By Michael J. Panik

The hugely readable textual content captures the flavour of a path in mathematical information with out enforcing an excessive amount of rigor; scholars can pay attention to the statistical techniques with out getting misplaced within the idea.

scholars who use this publication can be good on their strategy to pondering like a statistician. working towards statisticians will locate this booklet valuable in that it truly is replete with statistical attempt systems (both parametric and non-parametric) in addition to various distinct examples.

Â· entire assurance of descriptive statistics

Â· extra distinct remedy of univariate and

bivariate chance distributions

Â· Thorough insurance of likelihood idea with

a number of occasion classifications

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**Extra resources for Advanced Statistics from an Elementary Point of View**

**Sample text**

What about the different means issue? Even though units may not be a problem, it is 34 Chapter 2 Elementary Descriptive Statistical Techniques the case that a set of very large numbers invariably has a large standard deviation relative to a set of very small numbers, even though there may be more variability associated with the values within the latter. For instance, we may address the question: Is there more variation among weights of mice relative to that of elephants? It should be clear that the standard deviation computed from the elephants (converted to grams) will always be larger than the comparable figure for mice (also in grams) even though there may be more uniformity among the weights of the elephants.

So if X and Y are independent, then there is no relationship of any sort (linear or otherwise) between these variables so that X and Y must also be uncorrelated. But if X and Y are uncorrelated, we cannot generally conclude that they are also independent. It is also important to note that correlation does not imply causation. That is, finding that ρXY = 0 does not imply that movement in X causes movement in Y or vice versa. In fact, some other unobserved variable Z may be causing movements in both X and Y.

13 Standard kurtosis as a measure of kurtosis. D. 263. 6 Relative Variation How may we compare the dispersions of two (or more) absolute frequency distributions? For convenience sake, let us limit ourselves to the discussion of distributions A and B. Our approach is the following: (1) If they have the same (or nearly the same) mean and are expressed in the same units, then we can simply compare their standard deviations. ) (2) If they have different means or are expressed in different units, then we need to convert the standard deviation of each distribution to a measure of relative variation.