What an easy way to remember alternative and null hypothesis?

U dont have to answer this part, but if u could...when do you reject the null and how do u tell if something is one or two tailed and if its significant??|||Let's take an example of a research study. Let's say that you believe that a high fat diet leads to weight gain. You construct a study whereby participants are fed either a high fat or a low fat diet for a given period of time.





You need to start with the null hypothesis. Your null hypothesis is that fat has nothing to do with weight gain (essentially). Remember "null" as "no" (they sound similar). Your null hypothesis says there is NO difference (e.g., there will be no significant difference in weight gain among participants fed a high fat diet and those fed a low fat diet).





The "alternative" is the ALTERNATIVE to no difference (i.e., there IS a difference). The alternative hypothesis is what you EXPECT is going to happen (e.g., people fed a high fat diet will report higher weight gains than those given a low fat diet).





You REJECT THE NULL if your p%26lt; .01 (or .05 or wherever you set your alpha). The "p" tells you HOW LIKELY IT IS THAT YOU ARE CORRECT. In the case of the null hypothesis, "correct" means that there is no difference between the group. If there is a low liklihood that you are correct (e.g., that there is no difference between the groups), then you REJECT the null (means that there IS a difference).





To remember what "one tailed" means, think of it this way: one tailed means you have ONE SHOT at being right. You've made a prediction that goes only one direction (e.g., those fed a high fat diet will gain MORE weight than those who are fed a low fat diet).





A two tailed test means you have TWO shots at being right. You are saying that there will be a difference between your two groups, but you're not committing to the direction of that difference (e.g., there will be A DIFFERENCE - not saying which way - in weight gain between those fed low and high fat diets).





Hope that helps :)





~M~





Here's the short summary:


Null = no = no difference


Alternative = different = there IS a difference


1 tailed = 1 shot at being right (you state the direction of the difference)


2 tailed = 2 shots at being right (you state there will be a differernce, but do not state the direction of that difference)|||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 渭 = d vs the alternate hypothesis 渭 鈮?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 渭 鈮?100,000 vs the alternate 渭 %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 渭 鈮?100,000 vs. the alternate 渭 %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.














Let 伪 be the significance level of the test





consider the following table





_ _ _ _ _ _ Reject H0 _ _ _ _ Fail to Reject H0


H0 is true _ Type I error _ _ _ _ _ 鈽?_ _ _


H0 is false _ _ _ 鈽?_ _ _ _ _ _ Type II error _








So, a type I error is rejecting H0 when H0 is true, like sending an innocent person to prison


a type II error is letting a guilty person go free after the trial.





P(Type I Error) 鈮?伪





P(Type II Error) = 尾





We generally don't work with Type II errors and instead talk about Power





Power = 1 - P(Type II Error) = 1 - 尾





in developing tests we try to maximize the Power and minimize 伪.