# Promoting Optimal User Experience through Composite Challenge Tasks
## 5 Flow Experiment
### Results  
The Student's \(t\)-test was applied to check the statistical significance of the experiment. This test is used for verifying a statistical hypothesis about the mean of a normal population with dependent samples of a relatively small size [26]. As the data is dependent--i.e., all the participants played both versions but in different order--the Student's \(t\)-test was split in two parts: in the first the participants played first the BG and then the NBG versions and in the second played the reversed order. These results are shown in Tables 8 and 9 respectively. The parameter \(t\) is the computed \(t\) statistic, as explained below, and \(df\) stands for degrees of freedom. The significance level was \(\alpha=0.05\) and the analysis was performed using the GNU PSPP software [27]. The Student's \(t\)-test holds only when the data has a normal distribution. The Shapiro-Wilk test [28] is used to verify this latter condition for small samples (less than 50). If the Sig. value of the Shapiro-Wilk test is greater than 0.05, the data is normal; otherwise the data deviate significantly from a normal distribution. The Sig. value for the present data is 0.952, hence it follows a normal distribution and the Student's \(t\)-test is applicable. The tested hypothesis is accepted--and the null hypothesis is rejected--if the bilateral significance or \(p\)-value is \(\leq\) 0.05 and vice versa. The \(p\)-value in Table 8 is 0.036; hence, there is a statistical significance to support that the average in the global BG flow score is higher than the average of the NBG when the users played the game in this order. The mean is calculated by subtracting the mean of the second group from the mean of the first. The sign of the mean difference corresponds to the sign of the \(t\) value. A positive \(t\) value, as in this case, indicates that the mean for the BG is significantly greater than the mean for NBG. \begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline  & \multicolumn{6}{c}{**Related Differences**} \\ \hline  & \multicolumn{2}{c}{**Mean**} & \multicolumn{2}{c}{**Deviation Standard**} & \multicolumn{2}{c}{**Standard Error**} & \multicolumn{2}{c}{**95\% Confidence Interval for the Difference**} & \multicolumn{2}{c}{**t**} & \multicolumn{2}{c}{**df**} & \multicolumn{2}{c}{**Bilateral Significance**} \\ \cline{5-8}  & & & & & **Lower** & **Upper** & & & \\ \hline
**BG–NBG** & 0.24750 & 0.27059 & 0.09567 & 0.2128 & 0.47372 & 2.587 & 18 & 0.036 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Result of the Student’s \(t\)-test for the BG–NBG group. \begin{table}
\begin{tabular}{l l l l l l l l l l} \hline \hline  & \multicolumn{6}{c}{**Related Differences**} \\ \hline  & \multicolumn{2}{c}{**95\% Confidence Interval**} & \multicolumn{2}{c}{**df**} & \multicolumn{2}{c}{**Bilateral Significance**} \\ \cline{5-8}  & \multicolumn{2}{c}{**Mean**} & \multicolumn{2}{c}{**Deviation Standard**} & \multicolumn{2}{c}{**Standard Error**} & \multicolumn{2}{c}{**f**} & \multicolumn{2}{c}{**df**} & \multicolumn{2}{c}{**Bilateral Significance**} \\ \cline{5-8}  & & & & **Lower** & **Upper** & & & & \\ \hline
**NBG–BG** & \(-0.07000\) & 0.36174 & 0.12790 & \(-0.372242\) & 0.23242 & \(-0.547\) & 18 & 0.601 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Result of the Student’s \(t\)-test for the NBG–BG group. However, Table 9 shows that the \(p\)-value is 0.601 and null hypothesis is accepted. This indicates that there is no statistical significance to affirm that the average in the global BG flow score is higher than the average of the NBG when the users played the NBG game first. These results accord with the intuition that playing first a balanced game improves flow, and when the setting changes to an unbalanced one the flow is diminished. The intuition on the second setting should be that the flow is low playing a non-balanced game, but it should improve when the balanced one is played afterwards. However, the result is not significant in the latter order.