SOLUTION: What decision is reached when 'a' is greater than the p-value? When 'a' is greater than the p-value, the null hypothesis is rejected. Why is this decision reached?

Question 927704: What decision is reached when 'a' is greater than the p-value?
When 'a' is greater than the p-value, the null hypothesis is rejected.
Why is this decision reached?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
a is the critical value in a decision, if i understand the question correctly.
p is the value that you get from the analysis.
a is the cutoff value to indicate if the study results are statistically significant or not.
if p is greater than a, then the results are considered to be possible due to chance variations in each sample, and the null hypothesis cannot be rejected.
if p is less than a (this is the same as a is greater than p), then the results of the study are considered to not be likely just due to chance variations in each sample, and the null hypothesis is rejected.

this all depends on the selection of a as the arbitrary cutoff point.

if a is loose, like maybe = 10%, then it's not as hard to reject the null hypothesis as it would be if a was very strict, like 1%.

you have a population and you have samples taken from that population.
if a = 10%, then 90% of the sample means are expected to have a p greater than 10%.
if a = 1%, then 99% of the sample means are expected to have a p greater than 1%.

when a = 10% and you get a sample mean that has a p less than 10%, this means that a sample with the same results as this sample is only expected to occur less than 10% of the time.

obviously, an alpha of 10% is not as strict as an alpha of 1%.

the choice of alpha is dependent on many factors, and it is critical to the results of the study.

the choice of alpha is agreed on before the study is performed and the researchers are ethically bound not to change it regardless of the results of the study.

here's one reference out of many that you can find on the web it you do a search for alpha and p value and the difference between them.

http://statistics.about.com/od/Inferential-Statistics/a/What-Is-The-Difference-Between-Alpha-And-P-Values.htm

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