4

I cannot reproduce the rightmost column in the table. It is evident that each row summarizes a table of counts by giving the frequencies $f_i$ of 0, 1, 2, and 3 or more, of which there are $N$ altogether. It uses Maximum Likelihood to fit a Poisson distribution to these frequencies: the Poisson parameter estimates are the numbers $\lambda$ in the $Np(k;\...


2

Suppose I have 10,000 observations precisely from $\mathsf{Gamma}(shape=5, rate=0.1).$ Generate them in R as follows: set.seed(2020); x = rgamma(10^4, 5, .1) (1) Then, because we know the distribution and its parameters, a basic Kolmogorov-Smirnov test in R, finds that my observations are consistent with $\mathsf{Gamma}(shape=5, rate=0.1).$ ks.test(x, ...


2

Shapiro-Wilk test of normality. If you have your choice of goodness-of-fit tests, I think you might get better results with the Shapiro-Wilk test. Here is an example with $n = 200$ observations from $\mathsf{Norm}(\mu=100,\sigma=15).$ This procedure tests whether the data are consistent with some normal distribution. Using R: set.seed(2020) # for ...


1

If I got it right you want to merge all of your columns but one so you can test one specific mood against all the others. This is possible, you end up with a table that has the same number of lines but only two columns. You can then perform a $\chi^2$ test on this table, and you would indeed have $(n-1)\times (2 - 1) = n - 1$ degrees of freedom where $n$ ...


1

Have you tried plotting your data? Both histograms of the 2 summed scores and a scatter-plot of them against each other. When you start summing up responses (even if they are ordinal to begin with) the Central Limit Theorem comes into play and if you sum enough things together that are not too close to boundaries, then you will start to see something that ...


1

The answer is "kind of". Many goodness of fit tests boil down to computing a test statistic which is chi-squared distributed. The most notable example is the deviance goodness of fit test for a poisson regression. In the case where the poisson regression is used to model contingency tables, then the two test statistics are the same. But, I digress. Let'...


Only top voted, non community-wiki answers of a minimum length are eligible