design repeated measurements model

Hi, I've a table t =

      Group      day1_1    day1_2    day2_1    day2_2
    _________    ______    ______    ______    ______

    'Placebo'    12.023    12.719     12.11    12.554
    'Placebo'    11.806    12.186    12.788    12.164
    'Control'    11.763    12.008    11.481    13.325
    'Placebo'    11.703    11.678    12.073    12.234
    'Control'    11.558    12.696    13.692    12.732
    'Placebo'    13.633    13.253    11.347    12.432
    'Placebo'    12.374     12.41     11.49    11.457
    'Placebo'    11.476    11.564    12.542    11.112
    'Control'    12.496    10.661    12.199    12.382
    'Placebo'    12.659    12.863    11.844    11.799
    'Control'    11.611    11.447    12.838    12.592
    'Placebo'    12.524      13.7    11.772    11.387

where each row is a individual. individuals are tested on two following days with the same test (before and after). on the second day group Placebo is treated with a plecabo between measurement 1 and 2. We're seeking for differences placebo vs control that only appear on day two.

here is the rest of my code:

Win = [1 2 1 3];
rm = fitrm(t,'day1_1-day2_2 ~ Group','WithinDesign',Win);
tbl = ranova(rm);

is this correct? Probably not.

Edit: still struggling with that. And we added 'sex' and 'age' to our data. Any comment/help welcome !

Thanks

Dom

Answer 1

[Aditya]

Hi Dominik,

To analyze the differences between the "Placebo" and "Control" groups on the second day using repeated measures ANOVA, you need to ensure that your within-subjects design and between-subjects factors are correctly specified. With the additional factors like 'sex' and 'age', you can include them as covariates in your model.

% Sample data setup
Group = {'Placebo'; 'Placebo'; 'Control'; 'Placebo'; 'Control'; 'Placebo'; 'Placebo'; 'Placebo'; 'Control'; 'Placebo'; 'Control'; 'Placebo'};
day1_1 = [12.023; 11.806; 11.763; 11.703; 11.558; 13.633; 12.374; 11.476; 12.496; 12.659; 11.611; 12.524];
day1_2 = [12.719; 12.186; 12.008; 11.678; 12.696; 13.253; 12.410; 11.564; 10.661; 12.863; 11.447; 13.700];
day2_1 = [12.110; 12.788; 11.481; 12.073; 13.692; 11.347; 11.490; 12.542; 12.199; 11.844; 12.838; 11.772];
day2_2 = [12.554; 12.164; 13.325; 12.234; 12.732; 12.432; 11.457; 11.112; 12.382; 11.799; 12.592; 11.387];
sex = {'M'; 'F'; 'M'; 'F'; 'M'; 'F'; 'M'; 'F'; 'M'; 'F'; 'M'; 'F'};
age = [30; 32; 28; 35; 40; 29; 31; 33; 37; 34; 36; 38];

% Create a table
t = table(Group, day1_1, day1_2, day2_1, day2_2, sex, age);

% Define the within-subjects design
WithinDesign = table({'day1'; 'day1'; 'day2'; 'day2'}, {'before'; 'after'; 'before'; 'after'}, ...
    'VariableNames', {'Day', 'Time'});

% Fit the repeated measures model
rm = fitrm(t, 'day1_1-day2_2 ~ Group + age + sex', 'WithinDesign', WithinDesign);

% Perform repeated measures ANOVA
tbl = ranova(rm);

% Display the results
disp(tbl);

This setup should allow you to investigate the interaction effects and main effects of the treatments, while accounting for covariates like age and sex. Adjust the data and factors as necessary to fit your actual dataset.