12. Correlation “r” Means “add these terms for all the individuals” Begin with standardizing values e.g. x =height in cm and y = weight in kg and this data exists for n people and are the mean and standard deviation of the n heights
19. y = dependent variable x = independent variable a = intercept (value we would expect y to have if x is 0) b = slope Plot y (response variable) on vertical axis Plot x (explanatory variable) on horizontal axis Fit the line to the points distribution Slope is the amount by which y changes
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22. r 2 = variance of predicted values / variance of observed values Fraction of the Variation Explained The square of the correlation is the fraction of the variation in the values of y that is explained by the regression of y on x.
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25. Best line fit was Exponential not linear... Dataset provided by Triola, Bisotatistics - Bears.xls feel free to try some of the variables
Relate a scatter plot to the algebraic plotting of number pairs (x,y).
page 509 of text
page 507 of text Explain to students the difference between the ‘paired’ data of this chapter and the investigation of two groups of data in Chapter 8.
page 512 of text If using a graphics calculator for demonstration, it will be an easy exercise to switch the x and y values to show that the value of r will not change.
Although the term nonparametric strongly suggests that the test is not based on a parameter, there are some nonparametric tests that do depend on a parameter such as the median, but they don't require a particular distribution. Although distribution-free is a more accurate description, the term non, parametric is more commonly used.
Nonparametric methods can be applied to a wide variety of situations because they do not have the more rigid requirements associated with parametric methods. In particular, nonparametric methods do not require normally distributed populations. Unlike parametric methods, nonparametric methods can often be applied to nonnumerical data, such as the genders of survey respondents. Nonparametric methods usually involve simpler computations than the corresponding parametric methods and are therefore easier to understand and apply.
Nonparametric methods may appear to waste information in cases where exact numerical data are converted to a qualitative form. For example, in the nonparametric sign test, weight losses by dieters are recorded simply as negative signs; the actual magnitudes of the weight losses are ignored. Nonparametric tests are not as efficient as parametric tests, so with a nonparametric test we generally need stronger evidence (such as a larger sample or greater differences) before we reject a null hypothesis.
When the requirements of population distributions are satisfied, nonparametric tests are generally less efficient than their parametric counterparts, but the reduced efficiency can be compensated for by an increased sample size. For example, Section 13-6 will deal with a concept called rank correlation, which has an efficiency rating of 0.91 when compared to the linear correlation presented in Chapter 9. This means that all other things being equal, non parametric rank correlation requires 100 sample observations to achieve the same results as 91 sample observations analysed through parametric linear correlation, assuming the stricter requirements for using the parametric method are met. Table 13-1 lists the nonparametric methods covered in this chapter, along with the corresponding parametric approach and efficiency rating. Table 13-1 shows that several nonparametric tests have efficiency ratings above 0.90, so the lower efficiency might not be a critical factor in choosing between parametric or nonparametric methods. More important is that we avoid using the parametric tests when their required assumptions are not satisfied.
