@abig so, the difference begins with identifying the type of sampling you are doing. Attributes sampling (usually identified by a yes or no answer, such as is this control authorized) deals with controls. This sampling is often used to identify if controls are working effectively. Further, attribute sampling deals with risk of assessing control risk too high/too low. Risk of assessing control risk too low would be accepting that the control is properly working when in fact it is not. You think it's fine so you say low risk of material misstatement here. You have accepted it but you shouldn't have. On the contrary, risk of assessing control risk too high is saying that a control is not working, when in fact it is. Here you are saying the control is not working so the risk is high that the control leads to a misstatement. Here, you end up doing more work because you assessed it at high risk. The most import of the two is risk of assessing control risk too low. This is more important because accepting a control & deeming it to be working when it is not, could eventually cause a material misstatement in the financials due to that control deficiency. This impacts the “effectiveness” of your testing, because you are in fact wrong in your assumption that it's working. They call this the “beta risk” because it is the more important of the two in attribute sampling. On the contrary, risk of assessing control risk too high is when you, as an auditor, say that the control is not working effectively when in fact it is. This is less important because all it means is you are going to do more, unnecessary work to come to the right conclusion that the control is in fact working. As opposed to impacting the effectiveness of your testing as I previously stated, this only impacts the efficiency of your testing as you will be doing more work which is not necessary.
That being said, now we move on to variable sampling. The idea is very similar. To simplify it, you could re read the above paragraph, substituting the risk of assessing control risk too high for risk of incorrect rejection (efficiency), & then swapping out risk of assessing control risk too low for risk of incorrect acceptance (effectiveness). The risk of incorrect acceptance is the beta risk here (more important),because it states that you are accepting a sample to be representative of the population, when in fact it is not. I'll provide chart below to summarize this.
Attribute sampling (used to test internal controls):
-Risk of assessing control risk too high (impacts the efficiency of your testing)
-Risk of assessing control risk too low (beta risk, impacts the effectiveness of your testing)
Variables sampling:
-Risk of incorrect rejection (impacts the efficiency of your testing)
-Risk of incorrect acceptance (beta risk, impacts the effectiveness of your testing)
Hope this helps! I've taken audit twice, with a 74 & a 71. I'm taking it for my third time on May 16th. I also have a year of experience now, so this is a little more clear to me now. Hopefully now mistakes were made above, I typed it quick. If you need anymore clarification just ask!
-Josh