You are correct in considering that similarity or lack of difference between groups can be an important finding. In social sciences, it is essential to report both significant and non-significant results to provide a comprehensive understanding of the phenomenon under investigation.

To measure similarity between groups, you can use effect size measures, which help in quantifying the degree of difference or similarity between groups. One widely used effect size measure is Cohen's d, which measures the difference between two means in terms of the number of standard deviations. In SPSS, you can compute Cohen's d for independent samples using the "T-Test" procedure under the "Compare Means" menu, and selecting "Estimate effect size" option.

For Cohen's d, values around 0.2 are considered small effects, 0.5 are medium effects, and 0.8 are large effects. If the effect size is close to zero, it indicates that there is little or no difference between the groups, and thus a degree of similarity.

In cases where you don't have an inherent order or direction (such as in your examples of recovery time from separation and responsibility for keeping in touch), you might want to consider using the Intraclass Correlation Coefficient (ICC) as a measure of similarity. ICC measures the agreement or consistency between two or more groups. In SPSS, you can use the "ICC" procedure under the "Analyze" menu, then "Scale," and finally "Reliability Analysis."

It is important to mention that non-significant results do not necessarily imply similarity between groups, as they might be due to low statistical power or other factors. Reporting effect sizes and measures of similarity can help provide a clearer picture of the relationship between groups beyond statistical significance.

The output for your t-tests will include the mean difference with a 95% CI. Have you considered reporting that?

Hi Bruce, in the meantime my colleagues suggested that I get to know a procedure called the equivalence testתHi Bruce, in the meantime colleagues have suggested that I familiarize myself with a procedure called equvivalnece test

It's a bit more complicated than the BSPS T-test but calculates the probability of similarity instead of difference

Thank you Ali ;-)

Ornat Turin yes equivalence tests can be very useful, but there is not THE one method and (relative) probabilities are only possible with a Bayesian approach, called Bayes Factor (BF). You can find similar suggestions here: https://www.researchgate.net/post/Exploring_the_Null_Strategies_for_Proving_No_Effect_in_Research_Studies

I just copied what I suggested there, but you should read also the other comments

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There are frequentistic and Bayesian approaches to find "evidence" for the null hypothesis. But all need that you define not only a point null hypothesis (as it is usual in typical frequentist approaches, e.g. correlation = 0 or mean difference = 0), but a region of values, which you would consider a null effect, i.e. these values are so small that they are of no practical interest. For this you might consult some papers concerning the term Smallest Effect Size Of Interest (SESOI).

If you have defined such a region you might use one of these approaches:

1) The frequentistic Two One Sided Tests (TOST), see publications by Daniël Lakens for example.

2) The Bayesian Region Of Practical Equivalence (ROPE), see publications by John Kruschke for example

3) The Bayesian Bayes Factor (BF), see publications by Eric-Jan Wagenmakers for example.

All approaches have their pros and cons in my opinion and it depends what you are specifically looking for. I personally favour the ROPE approach, but this is only my opinion, since it follows the model workflow I would use. For a comparison of approaches see:

Linde, M., Tendeiro, J. N., Selker, R., Wagenmakers, E. J., & van Ravenzwaaij, D. (2021). Decisions about equivalence: A comparison of TOST, HDI-ROPE, and the Bayes factor. Psychological Methods, 28(3), 740.

and for a critique about their general finding and conclusion in favour of the BF:

Campbell, H., & Gustafson, P. (2021). re: Linde et al.(2021): The Bayes factor, HDI-ROPE and frequentist equivalence tests can all be reverse engineered--almost exactly--from one another. arXiv preprint arXiv:2104.07834.

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Hello Ornat Turin. If you do want to read up on equivalence testing, I think the following articles are quite accessible:

Article Understanding Equivalence and Noninferiority Testing

Article Equivalence Testing for Psychological Research: A Tutorial

Wow, what a detailed and respectful answer, thank you from the bottom of my heart