At interpreting the results of a data, I noticed that, the results for a given factor are presented at different magnitudes in graphs but the when I apply an ANOVA analysis, no significant difference can be detected. How should I interpret the data so that I can obtain significant differences at ANOVA analysis? Any suggestion may be helpful.
Thanks.
Graphical impressions may depend on the adopted scales and can be misleading. Large scales are likely to give impression of large differences more than small scales. A scale of 1 cm to 1000km is larger than that of 1 cm to 100km and they cannot give the same impression. ANOVA is bound to be more objective than the visual graphical impression.
Graphical presentation of a data without analyzing (ANOVA) does not say much about the data or comparison. ANOVA compares the variability of your data among groups (treatment levels) and within group (replications). If the variability among the treatment levels is higher than the variability within replications, then there exists a significant difference among the treatment. This does not depend on the scale if your measurements are fairly comparable. But there are other steps you probably need to follow before ANOVA. You may need to test assumption of ANOVA, at least two of them: Normality and Uniformity of variance. If these are not met, there is a need to transform the data before doing ANOVA.
For instance, when the variability in the data is so huge (like @Ette Etuk mentioned in his example), the data need to be log10 or Ln transformed before ANOVA. A significant ANOVA tells us that there exists at least one pair of means that ate different from each other. After a significant ANOVA, a mean separation technique should be used to show which specific means are different. Depending on the nature of the data and the types of variability, other transformation or analysis methods may be considered. I hope this helps. Thanks
Your question makes no sense: "How should I interpret the data so that I can obtain significant differences at ANOVA analysis?" - The significance is a feature of your data (relative to a model - in your case the ANOVA model). If this too low (p-value "too large" -> "not significant"), then this is already an interpretation of one aspect of your data, namely that the magnitude of the interesting signal* in the data is too low compared to the statistical noise to be able to make any confident statement about the signal.
Assuming the ANOVA makes sense (e.g., its assumptions are reasonable for your data -see comment above), then the "non-significant result" means that your data is not sufficient to be interpreted w.r.t. the effect of the predictor. Because the statistical noise decreases with sample size, it is usually just a matter of sample size to get a sufficiently small p-value. Thus you have two options: state that the data is inconclusive (="non-significant") or collect more data.
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* here, the signal is the reduction of the residual variance due to the information given by the predictor(s).
if your ANOVA didnt show any significance with respect to among groups(treatments), i do not think there is a way to interprete your data to have significant effect unless you subject your data to another formof statistical analysis
If there are issues about homogeneity, normality, sample size etc. in your data, you may try non-parametric test i.e. kruskall wallis. One more thing, lack of significance does not always mean lack of effect size. You can still work on effect size. After all, there may not be significant difference among groups and there is nothing to about it.
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