In statistics- What is the difference between the critical and observed value?

I am doing an unrelated t test for my psychology coursework and am confused as to what the difference is, is my result of the test the crit or obs value?

In statistics- What is the difference between the critical and observed value?
Critical value is the value that would have been obtained if chance alone contributed to the outcome at the chosen level of significance. Observed value is the value you obtain from the test statistic to be compared with the critical value.
Reply:the critical value is used in fixed level hypothesis testing. When you are, for example, using a z-test for the mean, at the 5% level, then the critical values are z = -1.96 and z = 1.96.





the observed value, the values found from the data, is translated into z-scores.





if the absolute value of the observed z-score is greater than 1.96, i.e., greater than the crical value, then you reject the null hypothesis.





Think of it this way. The critical value is the zscore(s) such that it the maximum distance from the mean you will accept for random error under the assumption the null hypothesis is true. If the observed value is further way from the null mean than the critical value then you have observed something very unlikely under the assumption that the null is true and you reject the null.








I personally find the fixed hypothesis testing levels to be difficult to teach to my students and even more pointless when witting a paper. I, and many others, prefer to use p-values and report them because the information is not as limited.





Consider the hypothesis as a trial against the null hypothesis. the data is evidence against the mean. you assume the mean is true and try to prove that it is not true. After finding the test statistic and p-value, if the p-value is less than or equal to the significance level of the test we reject the null and conclude the alternate hypothesis is true. If the p-value is greater than the significance level then we fail to reject the null hypothesis and conclude it is plausible. Note that we cannot conclude the null hypothesis is true, just that it is plausible.





If the question statement asks you to determine if there is a difference between the statistic and a value, then you have a two tail test, the null hypothesis, for example, would be μ = d vs the alternate hypothesis μ ≠ d





if the question ask to test for an inequality you make sure that your results will be worth while. for example. say you have a steel bar that will be used in a construction project. if the bar can support a load of 100,000 psi then you'll use the bar, if it cannot then you will not use the bar.





if the null was μ ≥ 100,000 vs the alternate μ %26lt; 100,000 then will will have a meaningless test. in this case if you reject the null hypothesis you will conclude that the alternate hypothesis is true and the mean load the bar can support is less than 100,000 psi and you will not be able to use the bar. However, if you fail to reject the null then you will conclude it is plausible the mean is greater than or equal to 100,000. You cannot ever conclude that the null is true. as a result you should not use the bar because you do not have proof that the mean strength is high enough.





if the null was μ ≤ 100,000 vs. the alternate μ %26gt; 100,000 and you reject the null then you conclude the alternate is true and the bar is strong enough; if you fail to reject it is plausible the bar is not strong enough, so you don't use it. in this case you have a meaningful result.





Any time you are defining the hypothesis test you need to consider whether or not the results will be meaningful.
Reply:critical value is the one you look up from the table


obs value is the value you want to test (test value). You want to see where obs values falls. If obs fails inside the reject region, you reject null





Here is some more info





http://www.psychstat.missouristate.edu/i...


http://www.ruf.rice.edu/~bioslabs/tools/...


http://davidmlane.com/hyperstat/glossary...