Every time we host a party at our home, we engage in a brief and spirited… let’s go with the word “discussion”.
Said discussion is not about what is going to be on the menu – we usually find ourselves in agreement about this aspect. It is, instead, about the quantity.
In every household around the world, I suppose, this discussion plays out every time there’s a party. One side of the debate will worry about how to fit in the leftovers in the refrigerator the next day, while the other will fret about – the horror! – there not being enough food on the table midway through a meal.
There is, I should mention, no “right” answer over here. Each side makes valid arguments, and each side has logic going for it. Now, me, personally, I quite like the idea of leftovers, because what can possibly be better than waking up at 3 in the morning for no good reason, waddling over to the fridge, and getting a big fat meaty slice of whatever one may find in there? But having been a part of running a household for a decade and change, I know the challenges that leftovers can pose in terms of storage.
You might by now be wondering about where I am going with this, but asking yourself which side of the debate you fall upon when it comes to this specific issue is also a good way to understand why formulating the null hypothesis can be so very challenging.
Let’s assume that there’s going to be four adults and two kids at a party.
How many chapatis should be made?
Should the null hypothesis be: We will eat exactly 16 chapatis tonight
With the alternate then being: 16 chapatis will either be too much or too little
Or should the null hypothesis be: We will eat 20 chapatis or more
With the alternate being: We will definitely eat less than 20 chapatis tonight.
The reason we end up having a “discussion” is because we can’t agree on which outcome we would rather avoid: that of potentially being embarrassed as hosts, or the one of standing, arms exasperatedly akimbo, in front of the refrigerator post-party.
It is the outcome we would rather avoid that guides us in our formation of the null hypothesis, in other words. We give it every chance to be true, and if we reject it, it is because we are almost entirely confident that we are right in rejecting it.
What is “almost entirely“?
That is the point of the “significant at 1%” or “5%” or “10%” sentence in academic papers.
Which, of course, is another way to think about it. This set of the null and the alternate…
H0: We will eat 20 chapatis or more
Ha: We will eat less than 20 chapatis
… I am not ok rejecting the null at even 1%. Or in the language of statistics, I am not ok with committing a Type I error, even at a probability (p-value) of 1%.
A Type I error is rejecting the null when it is true. So even a 1% chance that we and our guests would have wanted to eat more than 20 chapatis* to me means that we should get more than 20 chapatis made.
At this point in our discussions (we’re both economists, so these discussions really do take place at our home), my wife exasperatedly points out that not once has the food actually fallen short.
Ah, I say, triumphantly. Can you guarantee that it won’t this time around? 100% guarantee?
No? So you’re saying there’s a teeny-tiny 1% chance that we’ll have too few chapatis?
Kam nahi padna chahiye!
*Don’t judge us, ok. Sometimes the curry just is that good.