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Understanding Nonparametric Statistics: Chi-Square Tests and Their Applications

In Chapter 16, we explore the realm of nonparametric statistics, focusing on Chi-Square tests and their applications. Learn when to utilize these tests to analyze data that doesn't meet parametric assumptions. This chapter covers the fundamental concepts of Chi-Square tests, including one-sample goodness-of-fit and two-sample tests, alongside the critical hypotheses needed for analysis. Additionally, discover how to compute Chi-Square values, interpret results, and the significance of p-values. Gain valuable insights into using SPSS for Chi-Square calculations and other nonparametric tests.

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Understanding Nonparametric Statistics: Chi-Square Tests and Their Applications

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  1. Part IVSignificantly DifferentUsing Inferential Statistics Chapter 16     What to Do When You’re Not Normal: Chi-Square and Some Other Nonparametric Tests

  2. What you will learn in Chapter 16 • A brief survey of nonparametric statistics • When they should be used • How they should be used

  3. Introduction • Parametric statistics have certain assumptions • Variances of each group are similar • Sample is large enough to represent the population • Nonparametric statistics don’t require the same assumptions • Allow data that comes in frequencies to be analyzed…they are “distribution free”

  4. One-Sample Chi-Square • Chi-square allows you to determine if what you observe in a distribution of frequencies is what you would expect to occur by chance. • One-sample chi-square (goodness of fit test) only has one dimension • Two-sample chi-square has two dimensions

  5. Computing Chi-Square • What do those symbols mean?

  6. More Hypotheses • Null hypothesis • Research hypothesis

  7. Computing Chi Square

  8. Computing Chi Square: You Try!! Critical Value pg. 364;

  9. Computing Chi Square: You Try!!

  10. So How Do I Interpret… • x2(2) = 20.6, p < .05 • x2 represents the test statistic • 2 is the number of degrees of freedom • 20.6 is the obtained value • p < .05 is the probability

  11. Using the Computer • One-Sample Chi Square using SPSS

  12. SPSS Output • What does it all mean?

  13. Other Nonparametric Tests

  14. Glossary Terms to Know • Parametric • Nonparametric • One-sample Chi Square

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