I think, you should first define your dependent and predictor variables. If you want to measure the diffrence of means of a continuous variable (dependent) in more than two groups (predictor), u can use ANOVA. ANOVA is a statistical technique that assesses potential differences in a continuous dependent variable by a nominal-level predictor variable having 2 or more categories. For example, you want to compare the mean blood glucose level in three groups of individuals.

With pair-wise t-tests, ideally using a pooled variance estimate (if variance homogeneity can be assumed).

@Jochenrs Wilhelm; sir is there any other test than pair-wise t-test because by using paired t-tests, I am able to find the significance of difference between pairs of variables but how can I conclude that all the four variables are significantly different from each other.

Don't chose a test which results fufill your hopes. Use the test that is approriate for the problem.

Given the assumptions of the t-test are sensible for your data, the t-test is the only and the most powerful test for mean differences. If it does not give you small enough p-values, then your data simply is not sufficiently conclusive.

Laxmi Narayan sir

                                 As you have 4 variables and wants to check the significance of difference you can apply ANOVA after conforming the assumptions for applying ANOVA.... ANOVA will clearly tell you which variable differ significantly from which one.... as per your requirement ANOVA will perform better.... 

If you want to test the significance of difference in MEANS for more than two levels (variables), you can use ANOVA. BUT, the assumptions: (1) Data must be Gaussian (Normal) (2) Variations are not statistically significantly different at four levels (variables), i.e. HOMOSKEDASTICITY (3) NO auto-correlation is present in the data, must be satisfied.

If your test statistic (F-statistic in case of ANOVA) is significantly high or p-value is lower than LOS (5% or 1%, as you choose), then it implies that the mean of at least one level (variable) is significantly different from that of others.

Then, you can use pair-wise tests (taking each combination of 2 variables out of 4) to identify which ones are similar and which ones are different. But remember that you can either use the same LOS or use a corrected LOS for multiple paired tests. There are several methods for calculating corrected LOS such as Bonferroni's adjustment, Holm's adjustment, Fisher's LSD, and Tukey's HSD. 

Fisher exact test for categorical variables

ANOVA test for continuous variables if the data is normally distributed, otherwise the alternative non-parametric test should be used.

I think, you should first define your dependent and predictor variables. If you want to measure the diffrence of means of a continuous variable (dependent) in more than two groups (predictor), u can use ANOVA. ANOVA is a statistical technique that assesses potential differences in a continuous dependent variable by a nominal-level predictor variable having 2 or more categories. For example, you want to compare the mean blood glucose level in three groups of individuals.

Dear Laxmi

In the case that your data meet the ANOVA assumptions, you can use SPSS or SAS Software and perform multiple comparisons ( Tukey, Duncan, ... ) for the means of these variables.

Good Luck

Kruskal-Wallis rank test Anova may be worth mentioning in non normal heteroskedastic cases

@Monyer,

Not your fault, but the link gives a really bad practice to teach.

On page 3 the author argues why one would use ANOVA at all:

Why not just test all possible pairs of sample means using the two-sample t-test? [...] A more serious problem is that this procedure is likely to lead to an incorrect conclusion [...] P(reject in at least 1) = 1−0.857=0.143 = P(type I error). This is much larger than 0.05!

Then the ANOVA procedure is described, ending in the conclusion on page 20:

We conclude that the population means are not all equal to each other, but we cannot be more specific than this. We often want to conduct additional tests to determine where the differences lie.

Isn't that "back to the start"?! But wait, there might still be some use of ANOVA. So let's read on:

Many different techniques for multiple comparisons exist — they usually involve

testing each pair of means individually while controlling the overall level of significance

α.

Bingo! ANOVA is useless. There are multiple pairwise tests that do control the "overall level of significance" (that's what the author was giving as argument to do ANOVA in the beginning). If you read what these procedures are you will find that these are all variations of t-tests, some use pooled variance estimates, some don't, som control the error-rate by "studentized" statistics, others by multiplying the p-values... Eventually, the ANOVA was not needed at all. ONLY the pairwise tests (that do correct for multiple testing) are needed.*

Allegorically, the red line goes as follows:

If you want to fly, you need wings, so you should use a nice machine and paint all doors black and then sort the pencils in your box by weight. After having done all this you still can't fly. But luckily, there are wings, so take some and fly.

*ANOVA can be abused(!) to control the overall error-rate in the very special case of 3 groups. When the standard pair-wise t-tests are done only when the ANOVA hypothesis is rejected, then the overall error-rate is kept. This is known as Fisher's LSD (least significant difference). It does not work for more than 3 groups. - This brings me to another faux pas in the linked PDF: the author could have used Fisher's LSD in the concrete example (there were 3 groups), but instead he advocated Bonferroni adjustment. This is quite conservative and may lead often to the result that none of the pairwise comparisons gets p* < alpha although the ANOVA got p < alpha.

Laxmi wrote:  "I have four variables and wants to test whether these variables are significantly different from each other." 

Most respondents seem to be interpreting this as 4 groups of individuals, with each individual being measured on the same (dependent) variable.  Is that really what it is? 

Laxmi, please clarify.  Do you have:

• 4 different variables measured in a single group of individuals?  (If so, what are the 4 variables?)
• One dependent variable measured in 4 independent groups of individuals?
• One dependent variable measured 4 times in the same individuals?
• Something else?

Thanks.