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I am currently during my final year of schooling. I am curious to know (and I want to put this in my Math assignment), what is better 1-tailed Hypothesis Testing, where you see if a claim is justifiable, or is it a confidence interval, we only deal with 95% ones.

I personally am torn between the two and sometimes can't even tell the difference.

Confidence intervals use sample data and create an interval on that and then you see how different the claim is based on the sample. But you get a range of values so you can test more claims more easily.

With Hypothesis testing, you are pretty much doing the same, seeing how unusual a claim is based on the sample using a Z-Test.

The context of my assignment is the 2013 election in Australia. We are testing out claims made by political parties against the data collected by polls.

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  • $\begingroup$ Check out stats.stackexchange.com/tags/self-study/info for guidelines here. Here are two hints: there is no absolute reason for a confidence interval to be a 95% interval; there are many hypothesis tests other than z-tests. $\endgroup$ – Nick Cox Sep 10 '13 at 11:19
  • $\begingroup$ ^ yes but what we look at in our course, we look at the z-test and judge the value found against 1.96 . My question is an extension of the course and I want to include it in. $\endgroup$ – Jineel Sep 10 '13 at 11:38
  • $\begingroup$ I do know that confidence intervals can be of any confidence not just 95%.. and you can do the same with hypothesis testing depending on your rejection area $\endgroup$ – Jineel Sep 10 '13 at 11:39
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There is a huge emphasis on hypothesis testing and the use of p values to dichotomize significant or non-significant findings throughout current literature. This, in turn, has detracted from more useful approaches to interpreting study results, such as estimation and confidence intervals (CI). In medical studies, investigators are usually interested in determining the size of difference of a measured outcome between groups, rather than a simple indication of whether or not it is statistically significant. Confidence intervals present a range of values, on the basis of the sample data, in which the population value for such a difference may lie.

Additionally, p values do not provide us with directionality of our results. For example, if we have a relative risk 90% CI of 1.4 to 1.9 in regards to development of lung cancer among patients that smoke, we can infer that the p value result is significant as 1 is not included within the confidence interval. In addition, we can state that patients that smoke are anywhere between 40 and 90% more likely to develop lung cancer in comparison to non-smoking patients.

On the other hand, if we have a relative risk 90% CI of 0.7 and 1.1 in regards to heart attacks among patients that eat chicken, we can infer that the p value result is NOT significant as 1 is included within the confidence interval. Additionally, we can state that we do not have evidence to conclude that patients that eat chicken are any more likely to have a heart attack than their non-chicken eating counterparts.

In other words, confidence intervals provide us with significance in the same way that p values do along with the added benefits of magnitude and direction! As such, confidence intervals > p values!

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  • $\begingroup$ Not sure about your formulation of meaning of CI (ie frequentist). Surely all you can say is that, on repeated sampling, 95% (or whatever) of the CIs will contain the relevant statistic - you can posit nothing about whether the statistic is within the CI of any one sample? (Unlike the Bayesians with their credible interval.) $\endgroup$ – DavidP Sep 10 '13 at 16:44
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    $\begingroup$ @DavidP: You mean "parameter", not "statistic". $\endgroup$ – Scortchi Sep 10 '13 at 20:28

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