Match the ANOVA term to its description: Group of answer choices Sum of Squares Between (SSB) [ Choose ] Always provides an unbiased measure of the population variance. A biased measure of the population variance where treatment effects are present. The average of squared deviations between group means and the overall mean. The ratio used to determine if there are significant differences between groups. Sum of Squares Within (SSW) [ Choose ] Always provides an unbiased measure of the population variance. A biased measure of the population variance where treatment effects are present. The average of squared deviations between group means and the overall mean. The ratio used to determine if there are significant differences between groups. Mean Square Between (MSB) [ Choose ] Always provides an unbiased measure of the population variance. A biased measure of the population variance where treatment effects are present. The average of squared deviations between group means and the overall mean. The ratio used to determine if there are significant differences between groups.
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- **Sum of Squares Between (SSB)**: This measures the variability between the group means and the overall mean. It reflects how much the group means deviate from the overall mean. - **Sum of Squares Within (SSW)**: This measures the variability within each Show more…
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When performing an analysis of variance (ANOVA) test, you are comparing the between sum of squares (SSB) to the within sum of squares error (SSE). What does the SSE represent? The difference between the group means and the overall mean. The difference between the group means. The difference between each value. The difference between each value and the group mean.
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11.1 You are working with an experiment that has a single factor with four groups, and five values in each group. How many degrees of freedom are there in determining: a. the between-group variation? b. the within-group variation? c. the total variation? 11.2 You are working with the same experiment as in problem 11.1. a. If SSB = 60 and SST = 120, what is SSW? b. What is MSB? c. What is MSW? d. What is the value of the test statistic F? 11.3 You are working with the same experiment as in problems 11.1 and 11.2. a. Form the ANOVA summary table and fill in all values in the body of the table. b. At the 0.05 level of significance, what is the upper-tail critical value from the F distribution? c. State the decision rule for testing the null hypothesis that all four groups have equal population means. d. What is your statistical decision? 11.4 You are working with an experiment that has one factor containing six groups with seven values in each. How many degrees of freedom are there in determining: a. the between-group variation? b. the within-group variation? c. the total variation? 11.5 You are conducting an experiment with one factor containing six groups, with five values in each group. For the following ANOVA summary table, fill in all the missing results. 11.6 You are working with the same experiment as in problem 11.5. a. At the 0.05 level of significance, state the decision rule for testing the null hypothesis that all six groups have equal population means. b. What is your statistical decision? c. At the 0.05 level of significance, what is the upper-tail critical value from the Studentised range distribution? d. To perform the Tukey–Kramer procedure, what is the critical range? 11.7 You are conducting an experiment with one factor containing five groups, with 10 values in each group. For the ANOVA summary table below, fill in all the missing results.
In some ANOVA summary tables you will see, the labels in the first (source) column are Treatment, Error, and Total. Which of the following reasons best explains why the within-treatments sum of squares is sometimes referred to as the "error sum of squares"? The within-treatments sum of squares measures random, unsystematic differences within each of the samples assigned to each of the treatments. These differences are not due to treatment effects because everyone within each sample received the same treatment; therefore, the differences are sometimes referred to as "error." The within-treatments sum of squares measures treatment effects as well as random, unsystematic differences within each of the samples assigned to each of the treatments. These differences represent all of the variations that could occur in a study; therefore, they are sometimes referred to as "error." Differences among members of the sample who received the same treatment occur when the researcher makes an error, and thus these differences are sometimes referred to as "error." Differences among members of the sample who received the same treatment occur because some treatments are more effective than others, so it would be an error to receive the less superior treatments. In ANOVA, the F test statistic is the of the between-treatments variance and the within-treatments variance. The value of the F test statistic is . When the null hypothesis is true, the F test statistic is . When the null hypothesis is false, the F test statistic is most likely . In general, you should reject the null hypothesis for .
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