Hypothesis confusion

[pooja_tandon]

Consider the hypothesis structured as H(null)=$48 versus H(Alt) not equal $48. At 5% level of significance. where mean was $50 and Standard deviation was $5. No. of observations was 25.

Using the t stest the test statistic comes to 2 however the Alpha is taken as 0.05. Why isnt it taken as 0.0025 since this is a 2 tailed test.

Thanks & Regards

[S2000magician]

It’s 5% split between the two ends: 2.5% in the right tail and 2.5% in the left tail.

Alpha refers to the total amount, not just the amount in one tail.

[pooja_tandon]

Got that!

However, the t table value with df=24 and 0.025 level of significance should be used. Since it is a two tailed test. Isn’t it? Please correct me if I am going wrong.

[S2000magician]

You should use the column corresponding to 0.025 for a 1-tail test, 0.05 for a 2-tail test; the critical value is 2.064.

[Harrogath]

For 1-tailed test you should use the 0.05 column because in that tail you have the whole alpha.

For 2-tailed test you should use the 0.025 column because you have only one half of the alpha. It is like the confidence interval critical values.

[tickersu]

@Harrogath

For 1-tailed test you should use the 0.05 column because in that tail you have the whole alpha.

For 2-tailed test you should use the 0.025 column because you have only one half of the alpha. It is like the confidence interval critical values. It’s not that you have half of alpha, it’s because you need the two sides of the rejection region. You have 0.025 in each tail beyond the critical value (0.05 total). If they tell you 5% significance level then it is a 5% significance level, irrespective of whether or not you have a one or two-tailed test. You don’t just cut the significance level in half since you’re conducting a one-tailed test.

[Harrogath]

@tickersu

@Harrogath

For 1-tailed test you should use the 0.05 column because in that tail you have the whole alpha.

For 2-tailed test you should use the 0.025 column because you have only one half of the alpha. It is like the confidence interval critical values. It’s not that you have half of alpha, it’s because you need the two sides of the rejection region. You have 0.025 in each tail beyond the critical value (0.05 total). If they tell you 5% significance level then it is a 5% significance level, irrespective of whether or not you have a one or two-tailed test. You don’t just cut the significance level in half since you’re conducting a one-tailed test.

Yes, indeed we have 5% significance level, but it is distributed 50% the lower tail and 50% the higher tail. At the end of the statistic calculation you will only use 1 tail (the lower or the upper), not both. So, the critical value will be higher and use the 0.025 column or the 0.975 columun, which in both cases the critical value is higher than when we use 1-tailed tests. Remember that we discussed what critical value to choose at each 1 or 2 -tailed cases.

[tickersu]

@Harrogath

@tickersu

@Harrogath

For 1-tailed test you should use the 0.05 column because in that tail you have the whole alpha.

For 2-tailed test you should use the 0.025 column because you have only one half of the alpha. It is like the confidence interval critical values. It’s not that you have half of alpha, it’s because you need the two sides of the rejection region. You have 0.025 in each tail beyond the critical value (0.05 total). If they tell you 5% significance level then it is a 5% significance level, irrespective of whether or not you have a one or two-tailed test. You don’t just cut the significance level in half since you’re conducting a one-tailed test.

Yes, indeed we have 5% significance level, but it is distributed 50% the lower tail and 50% the higher tail. At the end of the statistic calculation you will only use 1 tail (the lower or the upper), not both. If you’re conducting a two-tailed test, you are using both critical values to form a rejection region, not just one. If you’re conducting a one-tailed test, you will only use one critcial value to conduct the test.

My reply was that alpha is distributed differently in the case of a one-tailed vs. a two-tailed test, whereas you wrote that you “have only one half of the alpha” in a two-tailed test (which isn’t true). But, based on your reply, I’m guessing we were saying the same thing, but your initial wording was unclear to me.

[Harrogath]

Yes, we use both critical values in a 2-tailed test, but how I said, at the end of the t-calculation you will use only one value of them (+) or (-). You can realize what will you use just watching your mean and the Ho value. What is higher of both will tell you what sign will have your T-test. This is why, in my opinion, to save some time, we can look straight to the critical value we need (the + or - ).

I know saying “one half of the alpha” was not clear at all, but if we talk in the two-tailed test scenario the fact is kind of obvious right?, at least when you need to choose the correct critical value. You will have alpha / 2 in both sides (and many books state this, so not much problem! ) and you need to look at the 0.025 or the 0.975 column for T-table of course.

[tickersu]

@Harrogath

I know saying “one half of the alpha” was not clear at all, but if we talk in the two-tailed test scenario the fact is kind of obvious right? For people familiar with statistics, you are probably correct. However, my concern is that most people aren’t familiar with statistics, and these things are not “obvious”. This seems like a very good reason to be extremely clear and accurate when giving someone an answer.

You will have alpha / 2 in both sides (and many books state this, so not much problem! ) Right, but they tend to be clear in their explanations. You didn’t state that you will have half of alpha in each tail. You said you will only have half of alpha.

[Harrogath]

Yep, I am totally agree with you, we need to be the most clear possible. I just hope people look at books before coming here because sometimes I am afraid to write so much that is better to go back to the book instead of read my comment lol.

Regards