Analysis of Variance Using SPSS Problem 10.6 - Does the rate of voter turnout vary significantly by the type of election? A random sample of voting precincts displays the following pattern of voter turnout by election type: Assess the results for significance. 1.) ANOVA: Is the overall test significant? ANOVA Turnout Sum Squares Mean Square - 1671.444 Between Groups 3342.889 592.002 Within Groups 7265.417 220.164 Total 608.306 Multiple Comparisons 2) Multiple Comparisons: I know which groups are different from another. We need to examine the results from the post hoc test analysis. Dependent Variable: Turnout LSD Mean Difference 95% Confidence Interval Lower Bound Upper Bound - 22.1575 2.4909 Election Local Only Error State 83.333 0.5756 National 23.5000 0.5756 6.0576 0.000 35.8242 2.4909 -11.1758 22.1575 State Local Only 9.8333 National 13.6667 0.5756 0.031 25.9909 1.3425 National Local Only 23.5000 0.5756 0.000 11.1758 35.8242 State 66.667 0.5756 The mean difference is significant at the 0.05 level. 13.425 25.9909
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The null hypothesis is that there is no significant difference in voter turnout between different types of elections, while the alternative hypothesis is that there is a significant difference. Show more…
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An analysis of variance experiment produced a portion of the accompanying ANOVA table. (You may find it useful to reference the F table.) Click here for the Excel Data File a. Specify the competing hypotheses in order to determine whether some differences exist between the population means. Ho: μA = μB = αC = μD; HA: Not all population means are equal. Ho: μA ≥ μB ≥ αC ≥ μD; HA: Not all population means are equal. Ho: μA ≤ μB ≤ αC ≤ μD; HA: Not all population means are equal. b. Fill in the missing statistics in the ANOVA table. (Round intermediate calculations to at least 4 decimal places. Round "MS" to 4 decimal places and "P" to 3 decimal places.) ANOVA Source of Variation SS df MS F p-value Between Groups 25.08 3 0.0004 Within Groups 92.64 76 Total 117.72 79
David N.
In a hypothesis test for ANOVA, you are interested in the significance of the difference between (samples, population variances, sample variances, population means). You assume that you have (unbiased, isolated, independent, dependent) (unequal, stratified, minimal, random) samples from populations that are (exponentially, unequally, normally, equally) distributed with (random, independent, equal, unequal) variances. The test is designed to be used with (nominal, interval-ratio, ordinal, numerical) level dependent variables. What is the null hypothesis in an ANOVA? a. H0: Not all population means are equal. b. H0: All population means are different. c. H0: All population means are equal. d. H0: Some of the population means are equal. What is the alternative hypothesis in an ANOVA? a. H1: At least one of the population means is different. b. H1: All population means are equal. c. H1: All population means are different. d. H1: Some of the population means are equal. The F-test statistic is formed by taking the (product, sum, ratio) of two separate estimates of (correlation, variance, standard deviation, mean), where the estimate in the numerator is derived from the (sum of the variables, overall average, variation between categories, variation within categories) and the estimate in the denominator is derived from the (sum of the variables, overall average, variation between categories, variation within categories). The sampling distribution is the (p, z, F, t) distribution with (N - k, N - 1, k - 1, N) degrees of freedom within categories and (N - k, N - 1, k - 1, N) degrees of freedom between categories. Once you compute the F(obtained) statistic for your data, you compare its value with F(obtained, dependent, alternative, critical) determined by the given alpha level and the degrees of freedom. If the test statistic is in the critical region, you (confirm, reject, support, reevaluate) the null hypothesis and conclude that there (is/is not) a significant difference between the means.
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A one-way analysis of variance experiment produced the following ANOVA table. (You may find it useful to reference the q table). SUMMARY Groups Count Average Column 1 5 0.89 Column 2 5 1.55 Column 3 5 2.62 Source of Variation SS df MS F p-value Between Groups 9.34 2 4.67 8.81 0.0044 Within Groups 6.33 12 0.53 Total 15.67 14 a. Conduct an ANOVA test at the 1% significance level to determine if some population means differ. multiple choice Reject H0; we can conclude that some population means differ. Reject H0; we cannot conclude that some population means differ. Do not reject H0; we can conclude that some population means differ. Do not reject H0; we cannot conclude that some population means differ. b. Calculate 99% confidence interval estimates of μ1 − μ2, μ1 − μ3, and μ2 − μ3 with Tukey's HSD approach. (If the exact value for nT – c is not found in the table, then round down. Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round your answers to 2 decimal places.) c. Given your response to part b, which means significantly differ?
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