Question

Why would you blame the small sample size of a study for the lack of statistical significance? How are statistical significance and sample size connected?

Answer 1

If the sample size is small then sample is less presentative of population. With bigger sample sizes, you're less likely to get results that reflect randomness. Therefore we get results with higher level of statistical significance and with small sample size have lack of statistical significance.

The relation of sample size with statistical significance is higher sample size allows the researcher to increase the significance level of the findings, since the confidence of the result are likely to increase with a higher sample size. This is to be expected because larger the sample size, the more accurately it is expected to mirror the behavior of the whole group.