# Data visualization on original or transformed data?

I have a data set with two independent variables (species and life-stage) and one dependent variable (concentration of a protein). There are 5 replicates within each level (please see table below). I want to perform two tasks with this data: (1) visualize data as bar graph where mean value of independent variable (concentration of protein) will be on y axis and one independent variable will be on x axis (life-stage) and the data will be faceted by second independent variable (species). Please see the sample figure below. (2) Apply two-way ANOVA on this data. The original data did not meet equal variance assumption; hence, I had to square root transform the data before applying two-way ANOVA. Is it acceptable if I use the original data for creating the graphs but the transformed data for statistical analysis?

Sample Table:

  Species | Life-stage | protein concentration (nmol) | square root transformed |  |
---------|------------|------------------------------|------------------------|--|--
rt      | early      |                            5 |                2.24    |  |
rt      | early      |                            7 |                   2.65 |  |
rt      | early      |                            6 |                   2.45 |  |
rt      | early      |                            4 |                      2 |  |
rt      | early      |                            5 |                   2.24 |  |
rt      | late       |                            8 |                   2.83 |  |
rt      | late       |                           10 |                   3.16 |  |
rt      | late       |                            6 |                   2.45 |  |
rt      | late       |                            8 |                   2.83 |  |
rt      | late       |                           10 |                   3.16 |  |
ws      | early      |                            7 |                   2.65 |  |
ws      | early      |                            8 |                   2.83 |  |
ws      | early      |                            5 |                   2.24 |  |
ws      | early      |                            5 |                   2.24 |  |
ws      | early      |                            8 |                   2.83 |  |
ws      | late       |                           14 |                   3.74 |  |
ws      | late       |                            7 |                   2.65 |  |
ws      | late       |                           17 |                   4.12 |  |
ws      | late       |                           10 |                   3.16 |  |
ws      | late       |                           14 |                   3.74 |  |


Figure: bar graphs represent mean +- SEM (non transformed values)

Below is two way ANOVA on square root transformed data:

As you can see here that I have created graph with original data (non-transformed) but I have applied two-way ANOVA on square root transformed data (because equal variance test was failing on original data). Is this approach correct? Thank you!

• What is the goal of your visualization ? Jun 3 '19 at 7:02
• Just to show the trend of data. I want to create bar graphs with mean values of the dependent variable on y axis against independent variables on x axis. Jun 3 '19 at 7:40
• You should specify which variables you are transforming and which ones you want to plot on this graph and, ideally, add some actual plots to the question so we understand what you are referring to. Right now, we don't know anything about your variables or about any trends that you say exist, so the question is pretty vague. Jun 3 '19 at 7:52
• Thanks! I have modified the question and added some details. Jun 3 '19 at 9:02