Type 1 and type 2 errors?

In summary, the conversation is discussing a test of anti-spam software and the number of false positives and false negatives. The question is how many more messages would need to be tested to be 99.99% certain that the null hypothesis can/cannot be rejected. The null hypothesis is that a spam message will be correctly marked as spam. The remaining 20 messages are either true positives or true negatives. The conversation also mentions a confusion matrix for the test results.
  • #1
moonman239
282
0
Let's say I'm testing anti-spam software. The number of false positives (aka, friendly messages misidentified as spam, for those who don't know the term) is 40. The number of false negatives (spam messages misidentified as friendly) is also 40. I'm testing 100 messages. How many more messages would I need to test in order to be 99.99% that the null hypothesis can/cannot be rejected?
 
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  • #3
Thanks for the link, but I'm not seeing any equation whatsoever that will help. As far as I can see, all the listed equations have to do with means.
 
  • #4
Oh, so what's your null hypothesis? I thought you were to test that the average message is not spam.
 
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  • #5
I just don't see how a sample mean would be relevant. Your understanding of the question is correct.
 
  • #6
Be very specific, please: What is your null hypothesis?

Also, you have told us about 80 messages, what about the other 20?
 
  • #7
D H said:
Be very specific, please: What is your null hypothesis?

Also, you have told us about 80 messages, what about the other 20?

Let's say my null hypothesis is that a spam message will be correctly marked as spam. As for the 20 messages, let's say that those are false negatives.
 
  • #8
You already said you had 40 false positives and 40 false negatives out of 100 tests. That makes for a total of 80 out of 100. Those remaining 20 are either true positives or true negatives.

What does the confusion matrix for your test results look like?
 

1. What is the difference between type 1 and type 2 errors?

Type 1 and type 2 errors refer to the two types of mistakes that can occur in statistical hypothesis testing. A type 1 error, also known as a false positive, is when the null hypothesis is rejected when it is actually true. On the other hand, a type 2 error, also known as a false negative, is when the null hypothesis is accepted when it is actually false.

2. How are type 1 and type 2 errors related to the significance level?

The significance level, often denoted as alpha (α), is the probability of making a type 1 error. In other words, it represents the acceptable level of risk for rejecting the null hypothesis when it is actually true. A lower significance level means a lower chance of making a type 1 error, but it also increases the likelihood of making a type 2 error.

3. Can type 1 and type 2 errors both occur in a single hypothesis test?

Yes, both type 1 and type 2 errors can occur in a single hypothesis test. This is because the outcome of a hypothesis test is based on probability and is not guaranteed to be correct. The probability of making a type 1 error can be reduced by increasing the sample size or lowering the significance level, but it can never be completely eliminated.

4. How can we minimize the chance of making type 1 and type 2 errors?

To minimize the chance of making type 1 and type 2 errors, it is important to carefully design experiments and choose appropriate sample sizes and significance levels. It is also crucial to use reliable and accurate measurement tools and to conduct multiple tests to confirm results. Additionally, having a thorough understanding of the research question and the data being analyzed can help minimize errors.

5. Are type 1 and type 2 errors equally important?

The importance of type 1 and type 2 errors depends on the specific context and consequences of each type of error. In some cases, a type 1 error may have more serious consequences (e.g. falsely accusing someone of a crime), while in other cases a type 2 error may be more significant (e.g. failing to detect a harmful substance in a product). It is important to consider the potential impact of each type of error when conducting hypothesis tests.

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