Based on a 2018 study, the average elapsed time between when...

Based on a 2018 study, the average elapsed time between when a user navigates to a website on a mobile device until its main content is available was 14.6 seconds. This is more than a $20 \%$ increase from 2017 (searchenginejournal.com, https://www.searchenginejournal.com/). Responsiveness is certainly an important feature of any website and is perhaps even more important on a mobile device. What other web design factors need to be considered for a mobile device to make it more user friendly? Among other things, navigation menu placement and amount of text entry required are important on a mobile device. The following data provide the time it took (in seconds) randomly selected students (two for each factor combination) to perform a prespecified task with the different combinations of navigation menu placement and amount of text entry required. Navigation Menu Position $$ \begin{array}{ccc} & \text { Amount of Text Entry Required } \\ & \text { Low } & \text { High } \\ \text { Right } & 8 & 12 \\ & 12 & 8 \\ \text { Middle } & 22 & 36 \\ & 14 & 20 \\ \text { Left } & 10 & 18 \\ & 18 & 14 \end{array} $$ Use the ANOVA procedure for factorial designs to test for any significant effects resulting from navigation menu position and amount of text entry required. Use $\alpha=.05$.

Based on a 2018 study, the average elapsed time between when a user navigates to a website on a mobile device until its main content is available was 14.6 seconds. This is more than a $20 \%$ increase from 2017 (searchenginejournal.com, https://www.searchenginejournal.com/). Responsiveness is certainly an important feature of any website and is perhaps even more important on a mobile device. What other web design factors need to be considered for a mobile device to make it more user friendly? Among other things, navigation menu placement and amount of text entry required are important on a mobile device. The following data provide the time it took (in seconds) randomly selected students (two for each factor combination) to perform a prespecified task with the different combinations of navigation menu placement and amount of text entry required.
Navigation Menu Position
$$
\begin{array}{ccc}
& \text { Amount of Text Entry Required } \\
& \text { Low } & \text { High } \\
\text { Right } & 8 & 12 \\
& 12 & 8 \\
\text { Middle } & 22 & 36 \\
& 14 & 20 \\
\text { Left } & 10 & 18 \\
& 18 & 14
\end{array}
$$
Use the ANOVA procedure for factorial designs to test for any significant effects resulting from navigation menu position and amount of text entry required. Use $\alpha=.05$.

Key Concepts

Two-Way ANOVA

Two-Way Analysis of Variance (ANOVA) is a statistical technique used to determine the effect of two independent categorical variables on a continuous outcome. It simultaneously tests for the main effects of each factor and the interaction effect between them, making it suitable for designs where participants are exposed to combinations of different levels of each factor.

Significance Level

The significance level (?), often set at 0.05, defines the threshold for rejecting the null hypothesis in hypothesis testing. If the p-value obtained from the ANOVA is lower than this threshold, the effect under consideration is deemed statistically significant, meaning that it is unlikely to be due to random chance.

Replication in Experimental Design

Replication refers to the repeated measurement of the dependent variable under the same conditions (e.g., two randomly selected students for each combination of factors). Replication increases the reliability of the experimental results and provides a better estimate of the within-group variability, which is essential for conducting ANOVA.

Hypothesis Testing

Hypothesis testing in ANOVA involves setting up null hypotheses that assume no differences among group means for each factor (and no interaction) and then using statistical tests to determine if observed differences are unlikely to have occurred by chance. Rejection of the null hypothesis indicates a significant effect of the factor or an interaction effect.

Factorial Experimental Design

A factorial experimental design involves two or more factors, or independent variables, each with multiple levels, arranged so that each level of one factor is combined with each level of the other factors. This design allows researchers to examine not only each factor's main effect on the dependent variable but also any potential interaction effects between factors.

Main Effects

The main effect refers to the individual impact of an independent variable on the dependent variable, averaging across the levels of the other factor. In the context of web design, it would involve assessing whether navigation menu placement or the amount of text entry required, on its own, significantly influences user task performance times.

Interaction Effects

An interaction effect occurs when the effect of one independent variable on the dependent variable differs depending on the level of another independent variable. This concept is crucial because it indicates that the factors do not operate independently, and the combination of specific levels of navigation menu placement and text entry requirements may have a combined effect on performance.

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