# Statistical difference between multiple groups using percentage data

I have 3 groups of data. Group 1 contains 11 values, group 2 contains 7 and group 3 contains 11 values. The values are in the form of 'percentage change over time'.

I would like to test to see if the groups averages are statistically different from one another. It seems like Chi-squared would work but the data is continuous. Any help would be greatly appreciated.

It seems that your analysis is more amenable to ANOVA 1-way. You want to test equality of means against the alternative that at least one group has a different mean.

Assuming approximate normality of the data (but ANOVA is quite robust against non-normality), independence of observations and same variances (a much more critical assumption), this would be a simple ANOVA analysis, were it not because the data is unbalanced (not same number of observations per group).

You can work around this using a simple regression model such as $$y_{ij} = \beta_i + \epsilon_{ij}$$ where $y_{ij}$ is the $j$-th observation in the $i$-th group and testing $H_0: \beta_1 = \beta_2 = \beta_3$ agains the alternative that at least one is different from the rest.

• Thank you very much for your help - could I just ask how I would go about carrying out that type of regression? Would I do the regression then the ANOVA? – NAR Jul 20 '18 at 8:47
• No, you just perform the regression and test equality of the three coefficients $\beta_1$, $\beta_2$ and $\beta_3$. – F. Tusell Jul 20 '18 at 9:03