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Updated Results section: hypothesis 1

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CHIpaper/MarketPaper.tex View file @ d64f6c2
... ... @@ -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