ANOVA is used when all observations are independent. When you have measured some observations on the same individuals they are no longer independent and ANOVA cannot be used anymore. One way out of this is to use repeated measures ANOVA. An example would be e.g. if your experimental units are plants and you have measured something every hour for a whole day. Obervations from a single plant are related to each other and therefor not independent.

ANOVA is used when all observations are independent. When you have measured some observations on the same individuals they are no longer independent and ANOVA cannot be used anymore. One way out of this is to use repeated measures ANOVA. An example would be e.g. if your experimental units are plants and you have measured something every hour for a whole day. Obervations from a single plant are related to each other and therefor not independent.

ANOVA is used to compare 3 or more groups (between groups means) on a one continuous variable. It is like independent sample ttest, but here we have 3 or more groups Repeated measure ANOVA is a comparison (within group) changes over time, it is like pair wise comparison in ttest, but here we have 3 or more times

Analysis of Variance (ANOVA) is a statistical method used to test differences between two or more means. It may seem odd that the technique is called "Analysis of Variance" rather than "Analysis of Means." As you will see, the name is appropriate because inferences about means are made by analyzing variance.

One addition to what Hageman said: You should check to make sure that the correlation is present. I measure something on a person every hour for a whole day. The correlation is nearly certain. I do this again but measure on the same person once per day for 24 days, or once a month for 24 months, or once per year for 24 years. I would keep going to once per decade but people don't live that long. At some point the variability in the between-sample interval is such that any correlation is no longer detectable with any reasonable sample size. At that point, you will be better off not using repeated measures.

Differences between Simple ANOVA and Repeated Measures ANOVA

Please let me know if these references/sites are helpful to you:

1. Repeated Measures ANOVA - Understanding a Repeated

https://statistics.laerd.com/statistical-guides/repeated-measures...

A repeated measures ANOVA is also referred to as a within-subjects ANOVA or ANOVA for correlated samples. All these names imply the nature of the repeated measures ANOVA, that of a test to detect any overall differences between related means.[PDF]

2. Chapter 14: Repeated Measures Analysis of Variance (ANOVA)

www.skidmore.edu/~hfoley/Handouts/_baks/S.Ch14.pdf.0002.3afe.bak

Ch. 14 Repeated Measures ANOVA - 1 Chapter 14: Repeated Measures Analysis of Variance (ANOVA) First of all, you need to recognize the difference between a repeated ... Authors: Brian Everitt Affiliation: King S College London About: Mauchly's sphericity test · Multivariate analysis of variance · Repeated measures de…

Dennis

Dennis Mazur

Repeated measures ANOVA is the equivalent of the one-way ANOVA, but for related, not independent groups, and is the extension of the dependent t-test. A repeated measures ANOVA is also referred to as a within-subjects ANOVA or ANOVA for correlated samples.

Thank you all! It was really nice to have different explanations, and helpful for me to understand more.

I think J. A. Hageman is right.