W3 Lecture Part I

# W3 Lecture Part I - Week Three Lecture Part I Introduction The previous lectures and learning discussed and applied two of the three test

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Week Three Lecture – Part I Introduction The previous lectures and learning discussed and applied two of the three test statistics. The z and t test statistics were used in hypothesis testing when there were large (> 30) and small (</= 30) observations. In these applications, we examined populations that were interval or ratio data, and assumed that the population was normal. We may ask then, can tests be made if the data are nominal and ordinal, and no assumptions made about the distribution and shape of the parent population? Remember that nominal data are the lowest type of data. This data can only be classified into categories such as male and female, Protestant, Roman Catholics, Jewish, and all others. In ordinal level data, we have seen that this level includes one category that is ranked higher than another. Notwithstanding the argument about statistical meaningfulness, let’s assume that rating a product (excellent, good, fair, and unsatisfactory) is interval. This means that a ranking of excellent is higher than good, and so forth. Goodness-of-Fit Test: Equal Expected Frequencies Hypothesis tests related to nominal and ordinal levels of measurement are called nonparametric tests, sometimes referred to as distribution-free tests. Tests that are distribution free imply that the tests are free from assumptions regarding the distribution of the parent population. This set of hypothesis testing has several forms of testing. We will focus on “goodness of fit” testing and use the Chi Square, X 2 as the test statistic, our third application of test statistics in this course. In this regard, our interest is to determine how well an observed set of data fits an expected set of nominal or ordinal data. Moreover, this testing assumes “equal expected frequencies” in the distribution. Let’s explain this form of testing with an example. Let’s assume an athletic shoe store plans to sell six new styles of running shoes that are now available on the market. After one week of sales the store sold the following: Shoe Sold Nike 13 Saucony 33 Adidas 14 New Balance 7 Rebok 36 Zepher 17 Total 120

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At the end of the first week of sales, can the store conclude the sales of new running shoes are the same for each brand? Or should the store conclude that the sales are not the same? If there were no significant difference between the observed frequencies and the expected frequencies, we would expect that the observed frequencies would be equal, or nearly equal. That is we would expect to sell as many Nike shoes as for New Balance, and so forth. Thus, any discrepancy in the set of observed and expected frequencies could be attributed to sampling (chance). Let’s explain expectancy further. Because there are 120 sold running shoes in the
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## This note was uploaded on 10/10/2010 for the course STATS Stats301 taught by Professor Regis during the Spring '10 term at DeVry Irvine.

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W3 Lecture Part I - Week Three Lecture Part I Introduction The previous lectures and learning discussed and applied two of the three test

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