Sometime we might have a non-significant difference between two samples but they are really different inside. For example: color.
"Truth" is a mental concept. Statistics deals with quantifying uncertainty. And "statistical significance" is the least understood and most misinterpreted thing in all empirical sciences. Do not confuse all these things.
A statistic by itself is not and can never be meaningful in any way. But it can be helpful. This a something completely different! - Science, or scientific questions, (design of) experiments, in the context of expertise and common sense, also in the context of experience and aim, can be meaningful.
Good answer, Peter. I just want to stress on little point. You said "If the experimental design was to measure the difference in CIE Lab coordinates then your conclusion is there is no difference." (bcause the result was not significant). This conclusion should *only* be drawn when the test was done according to Neyman/Pearson, that is, when both, alpha *and* beta have been specified depending on the anticipated cost/benefit ratio of wrong and correct decisions, and the sample size was chosen to ensure the desired beta (or power). Only then a real decision can be justified, what is neccesarily a decision between two exclusive alternatives (eiter rerect H0 or accept it). Otherwise, if alpha and beta (particularily) were not fixed, there is no testing "procedure" possible. Then, the P value can at best serve as a "surprise index" of the data under the null hypothesis, where a "significant" result indicates that further research might be worthwhile where as a "non-significant" result indicates that further research doesn't seem promising (not because there was no effect, but simply because the data is obviousely not good enough, for whatever reason) (Fisher's significance "test").
A big downside of the parametric tests is their reliance on the normality of the underlying distribution(s). I think if you used a nonparametric test (Kolmogorov-Smirnov?), you could get a more definitive result.
I think it very essential when studying any parameter in food where we need to express quantitative data and describe effect of different parameters ( For example Temperature, Moisture, Ripening, packaging etc....) on the desired responses (Example: Color difference, nutritional content, sensory quality...etc)
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