That suggests these possibilities:

1. The difference between low and medium is not significant.

2. There are more medium than high respondents.

3. Did the ANOVA use medium as the reference level?  Maybe the difference between medium and high is not significant either.

I am not sure but ANOVA need normality assumption did u chk?

Subrata, only the residuals need to be normally distributed.  (Though this requirement is rarely enforced in science papers)

Thank you for your answer. Henry, as a matter of fact I have 5 income groups according with their monthly salary (being from 1 the lowest salary to 5 the highest) from the t-test there was statistically significant difference in the mean between group 1 and group 5 regarding social comparison orientation (apologies for not being clear at the beginning of my question). Am I right thinking that (from the Anova) that difference in the means 'is not significant'? 

Sorry for that, but your question comes too late...

Statistics is very relevant before the experiment, not afterwards. In your case, one should have thought about the question: "how does SOC depend on income?". How could this be modelled? I would think of a regression model, possibly something like SOC(income) = b0 + b1*log2(income) (not sure if this model would be appropriate for your data - that is just an example). Then one would think what kind of data would be suited for such a model. The next critical point is to evaluate the nature of the DV. I have no idea what SOC is or how it is measured. The nature of the SOC data would further indicate what stochastic properties the model should obey (in other words: will it be a linear regression, a logistic regression, a Poisson-, gamma, or beta-regression?).

So if you had the income values it would be easy to fit a regression model and directly adress your relevant scientific question. You would be able to estimate the coefficients of the model, and in the model above the value of b1 would tell you by what amout SOC changes per doubling of the income. This etimate would use ALL of the data in one shot. It would not need any arbitrary grouping and multiple tests of meaningless hypotheses.

The second best is to try to substutute the group index by some representative income value for the group and do a regression analysis with these values.

Yes, it can happen.

If you are using anova, you should certainly check the assumptions of anova, as data which don't meet the assumptions can decrease the power of the test.  (And would also make the results invalid).

Use plots to check the normality of the residuals, and homoscedasticity of the residuals.

It might also be helpful to start with boxplots of each group on the same axis, to see what's going on with your data:  if there is a trend, and if groups have equal variance.

      http://www.tutorialspoint.com/r/images/boxplot.png

However, I would also suggest you think about the points Jochen Wilhelm made. In particular: Would you really rather treat income as a numeric variable?

Dear Magda

The use of ANOVA required that your data met many assumptions , and I expected you did the required tests for data . In case of T test, you performed separated tests between DV and each case of economic status ( Low , Medium , High ) so you did three statistical decisions ( one for each test ) and you have chance to got Type I Error for each decision , while in case of ANOVA you deal with pooled variance as MSE and you take one statistical decision with one chance for Type I Error.

For example: If the probability of a Type I error for the analysis is set at 0.05 and three  t-tests are done, the overall probability of a Type I error for the set of tests = 1 – (0.95)^3= 0.143* instead of 0.05.

Please, for more information read the in the following link:

https://statistics.laerd.com/statistical-guides/one-way-anova-statistical-guide-2.php

and:

http://www.biostat.umn.edu/~susant/Fall11ph6414/Section13_Part1.pdf

Good Luck

Better you Check the normality of the residuals, and homoscedasticity of the residuals.

 Thank you very much for all the observations and suggestions. Im working on it. Kind regards, 

There is one additional source of discrepant results of t-test and ANOVA: t-test can be one-sided ore two-sided. ANOVA does not distinguish between these cases, but in the case of two groups, ANOVA-results are equivalent to a two-sided t-test.

Apart from that, I agree with the others that income should be treated as an ordinal variable.

Yes it's definitely possible. The t test uses a different error term than a 2 - group post hoc test in a multiple group ANOVA.

If you only had 2 groups total, an ANOVA, a t test, a Pearson correlation and a linear regression would all give you identical answers as far as the observed p-value.

Try to use a non-parametric post-hoc test, maybe the data are non-normal and have different variances.

Magda, you seem to do analysis in the wrong direction. If you need to find if groups of SES differ in terms of their orientation (assuming continuous), ANOVA was the first analysis to be performed. If you had found a significant result from ANOVA then a post-hoc comparison would be convenient "to find where the difference lies". Generally speaking, a post-hoc comparison is something like a t-test in the sense that it compares groups in a pairwise fashion. Although there are other ways to do a post-hoc test without doing pairwise comparisons.

If I'm understanding this correctly, your dependent variable has three levels, and your initial t-test was just comparing low vs high income.  The issue is, I think, one of conserving the significance level of the test when performing multiple comparisons.  One way of doing this is only to perform pairwise comparisons if the omnibus test (in this case the ANOVA) shows a significant.  This provides a weak conservation of alpha.  Stronger control of alpha can be obtained in pairwise comparisons by using an adjustment of the significance level of the t-tests such as Bonferonni or Sidak.