Exam 11: Hypothesis Testing With Chi-Square

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A goodness-of-fit test tests can use χ2 to determine whether a program or policy exceeds a standard or norm.

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Practical significance examines the strength of relationships.

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(Optional, Appendix): When adding a control variable causes a previously significant relationship to become insignificant, the result is called explanation.

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(Optional, Appendix): other nonparametric examples include Kendals τ-b, Goodman-Kruskal's τ and the McNemar test.

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We first determine practical significance and then determine statistical significance.

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The critical value is compared against the test statistic for the purpose of hypothesis testing.

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The last step in hypothesis testing is looking up the critical value of test statistics.

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A 5% level of significance suggests a higher level of confidence than a 1% level of significance.

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The null hypothesis is stated in Greek letters because the null hypothesis refers to relations in the population.

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Kendall's τ-c can vary from +1.00 to -1.00. Scores of less than |0.25| indicate weak relationships; scores between |0.25| and |0.50| indicate moderate relationships; and scores of greater than |0.50| indicate strong relationships.

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The concept of statistical significance relates to the matter of confidence.

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When two variables are unrelated to each other, the χ2 test statistic is large.

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Practical significance examines by how much one variable changes as a result of changing another.

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Degree of freedom is a concept associated with determining the critical value.

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It is easier to reject the null hypothesis with a large sample than with a small sample.

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Generally, a critical value will be larger at the 1% level of significance than at the 5% level of significance.

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Kendall's τ-c is a nonparametric statistic which should never be used because it is less useful than χ2.

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A relationship that is reported as being significant at "p = 0.945" is statistically significant.

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When using the χ2 test statistic, "expected" frequencies are those that researchers observe in the sample.

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The χ2 test statistic is useful for determining the direction of relationships.

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