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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
 ... ... @@ -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