Can someone please help me understand NHST?
I study psychology and would like to have a good basics knowledge of relevant statistics. Thank you.
In: 8
Often, we will want to test what the difference is between two sets of data.
Whether it’s testing crop growth in two different fields, differences in height between males and females, or whether or not a trial lubricant gives better machine performance.
There will be something you’re measuring. E.g. for crop growth it might be crop height.
There will be something different between two sample sets. In this case, it’s the field that the crops are growing in.
You want to tell if there’s a difference in crop height between the two fields. If there’s no difference between the two fields, then the “null hypothesis” would be *there is no difference in height between the two fields.*
The null hypothesis is the boring assumption. It’s “nothing interesting is going on here”.
The alternative hypothesis is the interesting one. It’s the one that says “Something is not boring here”.
To set your hypotheses, you decide “What am I looking to find out?” *Crops are a different height in Field A vs Field B*.
The null hypothesis then is the boring answer that you need to default to if you can’t prove anything interesting. *The crops are the same height in Fields A and B.*
We can then use canned statistical tests like the “Student T Test”. We go measure the heights of a random sample of crops from both fields, take the average, standard deviation, and number of samples, and then use those to calculate t-scores and eventually a p-value.
The p-value will be a number between 0-100%. It’s the *probability that your test gave these results by random chance*.
E.g. Imagine you get an average height from field A of 2.05 meters, and an average from B of 1.86 m (difference of 0.19 m).
Using the standard deviation, average, and number of samples, you calculate your t-scores and p-scores, you get a p-value of 0.03. This indicates there’s a 3% chance that your samples just *happened to come out that way*, or a 97% chance that there’s a real difference between the fields. In this case, you’d likely reject the null hypothesis and say “There is statistical evidence that the crops in Field A are 0.19 m taller than in Field B”, presumably followed by “lets make sure we do what Field A is doing in the future.”
Another way to think of the p-value is “If fields A and B were actually the same height, there’s a 3% chance that I happened to grab samples that said one set was taller than the other.”
A way to remember what the p-value means is “If the p is low, the null must go”. It rhymes you see.
If the p value were higher, then there’s enough possibility that it was just random chance. A typical threshold is 5% or 0.05. So if your p-value came back at 6%, then that’s too much of a chance it was random variation that happened to tell you the averages are different. If you still think there might be a difference, you should repeat the test with a higher sample count and perhaps better measurement methods.
Otherwise, if the p-value is too high, sometimes it can come back at 80% or higher, indicating “There’s an 80% possibility that any difference you see is random chance”. In that case, you *fail to reject the null hypothesis*, and all you can conclude is that there’s no reason to believe there’s a difference in crop height.
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