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Question: Are p-values determined from t-tests?

What is the relationship between a p-value and a t-value? It states in this article here, the instructions to finding a t-value:

How to Calculate T:

  1. Calculate the mean (X) of each sample
  2. Find the absolute value of the difference between the means
  3. Calculate the standard deviation for each sample
  4. Square the standard deviation for each sample
  5. Divide each squared standard deviations by the sample size of that group.
  6. Add these two values
  7. Take the square root of the number to find the "standard error of the difference.
  8. Divide the difference in the means (step 2) by the standard error of the difference (step 7). The answer is your "calculated T-value."
  9. Determine the degrees of freedom (df) for the test. In the t-test, the degrees of freedom is the sum of the sample sizes of both groups minus 2.
  10. Determine the “Critical T-value” in a table by triangulating your DF and the “p value” of 0.05.

Is the article trying to say that the p-value is used to determine a t value? I'm confused here.

Jonathan Smith
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2 Answers2

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Please do not refer to the link you provide (https://www.biologyforlife.com/t-test.html).

It states: "A p-value s the probability of concluding there is a significant difference between the groups result when the null hypothesis is true (meaning, the probability of making the WRONG conclusion). In biology, we use a standard “p-value” of 0.05."

IT IS WRONG!

Instead, this is the definition of the type-I error rate, or significance level.

By the way, this confusion is one of the reasons why we should no longer use p-values!

ocram
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  • I agree that the definition used for $p$-value is wrong in that article. I agree that there are many problems with $p$-values. However, the alternatives aren't much better. Inference is jus a really really really hard (read impossible) problem, so whatever "solution" you choose it will strictly speaking be wrong. The question than becomes how to deal with that. The advantage of the $p$-value is that it is widely used, making it easier to build on previous research. The challenge for us is than to teach the correct interpretation. – Maarten Buis Jan 04 '18 at 09:22
  • @Maarten Buis: I do not totally agree. The p-value is in many cases counter-intuitive for non-statisticians. Instead of the p-value, they want the probability to have an effect given the data; which makes a lot of sense. They want it so much that the interpret the p-value as that probability. Therefore, I do not think that our challenge is to teach the correct interpretation. Our challenge, instead, is to get rid of the p-value and to provide the probability they expect. But let us not open that debate here... – ocram Jan 04 '18 at 15:43
  • For those who are not familiar with this debate: the key words to look for if you want to know more are "Bayesian" (@ocram) and "frequentist" (me). – Maarten Buis Jan 04 '18 at 15:47
  • @MaartenBuis: indeed ;-) – ocram Jan 04 '18 at 15:49
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No, you calculated the $t$-value from the data. Step 10 says that you look up the critical $t$-value in a table (e.g. this one). To do so you need to decide a priori a significance level. Typical values for that are 5% or 1%. You compare the $t$-value you computed in your data with the critical $t$-value you looked up in the table to see if the $t$-value is larger than or smaller than the critical $t$-value. If the $t$-value is larger than the critical $t$-value, then you reject the null-hypothesis at your chosen level of significance. Notice that no $p$-value was computed this way.

Maarten Buis
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