Respond to at least two of your fellow students' posts in a substantive manner and provide information
Question:
Respond to at least two of your fellow students' posts in a substantive manner and provide information that they may have missed or may not have considered regarding the application of ANOVA tables in business and economics. Do you agree with their conclusions? Why or why not?
Post 1:
For this analysis ANOVA is used to test variances among groups as part of a major revision of the homepage. Descriptive statistics will help to analyze if there are significant differences among the groups. The data will help to conclude the time spent by visitors to the Triple T Website based on the background colors, and font. The analysis from the Excel chart produces the following results. The mean / variance for the background colors are: White background = 271.47 / 2182.40; Pink background = 231.5 / 2567.57; Green background = 247.7 / 2332.7. The white background has the highest mean which I understood it had the highest time spent by the visitors with the lowest variance. The mean / variance for the fonts are: Arial= 272.17 / 2806.98; Calibri = 242.8 / 2947.34; Tahoma = 235.7 / 1391.11. Arial has the highest mean; the analysis suggest that the Arial font has the highest time spent by visitors. The variance for Tahoma font has the smallest variance compared to the other fonts. The data also concludes that visitors spent more time with the combination of white background and arial font. White background has a cleaner look and arial is a distinguish and popular choice among the three fonts.
The P value of 0.05, concludes that the hypothesis test for the three backgrounds is 0.004624, resulting in no significant effect. Based on the evidence is recommended to adopt the white background and arial font as they generate the highest mean time spent by the Triple T website visitors.
Post 2:
TourisTopia Travel (Triple T) wants to run a test for their webpage to determine whether the background or font and its combinations have an impact on the visitors' time spent on their website. After running an ANOVA: Two-Factor with Replication statistics, it seems that visitors spend most of the time on the homepage with the white background and the Ariel font. Even with the other two background colors, Ariel font seems to be the most liked by visitors.
TourisTopia Travel has utilized a controlled method to obtain the data for this experiment. The different combinations of prototype homepages and how the visitors are randomly directed to their preferred combination generated the data needed for this experiment.
The null hypothesis for the background colors assumes that the time visitors spend on each of the background colors is equal. The alternative hypothesis assumes at least one significant difference between the time visitors spend on each of the background colors. If the P value is less than alpha, we reject the null hypothesis, and the alternative hypothesis is supported. Since the P value is 0.0046, it is less than the level of significance (0.05). Therefore we reject the null hypothesis.
The null hypothesis for the fonts assumes that the time visitors spend on the homepages is equal for all three fonts. The alternative hypothesis assumes that visitors spend more time on at least one of the fonts. Since the P value is 0.0068 (rounded to four decimals) it is less than 0.05, therefore we reject the null hypothesis.
The null hypothesis for the combinations of background colors and fonts assumes that the time visitors spend on each of the combinations is equal. The alternative hypothesis assumes that visitors spend more time on at least one of the combinations of background color and font. Since the P value is 0.2269, it is greater than alpha therefore the null hypothesis is supported, and we fail to reject it.
Based on the ANOVA test results, the white background with the Ariel font had the highest average. My recommendation is for TourisTopia Travel to use this combination for their homepage.
Reference:
Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., Cochran, J. J., Fry, M. J., & Ohlmann. J. W. (2021).Essentials of modern business statistics with Microsoft Excel(8th ed.). Cengage Learning
Expert Answer:
