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Differences between two sample averages are most likely to be statistically significant if?
difference is large
What does it mean for the findings of a statistical analysis of data to be statistically significant?
Data is statistically significant if the p (probability) value is below a certain level (ex: 5% or 1%). The p value describes how often one would receive the results they got if left to chance alone. The lower the p value, the less likely it is that your results were due to chance and is stronger evidence against the null hypothesis. Also important to keep in mind is that just because something is statistically significant does not mean it is practically significant.
What circumstances can a small treatment effect be statistically significant?
For a given experiment, and a given sample size, there is a probability that a treatment effect of a given size will yield a statistically significant finding. That is, if the treatment effect is 1 unit, then that probability (the power) might be 50%, and the power for a treatment effect of 2 units might be 75%, etc. Unfortunately, before the experiment, we don't know the treatment effect size, and indeed after the experiment we can only estimate it. So a statistically significant result means that, whatever the treatment effect size happens to be, Mother Nature gave you a "thumbs up" sign. That is more likely to happen with a large effect than with a small one.
Why are new driver insurance rates so much higher for boys than for girls?
Driver insurance rates are higher for boys than for girls because it has been proven statistically that boys are more likely to get into car accidents than girls.
When using the distribution of sample mean to estimate the population mean what is the benefit of using larger sample sizes?
The variance decreases with a larger sample so that the sample mean is likely to be closer to the population mean.
