In the question and answer bank Q4.20 while carrying out the test why do we take null hypothesis (Ho) as not associated and (H1) as being associated? Why can't we take it other way round? Please explain the rule in general.
Hi That is because you can define a proper distribution (here chi-square) under Ho provided you set Ho as 'no association'. Without a proper distribution defined you wont be able to carry out the test and make an appropriate conclusion.
Sorry Sir but i don't get it. Could you please explain me in more detailed and some simpler form? I don't know what you meant by defining a proper distribution. Please help.
Hi In order to do hypothesis testing, you need to set the test statistic in such a manner that it has a 'properly defined' or 'completely specified' distribution. Like here you have the test statistic follow a chi-square distribution only if you assume that the null hypothesis is of the form 'no association'. Let's see if you have assumed 'association' as null hypothesis, then your test statistic will not follow chi-square. In fact you don't even know what it follows ! If you don't know the underlying distribution how will you conclude if the test can accept the null hypothesis or not ! Am I making sense now? PS: I suggest you read Sec 1.4 of Chapter 12 in the ActEd notes. It is explained there.
Hi Sir, To be very frank I would like to tell that I had grasped much of the thing but how can we 'properly define' or 'completely specify' a distribution? Thanks a lot Sir for you such great help.
Prayas For your exam purposes you just need to know how you set up the null hypothesis so the test statistic under Ho follows a known statistical distribution like chi-square in this case. You are not expected to know any unknown test strategy that is not covered in syllabus. If you are interested to know the theoretical basis of how the problems of hypothesis testing are set up, I suggest you go back to your graduate text books on Mathematical Statistics (in case you have done a degree in Statistics). I would suggest you read up the following wiki links to start with: 1. Null Hypothesis 2. Pearson's chi-squared test and other links on these pages. If you need books, I would suggest Mathematical Statistics by Bickel and Doksum or similar other books.
Remember we use the null hypothesis in our statistic. If they're not associated then we can assume they occur simply in proportion to their frequencies. But if we take H0 to be not associated then they could have any connection...so what would we choose to calculate the expected frequencies?
