++ Stats Killed Me But I Am Back

4-5 months ago, I decided I wanted to go back to school and get an advanced degree in mathematics. This would take a lot of work as I did not finish my undergrad in math. The class that did me in was when I hit the real “mean and potatoes” of statistics. I remember that this was a 400 level (first of 3 in the stats sequence for math majors). It was either MATH 411 or MATH 412 at University of Dayton.

++ Probability was OK

I got through the probability/combinatorics work. But stats ended up burying me. Now I had a lot more going on; freshman in classes with upperclassmen; 17 year old immature student; first time really away from home, etc.

++ What Was So Hard About the Material?

This point is for consumption for my students. When you get to college in challenging STEM work, what kills most students, as it did to me, is not knowing how to learn totally new material.

++  The Topic that Killed Me - Hypothesis Testing

It is beyond the scope of this post to explain what hypothesis testing is to any great detail. By example: Lets say you work for a company that manufactures tires. The tires have a mean expected life span of 14 months. That is, the mean of the population of all tires under consideration is 14 months.

If one was to take a random sample of tires, the mean won’t be exactly 14 months, due to randomness of the sample. But what if the dealers are reporting that their customers’ purchases (samples) seem to be consistently less than 14 months. Is it just randomness or is the original accepted assumption of 14 months now not accurate?

In statistical parlance, we would be saying that the 

Null Hypothesis is 

H0: (accepted mean) = 14;

The Alternate Hypothesis (what we are going to test) is

Ha: (mean under test) /= 14;

Now, again beyond the scope of this discussion, but this is considered a two-tail test as opposed to a 1 tail test.

So we are going to do what is called a z-test with the goal of either:

• Rejecting the Null Hypothesis (rejecting the assumption that 14 is truly the mean life span). From a graphical point of view that would mean our testing would leave us in the blue shaded area. This actually makes sense. This above is for all intents and purposes what you have come to know as a bell curve. The middle of the bell curve has most of the data and then decreases out to the tails. So, if one is “in the middle” of the bell curve, then you are closer to the mean (the vertical line in the middle). The chances of being further and further out on the tails is met with reduced probability. Once one strays into the rejection region, that means it is increasingly unlikely that it was by chance. The population mean must really be different than 14. Or more accurately stated, there is very little statistical chance to be out in the rejection region by chance.

• Failing to Reject the Null Hypothesis. This means we are on either side of the mean (or right on the mean) but within statistical randomness. For example, if the tire dealers stated that their customer data shows that the mean life expectancy is 13.9 months, then there is not enough data to Reject the Null Hypothsis.

**** Note: Do not assume that since I picked 13.9, then because that looks very close to the mean then there is no reason to reject the null hypothesis just because it looks “close”. I am only trying to illustrate what it means to be in “non-rejection” region

++ Moral to the Story

As a student, you WILL encounter material that leaves you scared, frustrated and inadequate. Don’t give up. Spend every minute you can with your teacher. If that is not a good solution. Find students that you trust to work with. Find a QUALITY tutor. RESEARCH. RESEARCH. RESEARCH.

But, do not rely on just one on-line source. Find sources that hit your problem target from different angles. I guarantee it will help.