If I may, I'd like to confuse Stu's response on the way toward a cleaner answer (well, try for cleaner, anyway).
for Chi sq, look in the equation and you will see the numerator is the square of the difference of observed and expected. So any deviation from expected will increase the total chi-sq. thus, as Stu said, the Chi sq is only a 1 side test. Either the observed is close to the expected, or it is not. Ho: will always be as you phrased it Ha: will always be as you phrased it. for Chi sq test. for a Student 't' test, we should think about the consequences a little, IMHO. A measurement may be near the 'expected' (aka standard, required, whatever) value. It may be much less than the expected, or much more. the t test assumes normally distributed data, which implies that a single measurement can take on any value from - infinity to + infinity. but let's not go into the exceptions just now, OK? When I write the Ho and Ha, I am going to assume a condition, and then try my best to prove that the assumption is false. Specifically, I will assume (Ho) that the observed data is close tot he expected, and then see if it really is different. I will not conclude: the observed equals the expected. I can never do this with a t test. I can only conclude: reject Ho - the data is not close to expected, or 'I cannot detect a difference between observed and expected.' So when you set up hypotheses, as one of my students put it, 'you make the alternate hypothesis what you really want to have.' I put it as: set the null H to be 'everything is copasetic (sp) - calm and natural.' (usually this is at least Ho obs = expected.) then ask, if observed is much less than expected, will I take action (get upset, change settings on the machine, scream at sales people, whatever)? If observed is much less than expected, will I take action? Write the alternate hypothesis to cover those cases where I will take action - case I care about. all cases where I don't 'care' - will take no action - go to the Ho: All cases where I really care - will take action - go to the Ha. Assure that the Ho & Ha take care of all possible outcomes. Then go for it. Proceed. I find that many intro stat books try to 'simplify' the situation by doing mostly 1 side tests. they also do not think through the case in question, so there is little guidance for selecting a one side or two side test, much less which side. In most cases the experimenter really needs to know if the obs is less OR more than the expected. this would be a 2 side test. For example: Sales representative claims the new paint is harder than the present paint. Here's a gallon to try out. Plant manager has a 10,000 gallon tank of production paint. Plant manager will try new paint (not in the big tank!), but will only consider changing paint if the new is definitely better than the present. If it is equal or worse than the present paint, forget the whole thing. This is a one side test. Ho: obs = or < present, Ha: obs > expected. but sales rep. needs to know how well the new paint stands up against the present paint. If it is better, the rep may make a sale. If it is worse, the news needs to get back to the paint designer, to see what happened and fix it. this is a 2 side test. Ho: obs = expected Ha: obs not = expected. so if you decide what will happen if obs is less, equal, or greater than expected, you can decide what sort of Hyp. to write. and it may change, depending on who pays for the test. Data costs money, you know. In example above, do you suppose sales rep decides? This help any? Jay janne wrote: > Lets say I do a x2(chi) test and have the hypothesis: > > Ho: there are no differences in opinion between techers and students > Ha: there are differences in opinion between techers and students > > Can it only then be: > > If X2 obs(observation) is > 2.32(for example) then Ho is rejected. So > if X2 obs is 3.20 Ho is rejected. > > Or can it in some cases be: > > If X2 obs is < 2.32 then Ho is rejected. So if X2 obs is 1.20 Ho is > rejected. > > If you can have < in hypothesis, then when is it < and when is it > I > should use? How do I know which one to use? > > I also wonder about t-tests the same question. When do I know if I > should use < or >? > > Janne > > ================================================================= > Instructions for joining and leaving this list, remarks about the > problem of INAPPROPRIATE MESSAGES, and archives are available at > http://jse.stat.ncsu.edu/ > ================================================================= -- Jay Warner Principal Scientist Warner Consulting, Inc. 4444 North Green Bay Road Racine, WI 53404-1216 USA Ph: (262) 634-9100 FAX: (262) 681-1133 email: [EMAIL PROTECTED] web: http://www.a2q.com The A2Q Method (tm) -- What do you want to improve today? ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ =================================================================
