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Chapter 15

summary for chapter 15

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Brent Berry

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Chapter 15
๎€Personโ€™s r correlation coefficient is the statistic we use to test the hypothesis of the
existence of a relationship/w 2 interval ratio variables, an independent variable X
and a dependent of Y
๎€When to test a hypothesise using bivariate correlation and regression analysis (t-
distribution, df n-2)
1)In general testing a hypothesis that a relationship exists between 2 interval ratio
2)There are two interval-ration variables
3)There are no restriction on sample size, but generally the larger the n, the better
4)A scatter plot of the coordinates of the two variables fits a linear pattern
๎€When using a sample data we must keep in mind to try and answer the following
question: does a linear relationship between X and Y truly exist in the population, or
is the linear pattern in this sample the result of sampling error
๎€As with any hypothesis test, the real interest lies in the parameter, the summary
measurements that applies to the entire population
๎€Personโ€™s r correlation coefficient allows us to test a hypothesise to answer this
๎€For the population the corresponding parameter is symbolized by the Greek letter
rho (p)- it is the correlation coefficient that would be obtained if Personโ€™s correlation
coefficient were computed for the entire population
๎€The effect of the test is the difference between an observed sample statistic and the
expected parameter when the null hypothesis is true. For a correlation hypothesise
the effect is the difference between the observed sample Personโ€™s r and the expected
rho of 0.
๎€The null hypothesis => Ho;p=0 (no relationship between X and Y)
๎€The statement of the alternative hypothesis can be two tailed, non directional, one
tailed positive or one tailed negative
๎€The standard error is inversely related to sample size, the larger the sample size the
smaller the standard error. The test statistic is (look in book p.557)
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