Lecture 6 inferential statistics Research hypotheses Statistical hypotheses Acceptable risks ‘Real world model’ Decision rules Experiment report Inferential statistics • Research hypotheses general questions; for example: does ESP exist is early school entrance useful are we learning to be more tolerant of other cultures Inferential statistics • Statistical hypotheses ESP if a person guesses card colour 80% or more often H:p(s=1) = .8 random variable S – guess result, s = 1, correct guess; s=0, incorrect no ESP => H: p(s=1) = .5 Inferential statistics • Acceptable risks One of two types of errors might be committed: Type I error: is committed when a true hypothesis is rejected risk level Type II error: is committed when we fail to reject a false hypothesis acceptable risks are established by whoever commissions the study, denoted by and Inferential statistics • Real world model: let p(s=1) = x and s=0)=y then for a sample of size n we have that the binomial theorem (x + y)n describes the distribution of expected successes software to calculate expected probabilities can for example be found in: http://faculty.vassar.edu/lowry/VassarStats.html Inferential statistics • Decision rules: establish decision rules which satisfy the acceptable risk, probabilities for a Type I error ≤ and for a Type II error ≤ Inferential statistics Experiment report: 1. developing a hypothesis - hunch, idea - in very general terms 2. translating this into a statistical hypothesis and an alternate, one of which can be tested 3. examining the corresponding ‘world models’ one for the hypothesis to be tested, one for the alternate hypothesis if the tested one is rejected 4. establishing a sample size which satisfies the acceptable error risk levels 5. The experiment for this report has a number of components that you might consider: 6. conducting the experiment 7. reporting on your conclusions taking into account the population to which you can generalize. As discussed in class you should think of selecting a random variable which holds some interest to you. Please note that we might possibly need to 'mutilate' your variable to fit a Bernoulli type observation. In order for you to develop a population model you'll need two hypotheses, use p(+)=.5 against a probability which you will select. Next select a sample size which will ensure that your risk of committing a type I error is smaller than .075 and the risk of committing a type II error smaller than .125. State your decision rule as part of the proposed experiment. You can of course change the error risks and hypotheses. Finally conduct the experiment and report your results. When you try to find a satisfactory sample size aim for one which is close to the requested one, it doesn't need to be the absolute optimum one. Critically discuss your approach used, indicate the problems raised by it.