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Lecture 06.docx

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University of Toronto Scarborough
Douglas Bors

th Lecture 06: June 13 , 2012 For the assignment, if you have not handed it in change: Mean = 20 and Standard deviation = 10 Introduction to Testing a Hypothesis now we are dealing with a group of scores rather than an individual score Testing a treatment want to make a Descriptive statistics cannot determine if differences are statement about the A sampling error occurs when apparent differences are by chgroup of scores and whether they come from a particular population or not, rather than a individual score juExample of Differences due to chance alone.ut the principles are still going to be the same: what do I expect? what do I observe 1 =how do I know 2ow much fluctuation/variance there is going to be due to chance alone in what I expect? =1Is there too big a difference between the expected and the observed in relation to the 1 expected spread for me to have 95 confidence that I cant reject whats going to be the known So now were going to deal with a group of observations, For example we are going to test a treatment, descriptive statistics cant answer inferential questions. Sampling error occurs when we have these apparent differences but they are due to chance alone. So the mean of the population 15 and I find that my score is 17, am I a member of that population or not? Is that difference just due to chance alone? Exampleofdifferencesduetochancealone: Example1: and has a population mean of 100 , lets say its IQ, we know Does that sample, mean that it comes from an observation mean of a 100? Is that difference to big to be due to chance alone? You cant know that because you only have the expected value, 100 and the observed value, 107, but you dont know the distribution to find out the 95% confidence limits to make a decision Or what about example two: Example1: and Is 100 different from 117? Whats the expected value if there is not difference? 100? What is the expected value if there is no difference? If there is no difference then the difference should be 0, but the difference we see is 10. So we know what the expected value should be in this case, its 0 between the two groups. But we see 10. Now we need to find what sort of distribution we would have in deference between means just due to chance alone. So we can set up our 95% confidence limits. How do we figure out whats to be expected, what do we observe? Look at the difference we need to find a way to map that difference onto the expected on some distribution due to chance alone.And so we can either say I suspect that this is due to chance alone or now the probability is less than 0.05 so I have evidence that it may be other than chance alone THIS IS ALL WE ARE DOING, OVER AND OVER AGAIN! This slide recaptures what we have just been talking about: Examples:es: We know that the mean IQ of the population is 100. We selected 50 people and gavegave them our new IQ boosting program. This sample, when tested after the treatment,ent, has a mean of 110. Did we boost IQ? IQ? We selected a sample of college students and a sample of university students. We found thatthat the mean of the college students was 109 and the mean of the university students was 113. Was Was there a difference in the IQs of college and university students? there a difference in the IQs of college and university students? Are both cases simply due to sampling error?ror? Remember, the sample mean is rarely the population mean and rarely do the means Remember, the sample mean is rarely the population mean and rarely do the means of two randomly selected samples end up being exactly the same We need a sampling distribution. Sampling distribution: describes the amount of sample-to-sample variability to expect Sampling distribution: describes the amount of sample-to-sample variability to expe
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