I have 3 groups of data which have the same mean as that is total number of participants in each group so in order to make comparison between group of data which statistical test is used?
The test depends on what you want to know. If you want to know whether there are significant differences in the average response between groups, I can promise you the answer is no. A statistical test will tell you the precise probability (and if the difference in means = 0, you are likely in the p > .98 range), but it is clearly no. If you want to know whether there are significant differences in the variance in responses between groups, you can calculate that (I believe it is an F test, check Hinkle, Wiersma, & Jurs (1988) Applied Statistics for the Behavioral Sciences for the computation formula. But there is nothing you can do statistically to make a difference of 0 into any kind of difference.
The test depends on what you want to know. If you want to know whether there are significant differences in the average response between groups, I can promise you the answer is no. A statistical test will tell you the precise probability (and if the difference in means = 0, you are likely in the p > .98 range), but it is clearly no. If you want to know whether there are significant differences in the variance in responses between groups, you can calculate that (I believe it is an F test, check Hinkle, Wiersma, & Jurs (1988) Applied Statistics for the Behavioral Sciences for the computation formula. But there is nothing you can do statistically to make a difference of 0 into any kind of difference.
As Julia suggests, you need to be clear on what you wish to compare between the groups. Are you seeking confirmation the means are the same or are you trying to determine if there are any differences in the properties of the group other than mean (such as difference in variance as Julia suggests)? You don't use stats to get nice numbers, you define a clear question first then use the correct statistical procedure to test that question. Without knowing what you need from the data we can only speculate what you may need.
Indeed julia and james have summerized it well. It's a common practice that people want to see statistical significnce. The tests should all be driven by a clearly stipulated hypothesis. This makes the result interpretation easy and sound, thereby, avoiding confounding any conclusions. Note and beware that there are so many statistical tests iut there to compare groups, most of them aimed at comparing measures of central tendencies while others compare variation. Just ensure you choose them carefully, if not sure, consult with a statistician or someone with experience in inferential statistics. Good luck.
dear .
in my opinion if the means of groups are same so no need to use statistics .
I fully agree with Julia. The mathematical proof of this can be seen in the value of the test statistic, where when the sample means are the same, generally result to zero, which will always be lower than the test critical value.
Well. well, well. I like what Julia said . . . "But there is nothing you can do statistically to make a difference of 0 into any kind of difference"
When you say "three groups of data" it sounds like you mean data populations, not samples taken from a population. As you appear to have recognised, identical means does not mean identical distribution concentration, skewness, maximum/minimum points etc. Each data group could be quite different. A starting point might be to chart the data points into a distribution for each of the three data populations. That would then provide a VISUAL map of the spread of your data which may tell you a lot and even prompt questions or observations you had not thought to ask at the outset. If that is unclear I will try to attach a short article I wrote showing how we use data distributions in risk management, which illustrates the principle.
Article Prioritizing risks for the future using Monte Carlo simulati...
Aftab, if your set of data comes from different populations or experiments and the means are the same (it´s unusual but possible), the groups can be different on variances (Bartlett or Levene test for homogeneity of variances) or their distribution (non-parametric Kruskal-Wallis test), and exploratory data analysis like Chris suggest will give you more information about the distribution, similarities or differences between the groups.
Two groups of means are equal means that both are equal and no need to apply any statistical test.
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