothesis testing the goal is to either accept or reject the null hypothesis (find it true or false). Sometimes DA’s or DS’s will incorrectly accept or reject the null. This is what is called a Type I error (false positive, when you incorrectly reject a null that was actually true), or, Type II error (false negative, when you incorrectly accept a false null).
So, if your confidence interval is 95%, you have a 5% probability of a false positive result.

This might help:
https://medium.com/analytics-vidhya/hypothesis-testing-type-1-and-type-2-errors-bf42b91f2972

Or, this:
https://math.stackexchange.com/questions/3691376/minimizing-type-i-and-type-ii-errors-simultaneously

And, my favorite explanations of hypothesis testing and stats from Mr. Nystrom:
Mr. Nystrom, stats teacher

[data7322309539]

This exercise is pretty poorly made in my opinion but hopefully, I can help clear it up a bit.

In the hypothetical experiment the exercise has you work with (NOT the volleyball experiment) there are 49 individuals that may be positive or negative for some trait. Each individual is assigned a number.
Thus, the vector actual_positives
c(2, 5, 6, 7, 8, 10, 18, 21, 24, 25, 29, 30, 32, 33, 38, 39, 42, 44, 45, 47) contains all the individuals that are positive for the trait, and the vector acutal_negatives
c(1, 3, 4, 9, 11, 12, 13, 14, 15, 16, 17, 19, 20, 22, 23, 26, 27, 28, 31, 34, 35, 36, 37, 40, 41, 43, 46, 48, 49) contains all individuals that are negative for the trait. As an example, individual #27 is not positive for the trait and is therefore listed in the second vector but not the first.

The hypothetical experiment tests all 49 individuals and gives us the experimental_positive/negative vectors as a result. The exercise asks us to find errors using the intersect() function. Recall that a type i error is finding a difference when in actuality there is none, so our “type I errors” here are instances where the experiment finds a positive when there should be a negative. We use the function intersect(actual_negatives,experimental_positives) to identify these false positives and vice versa for the false negatives or type II errors.

Now, you may be wondering what this has to do with null hypotheses, and the answer is nothing! This exercise has nothing to do with comparisons of mean or other statistical aggregates that we use when testing hypotheses. Furthermore, while it may be (and I’m not even sure about this) technically true that misidentifying a single negative in your sample as a positive counts as a type I error, that kind of language is usually reserved for talking about hypotheses and data analysis.

I really hope the creators of this lesson tweak this exercise, as I think it does more to confuse than educate users on the material.