Respuesta :
If the sample size is small and the sample variance is large then
small treatment effect still be statistically significant.
As we know that,
Statustical significance refers to claim that a result from data generated by testing or experimentation is likely to be attributable to specific cause.
Sample size is the total number of individuals or items that comprise a sample.
And, the variance is a descriptive statistic, which falls under the category of a measure of spread.
The circumstance in which a very small treatment effect can be found to be significant is best described by option A: If the sample size big and the sample variance is small.
A large sample size will increase the probability that the results of a statistical test will yield significant results. This is why most statistical tests are accompanied by a measure of effect size. A statistically significant result associated with a very large sample size, will likely have a small effect size, an undesirable result for a researcher, as it implies one of the only reasons significant results were obtained was due to the large sample, not necessary the magnitude of the experimental effect.
Likewise, if variance is small, this will also increase the probability that the results of a statistical test will yield significant results. Variance is simply another word in statistics for the error. A decrease in error will lead to an increased probability of obtaining significant results, hence the idea that a small amount of variance will lead to an increased probability of significant results.
Hence, if the sample size is small and the sample variance is large then
small treatment effect still be statistically significant.
Find out more information about statistical significance here:
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