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Boundless Lecture Slides

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  1. Boundless Lecture Slides Available on the Boundless Teaching Platform Free to share, print, make copies and changes. Get yours at www.boundless.com

  2. Using Boundless Presentations Boundless Teaching Platform Boundless empowers educators to engage their students with affordable, customizable textbooks and intuitive teaching tools. The free Boundless Teaching Platform gives educators the ability to customize textbooks in more than 20 subjects that align to hundreds of popular titles. Get started by using high quality Boundless books, or make switching to our platform easier by building from Boundless content pre-organized to match the assigned textbook. This platform gives educators the tools they need to assign readings and assessments, monitor student activity, and lead their classes with pre-made teaching resources. Get started now at: • The Appendix The appendix is for you to use to add depth and breadth to your lectures. You can simply drag and drop slides from the appendix into the main presentation to make for a richer lecture experience. http://boundless.com/teaching-platform • Free to edit, share, and copy Feel free to edit, share, and make as many copies of the Boundless presentations as you like. We encourage you to take these presentations and make them your own. If you have any questions or problems please email: educators@boundless.com Free to share, print, make copies and changes. Get yours at www.boundless.com

  3. About Boundless • Boundless is an innovative technology company making education more affordable and accessible for students everywhere. The company creates the world’s best open educational content in 20+ subjects that align to more than 1,000 popular college textbooks. Boundless integrates learning technology into all its premium books to help students study more efficiently at a fraction of the cost of traditional textbooks. The company also empowers educators to engage their students more effectively through customizable books and intuitive teaching tools as part of the Boundless Teaching Platform. More than 2 million learners access Boundless free and premium content each month across the company’s wide distribution platforms, including its website, iOS apps, Kindle books, and iBooks. To get started learning or teaching with Boundless, visit boundless.com. Free to share, print, make copies and changes. Get yours at www.boundless.com

  4. The t-Test Other Hypothesis Tests The Chi-Squared Test Tests for Ranked Data Nonparametric Statistics ] Other Hypothesis Tests Free to share, print, make copies and changes. Get yours at www.boundless.com

  5. Other Hypothesis Tests > The t-Test The t-Test • The t-Test • The t-Distribution • Assumptions • t-Test for One Sample • t-Test for Two Samples: Independent and Overlapping • t-Test for Two Samples: Paired • Calculations for the t-Test: One Sample • Calculations for the t-Test: Two Samples • Multivariate Testing • Alternatives to the t-Test • Cohen's d Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/statistics/textbooks/boundless-statistics-textbook/other-hypothesis-tests-13/the-t-test-60/

  6. Other Hypothesis Tests > The Chi-Squared Test The Chi-Squared Test • Categorical Data and the Multinomial Experiment • Structure of the Chi-Squared Test • How Fisher Used the Chi-Squared Test • Goodness of Fit • Inferences of Correlation and Regression • Example: Test for Goodness of Fit • Example: Test for Independence Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/statistics/textbooks/boundless-statistics-textbook/other-hypothesis-tests-13/the-chi-squared-test-61/

  7. Other Hypothesis Tests > Tests for Ranked Data Tests for Ranked Data • When to Use These Tests • Mann-Whitney U-Test • Wilcoxon t-Test • Kruskal-Wallis H-Test Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/statistics/textbooks/boundless-statistics-textbook/other-hypothesis-tests-13/tests-for-ranked-data-62/

  8. Other Hypothesis Tests > Nonparametric Statistics Nonparametric Statistics • Distribution-Free Tests • Sign Test • Single-Population Inferences • Comparing Two Populations: Independent Samples • Comparing Two Populations: Paired Difference Experiment • Comparing Three or More Populations: Randomized Block Design • Rank Correlation Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/statistics/textbooks/boundless-statistics-textbook/other-hypothesis-tests-13/nonparametric-statistics-63/

  9. Appendix Free to share, print, make copies and changes. Get yours at www.boundless.com

  10. Other Hypothesis Tests Key terms • alternative hypothesisa rival hypothesis to the null hypothesis, whose likelihoods are compared by a statistical hypothesis test • alternative hypothesisa rival hypothesis to the null hypothesis, whose likelihoods are compared by a statistical hypothesis test • binomial distributionthe discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability • binomial distributionthe discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability • binomial distributionthe discrete probability distribution of the number of successes in a sequence of independent yes/no experiments, each of which yields success with probability • blockexperimental units in groups that are similar to one another • blockingA schedule for conducting treatment combinations in an experimental study such that any effects on the experimental results due to a known change in raw materials, operators, machines, etc., become concentrated in the levels of the blocking variable. • bootstrapany method or instance of estimating properties of an estimator (such as its variance) by measuring those properties when sampling from an approximating distribution • central limit theoremThe theorem that states: If the sum of independent identically distributed random variables has a finite variance, then it will be (approximately) normally distributed. • central limit theoremThe theorem that states: If the sum of independent identically distributed random variables has a finite variance, then it will be (approximately) normally distributed. • chi-squared distributionA distribution with degrees of freedom is the distribution of a sum of the squares of independent standard normal random variables. • chi-squared distributionA distribution with degrees of freedom is the distribution of a sum of the squares of independent standard normal random variables. Free to share, print, make copies and changes. Get yours at www.boundless.com

  11. Other Hypothesis Tests • chi-squared distributionA distribution with degrees of freedom is the distribution of a sum of the squares of independent standard normal random variables. • Cohen's dA measure of effect size indicating the amount of different between two groups on a construct of interest in standard deviation units. • concordantAgreeing; correspondent; in keeping with; agreeable with. • confidence intervalA type of interval estimate of a population parameter used to indicate the reliability of an estimate. • confidence intervalA type of interval estimate of a population parameter used to indicate the reliability of an estimate. • confoundingDescribes a phenomenon in which an extraneous variable in a statistical model correlates (positively or negatively) with both the dependent variable and the independent variable; confounder = noun form. • contingency tablea table presenting the joint distribution of two categorical variables • correlation coefficientAny of the several measures indicating the strength and direction of a linear relationship between two random variables. • data transformationThe application of a deterministic mathematical function to each point in a data set. • degrees of freedomany unrestricted variable in a frequency distribution • degrees of freedomany unrestricted variable in a frequency distribution • degrees of freedomany unrestricted variable in a frequency distribution Free to share, print, make copies and changes. Get yours at www.boundless.com

  12. Other Hypothesis Tests • Fisher's exact testa statistical significance test used in the analysis of contingency tables, in which the significance of the deviation from a null hypothesis can be calculated exactly, rather than relying on an approximation that becomes exact in the limit as the sample size grows to infinity • goodness of fithow well a statistical model fits a set of observations • Hotelling's T-square statisticA generalization of Student's -statistic that is used in multivariate hypothesis testing. • hypergeometric distributiona discrete probability distribution that describes the number of successes in a sequence of draws from a finite population without replacement • Kruskal-Wallis testA non-parametric method for testing whether samples originate from the same distribution. • monotonic functiona function that either never decreases or never increases as its independent variable increases • multinomial distributionA generalization of the binomial distribution; gives the probability of any particular combination of numbers of successes for the various categories. • null hypothesisA hypothesis set up to be refuted in order to support an alternative hypothesis; presumed true until statistical evidence in the form of a hypothesis test indicates otherwise. • null hypothesisA hypothesis set up to be refuted in order to support an alternative hypothesis; presumed true until statistical evidence in the form of a hypothesis test indicates otherwise. • null hypothesisA hypothesis set up to be refuted in order to support an alternative hypothesis; presumed true until statistical evidence in the form of a hypothesis test indicates otherwise. • ordinalOf a number, indicating position in a sequence. • ordinal dataA statistical data type consisting of numerical scores that exist on an ordinal scale, i.e. an arbitrary numerical scale where the exact numerical quantity of a particular value has no significance beyond its ability to establish a ranking over a set of data points. Free to share, print, make copies and changes. Get yours at www.boundless.com

  13. Other Hypothesis Tests • p-valueThe probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true. • p-valueThe probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true. • p-valueThe probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true. • paired difference testA type of location test that is used when comparing two sets of measurements to assess whether their population means differ. • parametricof, relating to, or defined using parameters • pooled varianceA method for estimating variance given several different samples taken in different circumstances where the mean may vary between samples but the true variance is assumed to remain the same. • rank correlationAny of several statistics that measure the relationship between rankings of different ordinal variables or different rankings of the same variable. • residualsThe difference between the observed value and the estimated function value. • scaling parameterA special kind of numerical parameter of a parametric family of probability distributions; the larger the scale parameter, the more spread out the distribution. • sign testa statistical test concerning the median of a continuous population with the idea that the probability of getting a value below the median or a value above the median is • standard errorA measure of how spread out data values are around the mean, defined as the square root of the variance. • Student's t-distributionA family of continuous probability distributions that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown. Free to share, print, make copies and changes. Get yours at www.boundless.com

  14. Other Hypothesis Tests • Student's t-distributionA family of continuous probability distributions that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown. • t-testAny statistical hypothesis test in which the test statistic follows a Student's -distribution if the null hypothesis is supported. • t-testAny statistical hypothesis test in which the test statistic follows a Student's t-distribution if the null hypothesis is supported. • t-testAny statistical hypothesis test in which the test statistic follows a Student's -distribution if the null hypothesis is supported. • tieOne or more equal values or sets of equal values in the data set. • tieOne or more equal values or sets of equal values in the data set. • Type I errorAn error occurring when the null hypothesis () is true, but is rejected. • Type I errorAn error occurring when the null hypothesis () is true, but is rejected. • uniform distributiona family of symmetric probability distributions such that, for each member of the family, all intervals of the same length on the distribution's support are equally probable • Wilcoxon Rank Sum testA non-parametric test of the null hypothesis that two populations are the same against an alternative hypothesis, especially that a particular population tends to have larger values than the other. • Wilcoxon signed-rank testA nonparametric statistical hypothesis test used when comparing two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ (i.e., it is a paired difference test). • Wilcoxon t-testA non-parametric statistical hypothesis test used when comparing two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ (i.e., it is a paired-difference test). Free to share, print, make copies and changes. Get yours at www.boundless.com

  15. Other Hypothesis Tests Test for Independence For our example, this table shows the tabulated results of the observed and expected frequencies. Free to share, print, make copies and changes. Get yours at www.boundless.com OpenStax CNX."Mphekwane Mamahlodi, What is the Chi-Square Statistic?. June 17, 2013."CC BY 3.0http://cnx.org/content/m13487/latest/View on Boundless.com

  16. Other Hypothesis Tests Medical Treatment Research Medical experimentation may utilize any two independent samples t-test. Free to share, print, make copies and changes. Get yours at www.boundless.com Flickr."All sizes | U.S. Army Medical Research Unit - Improving malaria diagnostics, Kisumu, Kenya 05-2010 | Flickr - Photo Sharing!."CC BYhttp://www.flickr.com/photos/usarmyafrica/4567209763/sizes/z/in/photolist-7XA9kV-7XDnYu-7XDo8h-7XA9nB-7XA9h6-7XDo3q-7XA986-7XDo5U-7Wp9vE-7Wp9iW-7Wp7Am-7WpaSj-7WkRfD-7WkQ9r-7Wp9J1-7WkPsg-7Wp6uj-7WkRPT-7WkNfg-7Wp5uE-7Wp8rh-7Wp64W-7Wp7iC-7Wp8Ws-7WkMMr-7WkU7K-7WpacE-7Wpax5-7Wp7WQ-7Wp5R3-7WkT12-7WkPKR-aHBfuF-aHBoqR-8PfzU8-9x9tGe-7WkPV8-7WkVWr-7WkSe2-7WkVn6-7XA5uZ-7XDk3Q-7XDiBG-7XA4vz-7XA5ai-7XDjC1-7XDjQu-8rbVaq-8rmXYp-8r8qx6-8rbyth/View on Boundless.com

  17. Other Hypothesis Tests Pooled Variance This is the formula for a pooled variance in a two-sample t-test with unequal sample size but equal variances. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Student's t-test."CC BY-SAhttps://en.wikipedia.org/wiki/Student's_t-testView on Boundless.com

  18. Other Hypothesis Tests William Sealy Gosset Writing under the pseudonym "Student", Gosset published his work on the t-test in 1908. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."William Sealy Gosset."Public domainhttps://en.wikipedia.org/wiki/File:William_Sealy_Gosset.jpgView on Boundless.com

  19. Other Hypothesis Tests Unpooled Variance This is the formula for a pooled variance in a two-sample t-test with unequal or equal sample sizes but unequal variances. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Student's t-test."CC BY-SAhttps://en.wikipedia.org/wiki/Student's_t-testView on Boundless.com

  20. Other Hypothesis Tests Population Versus Area Scatterplots A scatterplot in which the areas of the sovereign states and dependent territories in the world are plotted on the vertical axis against their populations on the horizontal axis. The upper plot uses raw data. In the lower plot, both the area and population data have been transformed using the logarithm function. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Population vs area."CC BY-SAhttp://en.wikipedia.org/wiki/File:Population_vs_area.svgView on Boundless.com

  21. Other Hypothesis Tests Null Hypothesis A one-sample t-test has the null hypothesis that the population mean equals the hypothesized value. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikibooks."Statistics/Testing Data/t-tests."CC BY-SA 3.0http://en.wikibooks.org/wiki/Statistics/Testing_Data/t-testsView on Boundless.com

  22. Other Hypothesis Tests Spearman's Rank Correlation The formula for calculating Spearman's Coefficient. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikibooks."Statistics/Testing Data/Spearmans."CC BY-SA 3.0http://en.wikibooks.org/wiki/Statistics/Testing_Data/SpearmansView on Boundless.com

  23. Other Hypothesis Tests Formula for d This formula for d that occurs in Spearman's rank correlation formula. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikibooks."Statistics/Testing Data/Spearmans."CC BY-SA 3.0http://en.wikibooks.org/wiki/Statistics/Testing_Data/SpearmansView on Boundless.com

  24. Other Hypothesis Tests Cochran's Cochran's  test assumes that there are experimental treatments and that the observations are arranged in blocks. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Cochran's Q test."CC BY-SAhttps://en.wikipedia.org/wiki/Cochran's_Q_testView on Boundless.com

  25. Other Hypothesis Tests Contingency Table A contingency table used in McNemar's test tabulates the outcomes of two tests on a sample of subjects. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."McNemar's test."CC BY-SAhttps://en.wikipedia.org/wiki/McNemar's_testView on Boundless.com

  26. Other Hypothesis Tests Welch–Satterthwaite Equation This is the formula for calculating the degrees of freedom in Welsh's t-test. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Student's t-test."CC BY-SAhttps://en.wikipedia.org/wiki/Student's_t-testView on Boundless.com

  27. Other Hypothesis Tests Cochran's Test Statistic This is the equation for Cochran's test statistic, where Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Cochran's Q test."CC BY-SAhttps://en.wikipedia.org/wiki/Cochran's_Q_testView on Boundless.com

  28. Other Hypothesis Tests Shape of the -Distribution These images show the density of the -distribution (red) for increasing values of  (1, 2, 3, 5, 10, and 30 degrees of freedom). The normal distribution is shown as a blue line for comparison. Previous plots are shown in green. Note that the -distribution becomes closer to the normal distribution as  increases. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Student's t-distribution."CC BY-SAhttps://en.wikipedia.org/wiki/Student's_t-distributionView on Boundless.com

  29. Other Hypothesis Tests Blood Pressure Treatment A typical example of a repeated measures -test is in the treatment of patients with high blood pressure to determine the effectiveness of a particular medication. Free to share, print, make copies and changes. Get yours at www.boundless.com Flickr."All sizes | Hey look, it's my blood pressure!| Flickr - Photo Sharing!."CC BY-SAhttp://www.flickr.com/photos/skyfaller/2189601093/sizes/z/in/photolist-4kuh7Z-4maiqA-4oK1NN-4LP23V-5RCN5n-5RH6Au-5WiP8j-6i5pFU-6ig2Gj-6jjP6d-6qEThm-6s7cwT-6sbjwY-6sbjzJ-6sPNxe-6F44ap-79jKoE-7aaxZM-7jdFsz-7jdFwp-7jhzod-7jhzsj-7jhzy5-7rTQVr-7vA2iW-7wvscM-aEAnJD-9R1nE2-bKqjzt-8BFByE-9xVtxH-8zRtSz-ekcbCY-8KeytA-dvvSfb-9ASYdK-9ASYNM-9Hn9px-dYuZc2-dgZp6J-dShudJ-8BFBCy-8BCvBt-8BCvHk-8BCvQF-8BFBHb-8J76BX-8Jabi9-9PVenx-dR8c4d-dGJhBP/View on Boundless.com

  30. Other Hypothesis Tests Cohen's Plots of the densities of Gaussian distributions showing different Cohen's effect sizes. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Cohens d 4panel."CC BY-SAhttps://en.wikipedia.org/wiki/File:Cohens_d_4panel.svgView on Boundless.com

  31. Other Hypothesis Tests The Sign Test The sign test involves denoting values above the median of a continuous population with a plus sign and the ones falling below the median with a minus sign in order to test the hypothesis that there is no difference in medians. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikimedia."Plus-,minus-,and equality-sign."Public domainhttp://commons.wikimedia.org/wiki/File:Plus-,minus-,and_equality-sign.svgView on Boundless.com

  32. Other Hypothesis Tests Sir Ronald Fisher Sir Ronald Fisher is the namesake for Fisher's exact test. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."R.A. Fischer."CC BY-SAhttp://en.wikipedia.org/wiki/File:R._A._Fischer.jpgView on Boundless.com

  33. Other Hypothesis Tests Chi-Square Distribution Plot of the chi-square distribution for values of . Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Chi-square pdf."CC BY-SAhttp://en.wikipedia.org/wiki/File:Chi-square_pdf.svgView on Boundless.com

  34. Other Hypothesis Tests Table 2 The adjusted standardized residuals from Table 1. Free to share, print, make copies and changes. Get yours at www.boundless.com Critical Care Forum."Critical Care | Full text | Statistics review 8: Qualitative data - tests of association."CC BYhttp://ccforum.com/content/8/1/46View on Boundless.com

  35. Other Hypothesis Tests Table 1 Numbers of patients classified by site of central venous cannula and infectious complication. This table shows the proportions of patients in the sample with cannulae sited at the internal jugular, subclavian and femoral veins. Using the above formula to find the adjusted standardized residual for those with cannulae sited at the internal jugular and no infectious complications yields: . Subclavian site/no infectious complication has the largest residual at 6.2. Because it is positive, there are more individuals than expected with no infectious complications where the subclavian central line site was used. As these residuals follow a Normal distribution with mean 0 and standard deviation 1, all absolute values over 2 are significant. The association between femoral site/no infectious complication is also significant, but because the residual is negative, there are fewer individuals than expected in this cell. When the subclavian central line site was used, infectious complications appear to be less likely than when the other two sites were used. Free to share, print, make copies and changes. Get yours at www.boundless.com Critical Care Forum."Critical Care | Full text | Statistics review 8: Qualitative data - tests of association."CC BYhttp://ccforum.com/content/8/1/46View on Boundless.com

  36. Other Hypothesis Tests Best Cars of 2010 This image shows a graphical representation of a ranked list of the highest rated cars in 2010. Non-parametric statistics is widely used for studying populations that take on a ranked order. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikimedia."12 Best Car Brands in 2010 by Average of Overall Reliability Ratings."CC BY-SAhttp://commons.wikimedia.org/wiki/File:12_Best_Car_Brands_in_2010_by_Average_of_Overall_Reliability_Ratings.gifView on Boundless.com

  37. Other Hypothesis Tests Attribution • Wikipedia."t-test."CC BY-SA 3.0http://en.wikipedia.org/wiki/t-test • Wikipedia."Student's t-distribution."CC BY-SA 3.0http://en.wikipedia.org/wiki/Student's%20t-distribution • Wikipedia."Student's t-test."CC BY-SA 3.0https://en.wikipedia.org/wiki/Student's_t-test • Wiktionary."confidence interval."CC BY-SA 3.0http://en.wiktionary.org/wiki/confidence_interval • Wikipedia."chi-squared distribution."CC BY-SA 3.0http://en.wikipedia.org/wiki/chi-squared%20distribution • Wikipedia."Student's t-distribution."CC BY-SA 3.0https://en.wikipedia.org/wiki/Student's_t-distribution • Wikipedia."Student's t-distribution."CC BY-SA 3.0http://en.wikipedia.org/wiki/Student's%20t-distribution • Wikipedia."t-test."CC BY-SA 3.0http://en.wikipedia.org/wiki/t-test • Wikipedia."scaling parameter."CC BY-SA 3.0http://en.wikipedia.org/wiki/scaling%20parameter • Wiktionary."alternative hypothesis."CC BY-SA 3.0http://en.wiktionary.org/wiki/alternative_hypothesis • Wikibooks."Statistics/Testing Data/t-tests."CC BY-SA 3.0http://en.wikibooks.org/wiki/Statistics/Testing_Data/t-tests • Wikipedia."t-test."CC BY-SA 3.0http://en.wikipedia.org/wiki/t-test • Wiktionary."degrees of freedom."CC BY-SA 3.0http://en.wiktionary.org/wiki/degrees_of_freedom • Wikibooks."Statistics/Testing Data/t-tests."CC BY-SA 3.0http://en.wikibooks.org/wiki/Statistics/Testing_Data/t-tests • Wiktionary."null hypothesis."CC BY-SA 3.0http://en.wiktionary.org/wiki/null_hypothesis • Wikipedia."Student's t-test."CC BY-SA 3.0https://en.wikipedia.org/wiki/Student's_t-test • Wikipedia."blocking."CC BY-SA 3.0http://en.wikipedia.org/wiki/blocking Free to share, print, make copies and changes. Get yours at www.boundless.com

  38. Other Hypothesis Tests • Influential Points."The two-sample t-test: Use & misuse."CC BY-SAhttp://influentialpoints.com/Training/Two-sample_t-test_use_and_misuse.htm • Wikipedia."paired difference test."CC BY-SA 3.0http://en.wikipedia.org/wiki/paired%20difference%20test • Wikipedia."confounding."CC BY-SA 3.0http://en.wikipedia.org/wiki/confounding • Wikipedia."Paired difference test."CC BY-SA 3.0https://en.wikipedia.org/wiki/Paired_difference_test • Wikipedia."Student's t-test."CC BY-SA 3.0https://en.wikipedia.org/wiki/Student's_t-test • Wikipedia."Student's t-test."CC BY-SA 3.0https://en.wikipedia.org/wiki/Student's_t-test • Wikipedia."p-value."CC BY-SA 3.0http://en.wikipedia.org/wiki/p-value • Wiktionary."standard error."CC BY-SA 3.0http://en.wiktionary.org/wiki/standard_error • Wikipedia."Student's t-test."CC BY-SA 3.0https://en.wikipedia.org/wiki/Student's_t-test • Wikipedia."pooled variance."CC BY-SA 3.0http://en.wikipedia.org/wiki/pooled%20variance • Wiktionary."degrees of freedom."CC BY-SA 3.0http://en.wiktionary.org/wiki/degrees_of_freedom • Wikipedia."Student's t-test."CC BY-SA 3.0https://en.wikipedia.org/wiki/Student's_t-test • Wikipedia."Type I error."CC BY-SA 3.0http://en.wikipedia.org/wiki/Type%20I%20error • Wikipedia."Hotelling's T-square statistic."CC BY-SA 3.0https://en.wikipedia.org/wiki/Hotelling's_T-square_statistic • Wikipedia."Hotelling's T-square statistic."CC BY-SA 3.0http://en.wikipedia.org/wiki/Hotelling's%20T-square%20statistic • Wiktionary."central limit theorem."CC BY-SA 3.0http://en.wiktionary.org/wiki/central_limit_theorem • Wikipedia."Student's t-test."CC BY-SA 3.0https://en.wikipedia.org/wiki/Student's_t-test • Wikipedia."Wilcoxon signed-rank test."CC BY-SA 3.0http://en.wikipedia.org/wiki/Wilcoxon%20signed-rank%20test • Wikipedia."Wilcoxon Rank Sum test."CC BY-SA 3.0http://en.wikipedia.org/wiki/Wilcoxon%20Rank%20Sum%20test Free to share, print, make copies and changes. Get yours at www.boundless.com

  39. Other Hypothesis Tests • Wikipedia."Slutsky's theorem."CC BY-SA 3.0https://en.wikipedia.org/wiki/Slutsky's_theorem • Wikipedia."p-value."CC BY-SA 3.0http://en.wikipedia.org/wiki/p-value • Wikipedia."Cohen's d."CC BY-SA 3.0https://en.wikipedia.org/wiki/Cohen's_d%23Cohen.27s_d • Boundless Learning."Boundless."CC BY-SA 3.0http://www.boundless.com//statistics/definition/cohen-s-d • Wikipedia."Multinomial test."CC BY-SA 3.0http://en.wikipedia.org/wiki/Multinomial_test • Wikipedia."Multinomial distribution."CC BY-SA 3.0http://en.wikipedia.org/wiki/Multinomial_distribution • Wikipedia."multinomial distribution."CC BY-SA 3.0http://en.wikipedia.org/wiki/multinomial%20distribution • Wiktionary."binomial distribution."CC BY-SA 3.0http://en.wiktionary.org/wiki/binomial_distribution • Austrailian Bureau of Statistics."Error 400."CC BYhttp://www.abs.gov.au/AUSSTATS/abs@.nsf/Previousproducts/1304.5Main%20Features8Sep%202010?opendocument&tabname=Summary&prodno=1304.5&issue=Sep%202010&num=&view= • OpenStax CNX."Mphekwane Mamahlodi, What is the Chi-Square Statistic?. September 17, 2013."CC BY 3.0http://cnx.org/content/m13487/latest/ • Wikipedia."Fisher's exact test."CC BY-SA 3.0http://en.wikipedia.org/wiki/Fisher's%20exact%20test • Wikipedia."Chi-squared test."CC BY-SA 3.0http://en.wikipedia.org/wiki/Chi-squared_test • Wiktionary."degrees of freedom."CC BY-SA 3.0http://en.wiktionary.org/wiki/degrees_of_freedom • Wikipedia."p-value."CC BY-SA 3.0http://en.wikipedia.org/wiki/p-value • Wiktionary."hypergeometric distribution."CC BY-SA 3.0http://en.wiktionary.org/wiki/hypergeometric_distribution • Wikipedia."Fisher's exact test."CC BY-SA 3.0http://en.wikipedia.org/wiki/Fisher's_exact_test • Wiktionary."contingency table."CC BY-SA 3.0http://en.wiktionary.org/wiki/contingency_table • Wikipedia."Pearson's chi-squared test."CC BY-SA 3.0http://en.wikipedia.org/wiki/Pearson's_chi-squared_test • Boundless Learning."Boundless."CC BY-SA 3.0http://www.boundless.com//statistics/definition/goodness-of-fit Free to share, print, make copies and changes. Get yours at www.boundless.com

  40. Other Hypothesis Tests • Wiktionary."binomial distribution."CC BY-SA 3.0http://en.wiktionary.org/wiki/binomial_distribution • OpenStax CNX."Mphekwane Mamahlodi, What is the Chi-Square Statistic?. September 17, 2013."CC BY 3.0http://cnx.org/content/m13487/latest/ • Critical Care Forum."Critical Care | Full text | Statistics review 8: Qualitative data - tests of association."CC BYhttp://ccforum.com/content/8/1/46 • Wiktionary."correlation coefficient."CC BY-SA 3.0http://en.wiktionary.org/wiki/correlation_coefficient • Wikipedia."residuals."CC BY-SA 3.0http://en.wikipedia.org/wiki/residuals • Wiktionary."null hypothesis."CC BY-SA 3.0http://en.wiktionary.org/wiki/null_hypothesis • Wikipedia."Goodness of fit."CC BY-SA 3.0http://en.wikipedia.org/wiki/Goodness_of_fit • Wiktionary."null hypothesis."CC BY-SA 3.0http://en.wiktionary.org/wiki/null_hypothesis • Wiktionary."alternative hypothesis."CC BY-SA 3.0http://en.wiktionary.org/wiki/alternative_hypothesis • OpenStax CNX."Mphekwane Mamahlodi, What is the Chi-Square Statistic?. September 17, 2013."CC BY 3.0http://cnx.org/content/m13487/latest/ • Wiktionary."central limit theorem."CC BY-SA 3.0http://en.wiktionary.org/wiki/central_limit_theorem • Wiktionary."confidence interval."CC BY-SA 3.0http://en.wiktionary.org/wiki/confidence_interval • Wikipedia."Data transformation (statistics)."CC BY-SA 3.0http://en.wikipedia.org/wiki/Data_transformation_(statistics) • Wikipedia."data transformation."CC BY-SA 3.0http://en.wikipedia.org/wiki/data%20transformation • Wikipedia."Ranking."CC BY-SA 3.0http://en.wikipedia.org/wiki/Ranking • Wikipedia."Mann-Whitney U test."CC BY-SA 3.0http://en.wikipedia.org/wiki/Mann-Whitney_U_test • Wikipedia."ordinal data."CC BY-SA 3.0http://en.wikipedia.org/wiki/ordinal%20data • Wiktionary."tie."CC BY-SA 3.0http://en.wiktionary.org/wiki/tie • Wikipedia."Wilcoxon signed-rank test."CC BY-SA 3.0http://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test Free to share, print, make copies and changes. Get yours at www.boundless.com

  41. Other Hypothesis Tests • Wiktionary."tie."CC BY-SA 3.0http://en.wiktionary.org/wiki/tie • Wikipedia."Wilcoxon t-test."CC BY-SA 3.0http://en.wikipedia.org/wiki/Wilcoxon%20t-test • Wikipedia."Kruskal–Wallis one-way analysis of variance."CC BY-SA 3.0http://en.wikipedia.org/wiki/Kruskal%E2%80%93Wallis_one-way_analysis_of_variance • Wikipedia."Kruskal-Wallis test."CC BY-SA 3.0http://en.wikipedia.org/wiki/Kruskal-Wallis%20test • Wikipedia."Type I error."CC BY-SA 3.0http://en.wikipedia.org/wiki/Type%20I%20error • Wikipedia."chi-squared distribution."CC BY-SA 3.0http://en.wikipedia.org/wiki/chi-squared%20distribution • Wiktionary."parametric."CC BY-SA 3.0http://en.wiktionary.org/wiki/parametric • Wiktionary."ordinal."CC BY-SA 3.0http://en.wiktionary.org/wiki/ordinal • Wikipedia."Nonparametric statistics."CC BY-SA 3.0http://en.wikipedia.org/wiki/Nonparametric_statistics • Wikipedia."Nonparametric statistics."CC BY-SA 3.0http://en.wikipedia.org/wiki/Nonparametric_statistics • Wikipedia."Bootstrapping (statistics)."CC BY-SA 3.0https://en.wikipedia.org/wiki/Bootstrapping_(statistics) • Wikipedia."Anderson–Darling test."CC BY-SA 3.0https://en.wikipedia.org/wiki/Anderson%E2%80%93Darling_test • Wiktionary."bootstrap."CC BY-SA 3.0http://en.wiktionary.org/wiki/bootstrap • Wikipedia."uniform distribution."CC BY-SA 3.0http://en.wikipedia.org/wiki/uniform%20distribution • Wikipedia."Spearman's rank correlation coefficient."CC BY-SA 3.0https://en.wikipedia.org/wiki/Spearman's_rank_correlation_coefficient • Wikipedia."Kruskal-Wallis one-way analysis of variance."CC BY-SA 3.0https://en.wikipedia.org/wiki/Kruskal-Wallis_one-way_analysis_of_variance • Wikipedia."Wald–Wolfowitz runs test."CC BY-SA 3.0https://en.wikipedia.org/wiki/Wald%E2%80%93Wolfowitz_runs_test • Wikipedia."Kendall tau rank correlation coefficient."CC BY-SA 3.0https://en.wikipedia.org/wiki/Kendall_tau_rank_correlation_coefficient • Wiktionary."monotonic function."CC BY-SA 3.0http://en.wiktionary.org/wiki/monotonic_function Free to share, print, make copies and changes. Get yours at www.boundless.com

  42. Other Hypothesis Tests • Wiktionary."binomial distribution."CC BY-SA 3.0http://en.wiktionary.org/wiki/binomial_distribution • Wikipedia."McNemar's test."CC BY-SA 3.0https://en.wikipedia.org/wiki/McNemar's_test • Wikipedia."chi-squared distribution."CC BY-SA 3.0http://en.wikipedia.org/wiki/chi-squared%20distribution • Wikipedia."Friedman test."CC BY-SA 3.0http://en.wikipedia.org/wiki/Friedman_test • Wikipedia."block."CC BY-SA 3.0http://en.wikipedia.org/wiki/block • Wikipedia."Cochran's Q test."CC BY-SA 3.0https://en.wikipedia.org/wiki/Cochran's_Q_test • Wikipedia."Rank correlation."CC BY-SA 3.0http://en.wikipedia.org/wiki/Rank_correlation • Wikipedia."Kendall's tau rank correlation coefficient."CC BY-SA 3.0http://en.wikipedia.org/wiki/Kendall's_tau_rank_correlation_coefficient • Wikipedia."Kendall's tau rank correlation coefficient."CC BY-SA 3.0http://en.wikipedia.org/wiki/Kendall's_tau_rank_correlation_coefficient • Wikipedia."rank correlation."CC BY-SA 3.0http://en.wikipedia.org/wiki/rank%20correlation • Wiktionary."concordant."CC BY-SA 3.0http://en.wiktionary.org/wiki/concordant • Wikibooks."Statistics/Testing Data/Spearmans."CC BY-SA 3.0http://en.wikibooks.org/wiki/Statistics/Testing_Data/Spearmans • Wikidot."Ch13 Non-parametric tests - Statistics."CC BY-SAhttp://statistics.wikidot.com/ch13 • Wikipedia."Sign test."CC BY-SA 3.0http://en.wikipedia.org/wiki/Sign_test • Boundless Learning."Boundless."CC BY-SA 3.0http://www.boundless.com//statistics/definition/sign-test Free to share, print, make copies and changes. Get yours at www.boundless.com

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