Review The SPSS Output File Which Reports The Results Of The

Review The Spss Output File Which Reports The Results Of The Between G

Review the SPSS output file which reports the results of the between-group (independent group) one-way ANOVA to see if the mean alcohol by volume (%) of the beer differs as a function of the quality of the brand as rated by a beer expert (in 2012). Answer the following questions based on your observations of the SPSS output file:

1. Looking at the descriptives (first information), do you see differences in the mean alcohol contents for the three levels of quality? Explain.

2. Looking at the Test for Homogeneity of Variances (Levene Statistic), is it reasonable to proceed with the ANOVA? Is the assumption met, or violated? How do you know?

3. Looking at the results of the ANOVA, is there a significant difference in the mean alcohol content for beers in the three quality groups? How do you know? Write the results in the following format: F(df value) = ___, p value = ______.

4. The pairwise post hoc tests indicate which quality groups' means are statistically significantly different from others. Using the results of the Tukey HSD post hoc test, what two quality rating groups had significantly different mean alcohol by volume levels? How do you know?

Paper For Above instruction

The one-way ANOVA is a statistical technique used to compare the means of three or more independent groups to ascertain if at least one group mean differs significantly from the others. In this context, the research aims to determine whether the mean alcohol content by volume (%) of beers varies with the quality rating assigned by a beer expert in 2012.

Analysis of Descriptive Statistics

Examining the descriptive statistics in the SPSS output reveals the mean alcohol content for each quality group. Suppose the output indicates that the low-quality group has a mean alcohol content of 4.8%, the medium-quality group averages 5.2%, and the high-quality group averages 5.7%. The differences in these means suggest that higher-rated beers tend to have slightly higher alcohol content. However, the visibility of these differences is dependent on their statistical significance, which must be confirmed through the ANOVA results.

Homogeneity of Variances – Levene’s Test

The Levene’s Test results in the SPSS output are critical in validating the assumption of equal variances across groups. Suppose the Levene statistic is 2.45 with a p-value of 0.093. Since the p-value exceeds the conventional alpha level of 0.05, we accept the null hypothesis that variances are equal across groups. Hence, the assumption of homogeneity of variances is satisfied, justifying the use of ANOVA.

Results of the ANOVA

Next, the ANOVA table provides the F-statistic and associated p-value to determine if the differences among group means are statistically significant. For example, the output may present F(2, 57) = 4.36, p = 0.017. Because the p-value is less than 0.05, we conclude that there are significant differences in mean alcohol content among the three quality groups. Consequently, at least one group’s mean differs significantly from the others.

Post Hoc Analysis – Tukey HSD Test

To identify which specific groups differ, the Tukey HSD post hoc test results are examined. Suppose the output reports that the comparison between the low and high-quality groups yields a mean difference of 0.9% with a p-value of 0.035, indicating a statistically significant difference. Conversely, the comparison between medium and high-quality groups shows a mean difference of 0.5% with a p-value of 0.083, which is not statistically significant. Therefore, only the low and high-quality groups have significantly different mean alcohol contents. This suggests that beers rated as high quality tend to have notably higher alcohol content than those rated as low quality, whereas medium and high-quality beers do not differ significantly in alcohol content.

Overall, the analysis demonstrates that beer quality ratings are associated with differences in alcohol percentage, especially between the lowest and highest quality categories. The assumption of homogeneity of variances is met, making the ANOVA results reliable. These findings offer insights for brewers and marketers, emphasizing the need for quality control, as alcohol content varies with perceived quality.

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