# 100 Statistical Tests

This expanded and updated Third Edition of Gopal Kanji's best-selling resource on statistical tests covers all the most commonly used tests with information on how to calculate and interpret results with simple datasets.

## 100 Statistical Tests

100 Statistical Tests: Third Edition is the one indispensable guide for users of statistical materials and consumers of statistical information at all levels and across all disciplines. Introduction to Statistical Testing Examples of Test Procedures List of Tests Classification of Tests The Tests List of Tables Tables Very useful as a companion for data analysis - but not so much for teaching.

New to this edition:A brand new introduction to statistical testing with information to guide the reader through the book so that even non-statistics students can find information quickly and easily

Real-world explanations of how and when to use each test with examples drawn from wide range of disciplines.

A useful Classification of Tests table

All the relevant statistical tables for checking critical values

This expanded and updated Third Edition of Gopal K. Kanji's best-selling resource on statistical tests covers all the most commonly used tests with information on how to calculate and interpret results with simple datasets.

?This is a very valuable book for statisticians and users of statistics. It contains a remarkable number of statistical tests which are currently available and useful for practical purposes? - Statistical Papers

This expanded and updated Third Edition of Gopal Kanji?s best-selling resource on statistical tests covers all the most commonly used tests with information on how to calculate and interpret results with simple datasets.

Covers all the most commonly used tests with information on how to calculate and interpret results with simple datasets. Each entry begins with a short summary statement about the tests purpose, and contains details of the test objective, the limitations (or assumptions) involved, a brief outline of the method, a worked example, and the numerical calculation.

Table of contentsWhy does power matter in statistics?

What is a power analysis?

Other factors that affect power

How do you increase power?

Frequently asked questions about statistical power

On the flip side, too much power means your tests are highly sensitive to true effects, including very small ones. This may lead to finding statistically significant results with very little usefulness in the real world.

Statistical significance is a term used by researchers to state that it is unlikely their observations could have occurred under the null hypothesis of a statistical test. Significance is usually denoted by a p-value, or probability value.

100 Statistical Tests: Third Edition is the one indispensable guide for users of statistical materials and consumers of statistical information at all levels and across all disciplines. if (window['_OC_autoDir']) _OC_autoDir('search_form_input');AperÃ§u du livre Avis des internautes - RÃ©diger un commentaireLes avis ne sont pas validÃ©s, mais Google recherche et supprime les faux contenus lorsqu'ils sont identifiÃ©sEngineering ManagerAvis d'utilisateur - cookye - Overstock.comGood explaination of the equations. Nice concise summary of the major statistical equations. Kanjis book has a unique coverage in a single book. Consulter l'avis complet

This compares two tests of normality (with unspecified mean and variance) against a sequence of alternatives of increasingly skew gamma distributions. We can see that at the same significance level (5% in this case), the Shapiro Wilk has better power than the Lilliefors for this set of alternatives (at the sample size this was calculated at, I think it was for n=30 -- though the general pattern of behavior is similar at larger and smaller typical sample sizes).

So for a given significance level we can compare the power of two tests. It's quite common (but sometimes misleading) to ignore small samples and simply compute the asymptotic relative efficiency of tests - in effect, compare the ratio of their power vanishingly close to the null as the sample size goes off to infinity. There are theorems that help come up with tests with the highest asymptotic relative efficiency (and so will come to have the best power as samples become sufficiently large); these are sometimes (if potentially misleadingly) just called "efficient tests". Fortunately those tests usually have good properties in small samples as well.

An example of this is the widespread use of likelihood ratio tests (for which Wilks' theorem may be used), and so also Wald tests and score tests, which are asymptotically equivalent. However, unless you can work out the small sample distribution of the test statistic (or some function of it), the significance level you choose will generally only be approximately correct in small samples.

bias (does the test have its lowest rejection rate somewhere other than at the null? This is often of direct fairly practical import, since it represents behavior that is somewhere worse than just rejecting the null at random with probabilty $\alpha$ -- but people often tolerate somewhat biased tests in practice)

For the most common tests, many of these things are well understood; as an example, a chi-squared test of multinomial goodness of fit is known not to be unbiased in general but is asymptotically efficient. Most goodness of fit tests have bias issues (e.g. try the Anderson-Darling test with uniform null against a "hill shaped" symmetric beta alternative)

When calculation of power, significance level or robustness is not analytically tractable, simulation methods are often used. [You don't even need to be able to derive the distribution of the test statistic to invent new tests; simulations/resampling methods can be used]

Even on a cheap laptop hundreds of thousands of tests might be simulated in a few moments, allowing accurate calculation of (say) rejection rates under a variety of situations in a reasonably short period of time.

To return to the matter of a text that covers this sort of detail for a hundred tests, I don't think any text does so (one might, but I have never heard of one). Once the principles are understood, there's probably little need for an encyclopedia of power for 90 tests you never use, 5 you use once in a blue moon and 5 you use fairly often.

[For the little bit of actual hypothesis testing I do, the behavior of the t-test and F tests in regression and the similar asymptotic tests in a GLM probably cover most cases, along with the occasional chi-square -- but usually my interest is on effect sizes and prediction intervals rather than testing]

The probability that a statistical test will be positive for a true statistic is sometimes called the test's sensitivity, and the probability that a test will be negative for a negative statistic is sometimes called the specificity. The following table summarizes the names given to the various combinations of the actual state of affairs and observed test results.

Multiple-comparison corrections to statistical tests are used when several statistical tests are being performed simultaneously. For example, let's suppose you were measuring leg length in eight different lizard species and wanted to see whether the means of any pair were different. Now, there are pairwise comparisons possible, so even if all of the population means are equal, it is quite likely that at least one pair of sample means would differ significantly at the 5% level. An alpha value of 0.05 is therefore appropriate for each individual comparison, but not for the set of all comparisons.

Our hope is that after this course you will have developed a solid foundation in basic statistical ideas, learned how to relate those ideas to everyday life, and appreciate the importance of such an understanding.

The definition of statistics is always different, depending on your subject and methodology. In simple terms, it is a defined study, analysis, and manipulation of data that must be reviewed. The complex part of statistical analysis is drawing conclusions or coming up with reports. Since it all comes down to data interpretation, one must think about choosing good statistics research topics. Start by addressing various scientific, industrial, or social problems. It will make it easier to narrow things down and find the most efficient solution, be it a manual statistical interpretation or software automation. If things do not work for you, remember that you can pay for research paper and receive additional help with calculation or methodology choice. It will also help you to quote every statistical bit of data correctly if it has been taken from an outside source!

The trick here is to know what methodology will be used to collect and interpret statistical data. Even if you have not chosen your statistics project topic, think about it before going any further. It will help you learn about what kind of data will be researched as the sample will be picked correctly. Your basic outline for choosing the right topic should be this way: 041b061a72