Hi all,
I have collected some data from 3 treatment groups (n=5) with relation to 6 markers of fibrosis. When I was looking to analyse (with GraphPad Prism) these 6 data sets, I noticed that some data sets were normally distributed, while others are normally distributed after logarithmic transformation and one data set was not normally distributed (even after logarithmic transformation).
As I'm not too familiar with this kind of result, I thought to do the following. Please let me know if this is correct or if I have misunderstood.
- For data sets that are normally distributed: Analyse data as is with parametric one-way ANOVA
- For data sets that are normally distributed after logarithmic transformation: Analyse y=ln(x) transformed data with parametric one-way ANOVA
- For data set that is not normally distributed: Analyse data as is with the non-parametric Kruskal-Wallis One-Way ANOVA. (Is there any other way to transform data as a way of normalising it?)
Would it be strange to present these 6 data sets together when some have undergone log transformation where others have not?
What should I do? I would greatly appreciate any advice
Using an oblique rotation in Factor Analysis when data is highly correlated allows for a more realistic representation of the relationships among the underlying factors, leading to more interpretable and accurate results.
you can read this:
Ref (1). Tabachnick, B. G., & Fidell, L. S. (2007). Using Multivariate Statistics (5th ed.). Allyn & Bacon/Pearson Education. Chapter 12 specifically covers Factor Analysis and discusses the use of oblique rotation.
Ref (2) Gorsuch, R. L. (1983). Factor Analysis (2nd ed.). Lawrence Erlbaum Associates. This book provides a comprehensive overview of Factor Analysis, including discussions on rotation methods and when to use oblique rotation.
Zoe Pas, Log transformations do not always guarantee normality. Factors such as extreme outliers or heteroscedasticity may still prevent the data from becoming normally distributed even after transformation. Additionally, while log transformations can improve normality for some types of data, they may not be appropriate or effective for all datasets.
Please consult the following sources:
Chapter 6 provides a detailed discussion on transformations, including the log transformation, and its effects on data distribution.
Book Introduction to Robust Estimation and Hypothesis Testing
This article provides insights into different types of data transformations, including the Box-Cox transformation, which encompasses the log transformation as a special case.
Article Improving your data transformations: Applying Box-Cox transf...
For datasets that are normally distributed:
What to do: Proceed with the parametric one-way ANOVA as planned. This statistical test assumes that the data are normally distributed, which matches your scenario.
For datasets that become normally distributed after logarithmic transformation:
What to do: You can indeed apply a logarithmic transformation to these datasets and then use parametric one-way ANOVA on the transformed data. This approach is valid as long as you specify in your report or presentation that you transformed the data due to non-normality in its original form.
For the dataset that is not normally distributed, even after logarithmic transformation:
What to do: The Kruskal-Wallis test, which you’ve mentioned, is a suitable choice for this dataset. This test does not assume normality and is effective for comparing median differences between groups.
Alternative transformations: Besides logarithmic transformation, you could try other transformations such as square root or Box-Cox transformation to see if they help in achieving normality. However, if transformations do not result in normal distribution, sticking with a non-parametric approach like Kruskal-Wallis is recommended.
Is it okay to present these datasets together?
- Explain clearly: When presenting your results, be transparent about the methods you used for each dataset. Mention which datasets were transformed and which were analyzed in their original form.
- Justify the choice: Briefly explain why different approaches were necessary, emphasizing that these methods were chosen based on the statistical properties of each dataset to ensure the most accurate analysis.
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