Hi Sophie,

for the descriptive statistics an ANOVA would be appropriate in this case, because the ANOVA compares the observed differences among the sample means so that inferences sbout differences in corresponding population means can be made.

For the visualtization I would indicate using boxplots.

Hope that helps.

If I understand well your problem, you have a lot of people and for each, you got a time-series of weight, its gender and its date of start diet. If it is like that and anova will be useless. You can compute several inhomogeneity tests for each time-series and then compare (if there is a breakpoint) the timing with the date of start diet. Also, a boxplot per gender of the mean difference before and after the start of the diet will be useful.

Boxplot is ok if n per group > 20 or so (the boxplot shows 5 summary statistics per group; you should have some reasonable amount of data for that many statistics). For smaller sample sizes I would show all individual values in a scatterplot. It can be used also for larger sample sizes; I would always prefer to see the actual data rather than a summary.

Examples:

• https://lh6.googleusercontent.com/-pQ80HZSJVI0/TYqJztV1bMI/AAAAAAAAABU/QZbtVgv7r74/s1600/beeswarmfig00.png
• https://seaborn.pydata.org/_images/seaborn-swarmplot-6.png
• https://rkabacoff.github.io/datavis/datavis_files/figure-html/beeswarm1-1.png

Interesting that your example is the same as Lord's in his "Lord's Paradox." I'd look to the plots for those (btw, I am assuming you have data for each individual pre and post). Attached is a plot (that as @Jochen describes is preferable, @Jan and @Santiago, how do you plan to allow the boxplots to show what will be a large association between the two measurements) from https://www.degruyter.com/view/journals/edu/2/1/article-p45.xml . It allows you to compare the mean gain scores (a), the conditional differences (b, the ancova approach), look at the association of the variables, and the distributions. There are some cute things in here, like the line at b going from blue to red, that I assume can be done in the packages that you mention, but don't know.

I made this plot, and I like it, but would be interested in other people's thoughts.

You may try with t-test paired two sample mean