Paired Comparison Sentiment Scores
Table 1: Goodness-of-fit test statistic χ2 and p-values P(\em value>χ2) for the different score estimators. The last row gives the corresponding threshold for rejecting the null hypothesis that the model produced the result at a significance level α=0.05.
['[EMPTY]', '[ITALIC] G=600 LSQ', '[ITALIC] G=600 LSQ', '[ITALIC] G=600 ML', '[ITALIC] G=600 ML', '[ITALIC] G=800 LSQ', '[ITALIC] G=800 LSQ', '[ITALIC] G=800 ML', '[ITALIC] G=800 ML']
Surprisingly, the LSQ estimators lead to a clearly better goodness-of-fit than the ML estimators, with the ML estimators even yielding such a high value for χ2 that the model would be rejected as unlikely. As usual for χ2 tests, the result varies with the number of groups however, and the p-values are different for different numbers of groups G. Nevertheless, the relative values of χ2 for fixed G allow to compare different estimation methods, and in all cases the LSQ estimator yielded a clearly better fit. With respect to the distribution function F, the uniform distribution provides an impossible LSQ fit because it leads to wins with zero probability in some groups. χ2 is smallest for the logistic choice for F, which is therefore the model which conforms best to the observed test person answers.