What is the magic number? (#42)

Statistical Testing helps us understand the relationships between multiple sets of variables, data, inputs, etc. Often, when people use the One T Test in Minitab (or other statistical testing packages) they will just automatically trust that the P-Value will tell them if they should believe the Null Hypothesis.

Because of this belief, we’ve titled this article “When the ‘P’ is Low, the ‘Ho’ Must Go!” Upon initial impact, it’s pretty funny. But for those of you who are a little unfamiliar with the acronyms, the P stands for P-Value, and the Ho stands for Null Hypothesis.

Put aside the double meaning 😊 for just a second; what the title is saying is that if the P-Value of the Null Hypothesis is low, then you should assume that the Null Hypothesis should be thrown out. However, that is not always the case. Blindly trusting the P-Value without fully grasping the inputs can potentially lead you to faulty measurements. You need to completely understand all inputs akin to the One T Test to lead you to a sound decision.

Example is as follows:

A supplier of a part to a large organization claims that the mean (average) weight of a part is 90 grams. The organization took a small sample of 20 parts and found that the mean score is 84 grams and standard deviation is 11. Could this sample originate from a population of mean = 90 grams?

·         Hypothesised Mean = 90

·         N Sample size (# of Parts) = 20

·         X-Bar (Average of the Samples) = 84

·         S (Standard Deviation) = 11

·         Delta or Change = 6

The organization wants to test this at significance level of 0.05 (95% Confidence), i.e. it is willing to take only a 5 percent risk of being wrong when it says the sample is not from the population. Therefore:

·         Null Hypothesis (H0): “True Population Mean Score = 90”

·         Alternative Hypothesis (Ha): “True Population Mean Score is not = 90”

·         Alpha (Risk) is 0.05

Typically speaking, the higher the difference between the Measured Sample Mean and the Hypothesized Mean; it will be less likely (P-Value) the Null Hypothesis will be true. What is the cut off? How big of a difference is considered “too big?” Where do you draw the line between true and false?

From our example above, we can see that the Delta from the Sample Mean and Hypothesized Population Mean is 6, but can we say that a Delta of 6 is enough for us to dismiss our Null Hypothesis?

In this situation, no! The magic number of Sample Size is 30! We need to have at least 30 samples for us to find correct values. The sample size should be big enough that you can actually detect a variable difference.

For the example that we are using, our sample size should be 38. We found this using the One Sample T-Test Power and Sample Size calculator in Minitab (http://www.minitab.com/en-us/products/minitab/free-trial/).

Using a sample of 20 parts, we found that our Delta was 6; however this Delta was less than 8.4 and it cannot be determined to be sensitive enough to determine a true shift. Basically all of this means that our sample size was too small for us to find a true difference of the population of parts.

Using this small sample size, our P-Value results of the T-test are low. Therefore, we should assume that our Null Hypothesis can be kicked to the curb. So here jumps in our “When the ‘P’ is low, the ‘Ho’ must go,” but it is incorrect! Our sample size is too small for us to be able to really determine if our Null Hypothesis is false and those who are confident with Hypothesis Testing will probably confront your results. It is not a big deal if you don’t really understand all the calculations; many statistical packages to the math (Sample Size, T-Test, P-Value, etc.) for you.

The URL https://people.richland.edu/james/lecture/m170/tbl-t.html has a Critical T Value that you can contrast your T-Value; or you can cross reference your confidence level with the Degrees of Freedom (DF).

Critical T-Value is a boundary that helps guide the conclusion of whether or not to dismiss the Null Hypothesis based on the difference of Sample Mean and Hypothesized Population Mean. The Critical T-Value is a definitive “cut off.” If your Delta exceeds the Critical T-Value, you can conclude that your sample size is large enough to dismiss the H0.

We see that the Critical T-Value, found on the T-Distribution Tables, is +/- 2.093. From our 20 parts sample, our T-Value is -2.44, making it less than the Critical T-Value; leading us to reject our Null Hypothesis and question the supplier.

When performing Hypothesis Testing, have you ever been led to the wrong conclusion because of the wrong P-Value? 

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