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### Updated Results section: hypothesis 1

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CHIpaper/Figs/averageSeqLength.pdf
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CHIpaper/MarketPaper.pdf
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CHIpaper/MarketPaper.tex
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... | ... | @@ -52,6 +52,7 @@ |

52 | 52 | %ADDED |

53 | 53 | %\usepackage[pdftex]{graphicx} |

54 | 54 | \def \halfWidth {0.5\textwidth} |

55 | +\usepackage{siunitx} | |

55 | 56 | %\hypersetup{pageanchor=false} |

56 | 57 | %%%%%%%%%%%% |

57 | 58 | |

58 | 59 | |

59 | 60 | |

60 | 61 | |

... | ... | @@ -397,21 +398,53 @@ |

397 | 398 | %No market & 4.40 & 4.90\\ |

398 | 399 | %\end{tabular} |

399 | 400 | |

400 | -\begin{figure*}[htbp] | |

401 | +\begin{figure}[htbp] | |

401 | 402 | \begin{center} |

402 | 403 | \includegraphics[width=\halfWidth]{Figs/averageSeqLength.pdf} |

403 | 404 | \vspace{0cm} |

404 | 405 | \caption{Average sequence length for every game session, not considering the super circles and considering the super circles (e.g. a super circle |

405 | - of level 2 in a sequence counts for 2 circles). 'All' and 'All (2)' | |

406 | - represent the two tests with all the features on, 'No skills' represents the test without the skills, 'No market' represents the test without the | |

407 | - market and 'No chal.' represents the test without the challenges. | |

406 | + of level 2 in a sequence represents 10 circles in the solution). A, A-2 and A-3 represent the tests with all the features on; NS, NS-2 and NS-3 represent the | |

407 | + tests without the skills; NM, NM-2 and NM-3 represent the tests without the market; NC, NC-2 and NC-3 represent the tests without the challenges. | |

408 | 408 | }\label{fig_averageSeqLength} |

409 | 409 | \end{center} |

410 | -\end{figure*} | |

410 | +\end{figure} | |

411 | 411 | |

412 | -As shown in Figure~\ref{fig_averageSeqLength}, the game session in which we had the lowest average of sequence lengths (for all the sequences sold by | |

413 | -all the players) is the one that was played without the market, with an average of $4.40$. Even if we consider the super circles (the special circles that count | |

414 | -for more than one in the scoring function), the average sequence length is still the lowest for that session, with a value of $4.90$. Notice that even in | |

412 | +As shown in Figure~\ref{fig_averageSeqLength}, the three game sessions in which we had the lowest average of sequence lengths (for all the sequences sold by | |

413 | +all the players) are the ones that were played without the market, with averages of $4.40$ for NM, $4.19$ for NM-2 and $4.63$ for NM-3. | |

414 | +Even if we consider the super circles (the special circles that are actually 10 circles combined into one), the average sequence lengths for those | |

415 | +three sessions are still the lowest ones, with values of $4.90$ for both NM and NM-2, and $5.40$ for NM-3. | |

416 | + | |

417 | +%We performed statistical tests to make sure that the observed differences in the means are statistically significant. | |

418 | +Since the distribution of the | |

419 | +lengths for all the sequences sold to the system during a game session do not follow a normal distribution, we used a non-parametric test (Kruskal-Wallis) to | |

420 | +verify if the sequence lengths of the different game sessions seem to come from the same distributions. | |

421 | +The Kruskal-Wallis test revealed a significant effect of the game conditions on the sequence lengths without considering super circles | |

422 | +(${\chi}^2(2) = 1391.7$, $p < \num{2.2e-16}$) and also when considering super circles (${\chi}^2(2) = 1388.4$, $p < \num{2.2e-16}$). | |

423 | + | |

424 | +We then made a post hoc test (Dunn's test) to do pairwise comparisons between all the groups. With or without considering super circles, all the game conditions | |

425 | +were shown to be significantly different ($p < 0.01$), except a few shown in table~\ref{tab_Dunn}. Note that the strongest similarities are found between | |

426 | +the three 'All' groups and the three 'No market' groups. Some of the 'No skills' experiments are found to be similar to the 'All' groups, which could indicate | |

427 | +that the presence of the skills have a very limited effect on the sequence length. The NC experiment is found to be similar to two 'No market' groups, but that | |

428 | +can be explained by the fact the players for the NC experiment were very weak (see section~\ref{sect_hyp4}). | |

429 | + | |

430 | +\begin{table}[h] | |

431 | + \caption{Similar groups of sequence length distributions, as reported by Dunn's test. An 'n' in the table represent a similar pair when not considering | |

432 | + super circles, and an 's' in the table represents a similar pair when considering super circles.}\label{tab_Dunn} | |

433 | +\begin{center} | |

434 | +\begin{tabular}{c|cccccccc}\hline | |

435 | + & A-2 & A-3 & NS & NS-2 & NS-3 & NM & NM-2 & NM-3\\\hline | |

436 | + A & n/s & n & & n/s & & & & \\ | |

437 | + A-2 & & n & & n/s & & & & \\ | |

438 | + A-3 & & & n/s & & & & & \\ | |

439 | + NC & & & & & & n & & n/s \\ | |

440 | + NC-3 & & & & & n/s & & & \\ | |

441 | + NM & & & & & & & n/s & n \\\hline | |

442 | +\end{tabular} | |

443 | +\end{center} | |

444 | +\end{table} | |

445 | + | |

446 | +%WILL HAVE TO MOVE THE FOLLOWING SENTENCES TO HYPOTHESIS 4 SECTION | |

447 | +Notice that even in | |

415 | 448 | the two sessions for which we had the smallest total experience (see Figure~\ref{fig_totalXP}), both averages of sequence lengths were larger than the averages |

416 | 449 | of the game session without the market. Those observations confirm that the market is helping the players in the creation of longer sequences. |

417 | 450 | |

... | ... | @@ -633,7 +666,7 @@ |

633 | 666 | doing actions that are not specific to a certain subset of colors. Even if the market should be helpful in finding circles with the required |

634 | 667 | subset of colors, it seems highly probable that the players felt that this type of challenge was too hard and never tried to complete it. |

635 | 668 | |

636 | -\subsection{Testing hypothesis 4: relationship between total experience and percentage solved} | |

669 | +\subsection{Testing hypothesis 4: relationship between total experience and percentage solved}\label{sect_hyp4} | |

637 | 670 | %Coming back on the 4 tests, total game xp vs percentage of problem solved |

638 | 671 | As mentioned in the Experiments section, the initial plan was to measure the impact of each feature by analyzing how much of the problem can be solved |

639 | 672 | by the players in each of the game sessions. Interestingly, we observed a larger than expected variance in the participants' skills which made it practically |