Formally testing assumptions using your observed data is nonsense.

The assumptions are either reasonable or they are not, and this follows actually only from subject knowledge. But, well, it may be (quite often) the case that our subject knowledge is not sufficient to judge the reasonability. In such cases experience can help. Experience here means: data. A good bunch of data (does not need to be own data; it can be data on the same thing gathered by different people/labs) can provide a basis for a judgement. Generally, the t-test is robust against deviations from the assumptions, so it is sufficient to look for rather drastic deviations.The distribution of the data should be roughly symmetric and the variances should be roughly similar up to an order of magnitude.

So if you have (a lot of) data, plot the data and look. Histograms or densityplots are helpful. Be alarmed when you see considerable assymetry or heteroscedasticity. If you don't have a lot of data, there is not much you can conclude and you have to rely on your (or other people's) subject knowledge.

The most critical kind of deviation is asymmetry. If the distribution is clearly asymmetric (skewed), you have a problem. This already indicates that means and mean differences may not be statistics that have a straight-foreward or simple interpretation (practically)! This is often the problem in biological measurements that are related to concentrations (protein or mRNA expression, blood levels of whatsoever, to give some hints). They cannot be negative, and if the mean is close to 0 (relative to the variance), the distribution is typically right-skewed. This asymmetry gets smaller the larger the mean is (relative to the variance). We generally find this asymmetry when the change of the concentration depends on the actual concentration, what is typically the case when the concentration is controlled by a multiplicative process (think of transcription, where multiple mRNAs are produced in the presence of a single transcription factor molecule, that is itselv produces by the multiple translation of a single mRNA molecule, etc.).

For concentration-like measures, subject knowledge would tell us that a t-test is not a good choice anyway, but it might still be useful when the values are all "far enough away from 0" to ensure a rather symmetric distribution. But there is another problem: such values typically vary more when the mean is larger. This is observed as heteroscedasticity. If the means in the groups to be compared are "far away from 0" and also quite close together, then the distributions are quite symmetric and will have similar variances, and talking about a mean difference might make sense, and the t-test would be ok. But if the means are drastically different, then the variances will be drastically different as well, even when both distributions are quite symmetric. This already tells us that it may not make sense to talk about mean differences, and the t-test will be inappropriate.

In biological systems you will almost always see heteroscedasticity combined with asymmetry. If you face that problem, you should think about analyzing the a ratio rather then a difference. Funnily, this is obtained very simply by using the logarithms of your values for your analysis. The distributions of the logs will be (much more) symmetric and the variances will be (very) similar. And the mean difference between logs is a log-ratio. The t-test on the logs will test the hypothesis that the log-ratio is 0 (or that the ratio is 1).

If you really do not see asymmetry but a clear heteroscedasticity, then you should ask yourself if this makes sense or if you have a problem in your experimental setup. When the variance increases with the mean, it points back to the problem (and the solution) I discussed above. If the variances does not increase with the mean, then this really requires some thorough investigation of the data-generating process. Welch's t-test or normal t-test -- the question remains if the data make sense at all or if there is something wrong in your experiment, assay, or in the way the data have been processed.

Unpaired t-tests or in other words indepent samples t-test have two obvious assumption. First normality assupmtion, Dependent variable scores approximeltaly normally distrubeted across groups. Second homogenity of variance assuption.You have to examine homogenity of variance assumption using Levene test. SPSS calculate levene test automatically. Look Levene's Test for Equality of Variances 

Sig. If it is below .05, homogenity of variance assumption violated. In this case, you have to use Welch-Satewirtte correction or in others words separate variance t-test. It is performed automatically in SPSS. just report equal variance not assumed row.

I added a sample t-test results and explained each row look annex

F= Calculated F statistics for Levene Test

Sig. : Calculated significance value for Levene test.  If the value below .05 use second Equal variances not assumed column

t : Calculated t statistics. this calculated this formula: Mean Difference / Std. Error Difference in the Table.

df: degrees of freedom. In the independent samples t-test ıt is always  Your sample size- 2.    (N-2).

Sig. (2-tailed): Calculated significance value for t-test ıf the reslut below .05 ıt is significant. Reject null hyphothesis.

Mean Difference: the value of highest group mean subtracted from other group mean.

Std. Error Difference: Mean  Difference divided to  square root of total sample size.

95% Confidence Interval of the Difference: If 95 %  Confidence Interval of the Difference not include zero results are significant at least  .05.  ıt also gives information about true values in the population with 95% probability.

Best.

Formally testing assumptions using your observed data is nonsense.

The assumptions are either reasonable or they are not, and this follows actually only from subject knowledge. But, well, it may be (quite often) the case that our subject knowledge is not sufficient to judge the reasonability. In such cases experience can help. Experience here means: data. A good bunch of data (does not need to be own data; it can be data on the same thing gathered by different people/labs) can provide a basis for a judgement. Generally, the t-test is robust against deviations from the assumptions, so it is sufficient to look for rather drastic deviations.The distribution of the data should be roughly symmetric and the variances should be roughly similar up to an order of magnitude.

So if you have (a lot of) data, plot the data and look. Histograms or densityplots are helpful. Be alarmed when you see considerable assymetry or heteroscedasticity. If you don't have a lot of data, there is not much you can conclude and you have to rely on your (or other people's) subject knowledge.

The most critical kind of deviation is asymmetry. If the distribution is clearly asymmetric (skewed), you have a problem. This already indicates that means and mean differences may not be statistics that have a straight-foreward or simple interpretation (practically)! This is often the problem in biological measurements that are related to concentrations (protein or mRNA expression, blood levels of whatsoever, to give some hints). They cannot be negative, and if the mean is close to 0 (relative to the variance), the distribution is typically right-skewed. This asymmetry gets smaller the larger the mean is (relative to the variance). We generally find this asymmetry when the change of the concentration depends on the actual concentration, what is typically the case when the concentration is controlled by a multiplicative process (think of transcription, where multiple mRNAs are produced in the presence of a single transcription factor molecule, that is itselv produces by the multiple translation of a single mRNA molecule, etc.).

For concentration-like measures, subject knowledge would tell us that a t-test is not a good choice anyway, but it might still be useful when the values are all "far enough away from 0" to ensure a rather symmetric distribution. But there is another problem: such values typically vary more when the mean is larger. This is observed as heteroscedasticity. If the means in the groups to be compared are "far away from 0" and also quite close together, then the distributions are quite symmetric and will have similar variances, and talking about a mean difference might make sense, and the t-test would be ok. But if the means are drastically different, then the variances will be drastically different as well, even when both distributions are quite symmetric. This already tells us that it may not make sense to talk about mean differences, and the t-test will be inappropriate.

In biological systems you will almost always see heteroscedasticity combined with asymmetry. If you face that problem, you should think about analyzing the a ratio rather then a difference. Funnily, this is obtained very simply by using the logarithms of your values for your analysis. The distributions of the logs will be (much more) symmetric and the variances will be (very) similar. And the mean difference between logs is a log-ratio. The t-test on the logs will test the hypothesis that the log-ratio is 0 (or that the ratio is 1).

If you really do not see asymmetry but a clear heteroscedasticity, then you should ask yourself if this makes sense or if you have a problem in your experimental setup. When the variance increases with the mean, it points back to the problem (and the solution) I discussed above. If the variances does not increase with the mean, then this really requires some thorough investigation of the data-generating process. Welch's t-test or normal t-test -- the question remains if the data make sense at all or if there is something wrong in your experiment, assay, or in the way the data have been processed.

Thank you very much to both for providing valuable info. I will check with my data